Optimal Control of Hybrid Systems in Air Traffic Applications

NASA Astrophysics Data System (ADS)

Kamgarpour, Maryam

Growing concerns over the scalability of air traffic operations, air transportation fuel emissions and prices, as well as the advent of communication and sensing technologies motivate improvements to the air traffic management system. To address such improvements, in this thesis a hybrid dynamical model as an abstraction of the air traffic system is considered. Wind and hazardous weather impacts are included using a stochastic model. This thesis focuses on the design of algorithms for verification and control of hybrid and stochastic dynamical systems and the application of these algorithms to air traffic management problems. In the deterministic setting, a numerically efficient algorithm for optimal control of hybrid systems is proposed based on extensions of classical optimal control techniques. This algorithm is applied to optimize the trajectory of an Airbus 320 aircraft in the presence of wind and storms. In the stochastic setting, the verification problem of reaching a target set while avoiding obstacles (reach-avoid) is formulated as a two-player game to account for external agents' influence on system dynamics. The solution approach is applied to air traffic conflict prediction in the presence of stochastic wind. Due to the uncertainty in forecasts of the hazardous weather, and hence the unsafe regions of airspace for aircraft flight, the reach-avoid framework is extended to account for stochastic target and safe sets. This methodology is used to maximize the probability of the safety of aircraft paths through hazardous weather. Finally, the problem of modeling and optimization of arrival air traffic and runway configuration in dense airspace subject to stochastic weather data is addressed. This problem is formulated as a hybrid optimal control problem and is solved with a hierarchical approach that decouples safety and performance. As illustrated with this problem, the large scale of air traffic operations motivates future work on the efficient implementation of the proposed algorithms.

RES: Regularized Stochastic BFGS Algorithm

NASA Astrophysics Data System (ADS)

Mokhtari, Aryan; Ribeiro, Alejandro

2014-12-01

RES, a regularized stochastic version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method is proposed to solve convex optimization problems with stochastic objectives. The use of stochastic gradient descent algorithms is widespread, but the number of iterations required to approximate optimal arguments can be prohibitive in high dimensional problems. Application of second order methods, on the other hand, is impracticable because computation of objective function Hessian inverses incurs excessive computational cost. BFGS modifies gradient descent by introducing a Hessian approximation matrix computed from finite gradient differences. RES utilizes stochastic gradients in lieu of deterministic gradients for both, the determination of descent directions and the approximation of the objective function's curvature. Since stochastic gradients can be computed at manageable computational cost RES is realizable and retains the convergence rate advantages of its deterministic counterparts. Convergence results show that lower and upper bounds on the Hessian egeinvalues of the sample functions are sufficient to guarantee convergence to optimal arguments. Numerical experiments showcase reductions in convergence time relative to stochastic gradient descent algorithms and non-regularized stochastic versions of BFGS. An application of RES to the implementation of support vector machines is developed.

An optimal repartitioning decision policy

NASA Technical Reports Server (NTRS)

Nicol, D. M.; Reynolds, P. F., Jr.

1986-01-01

A central problem to parallel processing is the determination of an effective partitioning of workload to processors. The effectiveness of any given partition is dependent on the stochastic nature of the workload. The problem of determining when and if the stochastic behavior of the workload has changed enough to warrant the calculation of a new partition is treated. The problem is modeled as a Markov decision process, and an optimal decision policy is derived. Quantification of this policy is usually intractable. A heuristic policy which performs nearly optimally is investigated empirically. The results suggest that the detection of change is the predominant issue in this problem.

Optimal Control of Stochastic Systems Driven by Fractional Brownian Motions

DTIC Science & Technology

2014-10-09

problems for stochastic partial differential equations driven by fractional Brownian motions are explicitly solved. For the control of a continuous time...linear systems with Brownian motion or a discrete time linear system with a white Gaussian noise and costs 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 stochastic optimal control, fractional Brownian motion , stochastic

Stochastic Robust Mathematical Programming Model for Power System Optimization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Cong; Changhyeok, Lee; Haoyong, Chen

2016-01-01

This paper presents a stochastic robust framework for two-stage power system optimization problems with uncertainty. The model optimizes the probabilistic expectation of different worst-case scenarios with ifferent uncertainty sets. A case study of unit commitment shows the effectiveness of the proposed model and algorithms.

Ultimate open pit stochastic optimization

NASA Astrophysics Data System (ADS)

Marcotte, Denis; Caron, Josiane

2013-02-01

Classical open pit optimization (maximum closure problem) is made on block estimates, without directly considering the block grades uncertainty. We propose an alternative approach of stochastic optimization. The stochastic optimization is taken as the optimal pit computed on the block expected profits, rather than expected grades, computed from a series of conditional simulations. The stochastic optimization generates, by construction, larger ore and waste tonnages than the classical optimization. Contrary to the classical approach, the stochastic optimization is conditionally unbiased for the realized profit given the predicted profit. A series of simulated deposits with different variograms are used to compare the stochastic approach, the classical approach and the simulated approach that maximizes expected profit among simulated designs. Profits obtained with the stochastic optimization are generally larger than the classical or simulated pit. The main factor controlling the relative gain of stochastic optimization compared to classical approach and simulated pit is shown to be the information level as measured by the boreholes spacing/range ratio. The relative gains of the stochastic approach over the classical approach increase with the treatment costs but decrease with mining costs. The relative gains of the stochastic approach over the simulated pit approach increase both with the treatment and mining costs. At early stages of an open pit project, when uncertainty is large, the stochastic optimization approach appears preferable to the classical approach or the simulated pit approach for fair comparison of the values of alternative projects and for the initial design and planning of the open pit.

On stochastic control and optimal measurement strategies. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kramer, L. C.

1971-01-01

The control of stochastic dynamic systems is studied with particular emphasis on those which influence the quality or nature of the measurements which are made to effect control. Four main areas are discussed: (1) the meaning of stochastic optimality and the means by which dynamic programming may be applied to solve a combined control/measurement problem; (2) a technique by which it is possible to apply deterministic methods, specifically the minimum principle, to the study of stochastic problems; (3) the methods described are applied to linear systems with Gaussian disturbances to study the structure of the resulting control system; and (4) several applications are considered.

Initialization and Restart in Stochastic Local Search: Computing a Most Probable Explanation in Bayesian Networks

NASA Technical Reports Server (NTRS)

Mengshoel, Ole J.; Wilkins, David C.; Roth, Dan

2010-01-01

For hard computational problems, stochastic local search has proven to be a competitive approach to finding optimal or approximately optimal problem solutions. Two key research questions for stochastic local search algorithms are: Which algorithms are effective for initialization? When should the search process be restarted? In the present work we investigate these research questions in the context of approximate computation of most probable explanations (MPEs) in Bayesian networks (BNs). We introduce a novel approach, based on the Viterbi algorithm, to explanation initialization in BNs. While the Viterbi algorithm works on sequences and trees, our approach works on BNs with arbitrary topologies. We also give a novel formalization of stochastic local search, with focus on initialization and restart, using probability theory and mixture models. Experimentally, we apply our methods to the problem of MPE computation, using a stochastic local search algorithm known as Stochastic Greedy Search. By carefully optimizing both initialization and restart, we reduce the MPE search time for application BNs by several orders of magnitude compared to using uniform at random initialization without restart. On several BNs from applications, the performance of Stochastic Greedy Search is competitive with clique tree clustering, a state-of-the-art exact algorithm used for MPE computation in BNs.

Optimization Testbed Cometboards Extended into Stochastic Domain

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Pai, Shantaram S.; Coroneos, Rula M.; Patnaik, Surya N.

2010-01-01

COMparative Evaluation Testbed of Optimization and Analysis Routines for the Design of Structures (CometBoards) is a multidisciplinary design optimization software. It was originally developed for deterministic calculation. It has now been extended into the stochastic domain for structural design problems. For deterministic problems, CometBoards is introduced through its subproblem solution strategy as well as the approximation concept in optimization. In the stochastic domain, a design is formulated as a function of the risk or reliability. Optimum solution including the weight of a structure, is also obtained as a function of reliability. Weight versus reliability traced out an inverted-S-shaped graph. The center of the graph corresponded to 50 percent probability of success, or one failure in two samples. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure that corresponded to unity for reliability. Weight can be reduced to a small value for the most failure-prone design with a compromised reliability approaching zero. The stochastic design optimization (SDO) capability for an industrial problem was obtained by combining three codes: MSC/Nastran code was the deterministic analysis tool, fast probabilistic integrator, or the FPI module of the NESSUS software, was the probabilistic calculator, and CometBoards became the optimizer. The SDO capability requires a finite element structural model, a material model, a load model, and a design model. The stochastic optimization concept is illustrated considering an academic example and a real-life airframe component made of metallic and composite materials.

Modelling on optimal portfolio with exchange rate based on discontinuous stochastic process

NASA Astrophysics Data System (ADS)

Yan, Wei; Chang, Yuwen

2016-12-01

Considering the stochastic exchange rate, this paper is concerned with the dynamic portfolio selection in financial market. The optimal investment problem is formulated as a continuous-time mathematical model under mean-variance criterion. These processes follow jump-diffusion processes (Weiner process and Poisson process). Then the corresponding Hamilton-Jacobi-Bellman(HJB) equation of the problem is presented and its efferent frontier is obtained. Moreover, the optimal strategy is also derived under safety-first criterion.

Optimal growth trajectories with finite carrying capacity.

PubMed

Caravelli, F; Sindoni, L; Caccioli, F; Ududec, C

2016-08-01

We consider the problem of finding optimal strategies that maximize the average growth rate of multiplicative stochastic processes. For a geometric Brownian motion, the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction of resources at any step of the dynamics. We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance. We formulate the problem in terms of a stochastic process with multiplicative noise and a nonlinear drift term that is determined by the specific functional form of carrying capacity. We solve the stochastic equation for two classes of carrying capacity functions (power laws and logarithmic), and in both cases we compute the optimal trajectories of the control parameter. We further test the validity of our analytical results using numerical simulations.

Optimal growth trajectories with finite carrying capacity

NASA Astrophysics Data System (ADS)

Caravelli, F.; Sindoni, L.; Caccioli, F.; Ududec, C.

2016-08-01

We consider the problem of finding optimal strategies that maximize the average growth rate of multiplicative stochastic processes. For a geometric Brownian motion, the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction of resources at any step of the dynamics. We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance. We formulate the problem in terms of a stochastic process with multiplicative noise and a nonlinear drift term that is determined by the specific functional form of carrying capacity. We solve the stochastic equation for two classes of carrying capacity functions (power laws and logarithmic), and in both cases we compute the optimal trajectories of the control parameter. We further test the validity of our analytical results using numerical simulations.

Stochastic Evolutionary Algorithms for Planning Robot Paths

NASA Technical Reports Server (NTRS)

Fink, Wolfgang; Aghazarian, Hrand; Huntsberger, Terrance; Terrile, Richard

2006-01-01

A computer program implements stochastic evolutionary algorithms for planning and optimizing collision-free paths for robots and their jointed limbs. Stochastic evolutionary algorithms can be made to produce acceptably close approximations to exact, optimal solutions for path-planning problems while often demanding much less computation than do exhaustive-search and deterministic inverse-kinematics algorithms that have been used previously for this purpose. Hence, the present software is better suited for application aboard robots having limited computing capabilities (see figure). The stochastic aspect lies in the use of simulated annealing to (1) prevent trapping of an optimization algorithm in local minima of an energy-like error measure by which the fitness of a trial solution is evaluated while (2) ensuring that the entire multidimensional configuration and parameter space of the path-planning problem is sampled efficiently with respect to both robot joint angles and computation time. Simulated annealing is an established technique for avoiding local minima in multidimensional optimization problems, but has not, until now, been applied to planning collision-free robot paths by use of low-power computers.

Stochastic optimization for the detection of changes in maternal heart rate kinetics during pregnancy

NASA Astrophysics Data System (ADS)

Zakynthinaki, M. S.; Barakat, R. O.; Cordente Martínez, C. A.; Sampedro Molinuevo, J.

2011-03-01

The stochastic optimization method ALOPEX IV has been successfully applied to the problem of detecting possible changes in the maternal heart rate kinetics during pregnancy. For this reason, maternal heart rate data were recorded before, during and after gestation, during sessions of exercises of constant mild intensity; ALOPEX IV stochastic optimization was used to calculate the parameter values that optimally fit a dynamical systems model to the experimental data. The results not only demonstrate the effectiveness of ALOPEX IV stochastic optimization, but also have important implications in the area of exercise physiology, as they reveal important changes in the maternal cardiovascular dynamics, as a result of pregnancy.

On the decentralized control of large-scale systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Chong, C.

1973-01-01

The decentralized control of stochastic large scale systems was considered. Particular emphasis was given to control strategies which utilize decentralized information and can be computed in a decentralized manner. The deterministic constrained optimization problem is generalized to the stochastic case when each decision variable depends on different information and the constraint is only required to be satisfied on the average. For problems with a particular structure, a hierarchical decomposition is obtained. For the stochastic control of dynamic systems with different information sets, a new kind of optimality is proposed which exploits the coupled nature of the dynamic system. The subsystems are assumed to be uncoupled and then certain constraints are required to be satisfied, either in a off-line or on-line fashion. For off-line coordination, a hierarchical approach of solving the problem is obtained. The lower level problems are all uncoupled. For on-line coordination, distinction is made between open loop feedback optimal coordination and closed loop optimal coordination.

Supercomputer optimizations for stochastic optimal control applications

NASA Technical Reports Server (NTRS)

Chung, Siu-Leung; Hanson, Floyd B.; Xu, Huihuang

1991-01-01

Supercomputer optimizations for a computational method of solving stochastic, multibody, dynamic programming problems are presented. The computational method is valid for a general class of optimal control problems that are nonlinear, multibody dynamical systems, perturbed by general Markov noise in continuous time, i.e., nonsmooth Gaussian as well as jump Poisson random white noise. Optimization techniques for vector multiprocessors or vectorizing supercomputers include advanced data structures, loop restructuring, loop collapsing, blocking, and compiler directives. These advanced computing techniques and superconducting hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations, by permitting the solution of large multibody problems. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random aerospace fluctuations.

Finding optimal vaccination strategies under parameter uncertainty using stochastic programming.

PubMed

Tanner, Matthew W; Sattenspiel, Lisa; Ntaimo, Lewis

2008-10-01

We present a stochastic programming framework for finding the optimal vaccination policy for controlling infectious disease epidemics under parameter uncertainty. Stochastic programming is a popular framework for including the effects of parameter uncertainty in a mathematical optimization model. The problem is initially formulated to find the minimum cost vaccination policy under a chance-constraint. The chance-constraint requires that the probability that R(*)

Walking the Filament of Feasibility: Global Optimization of Highly-Constrained, Multi-Modal Interplanetary Trajectories Using a Novel Stochastic Search Technique

NASA Technical Reports Server (NTRS)

Englander, Arnold C.; Englander, Jacob A.

2017-01-01

Interplanetary trajectory optimization problems are highly complex and are characterized by a large number of decision variables and equality and inequality constraints as well as many locally optimal solutions. Stochastic global search techniques, coupled with a large-scale NLP solver, have been shown to solve such problems but are inadequately robust when the problem constraints become very complex. In this work, we present a novel search algorithm that takes advantage of the fact that equality constraints effectively collapse the solution space to lower dimensionality. This new approach walks the filament'' of feasibility to efficiently find the global optimal solution.

Algorithms and analyses for stochastic optimization for turbofan noise reduction using parallel reduced-order modeling

NASA Astrophysics Data System (ADS)

Yang, Huanhuan; Gunzburger, Max

2017-06-01

Simulation-based optimization of acoustic liner design in a turbofan engine nacelle for noise reduction purposes can dramatically reduce the cost and time needed for experimental designs. Because uncertainties are inevitable in the design process, a stochastic optimization algorithm is posed based on the conditional value-at-risk measure so that an ideal acoustic liner impedance is determined that is robust in the presence of uncertainties. A parallel reduced-order modeling framework is developed that dramatically improves the computational efficiency of the stochastic optimization solver for a realistic nacelle geometry. The reduced stochastic optimization solver takes less than 500 seconds to execute. In addition, well-posedness and finite element error analyses of the state system and optimization problem are provided.

Maximum principle for a stochastic delayed system involving terminal state constraints.

PubMed

Wen, Jiaqiang; Shi, Yufeng

2017-01-01

We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set. We firstly introduce an equivalent backward delayed system depicted as a time-delayed backward stochastic differential equation. Then a stochastic maximum principle is obtained by virtue of Ekeland's variational principle. Finally, applications to a state constrained stochastic delayed linear-quadratic control model and a production-consumption choice problem are studied to illustrate the main obtained result.

Simulated Stochastic Approximation Annealing for Global Optimization with a Square-Root Cooling Schedule

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liang, Faming; Cheng, Yichen; Lin, Guang

2014-06-13

Simulated annealing has been widely used in the solution of optimization problems. As known by many researchers, the global optima cannot be guaranteed to be located by simulated annealing unless a logarithmic cooling schedule is used. However, the logarithmic cooling schedule is so slow that no one can afford to have such a long CPU time. This paper proposes a new stochastic optimization algorithm, the so-called simulated stochastic approximation annealing algorithm, which is a combination of simulated annealing and the stochastic approximation Monte Carlo algorithm. Under the framework of stochastic approximation Markov chain Monte Carlo, it is shown that themore » new algorithm can work with a cooling schedule in which the temperature can decrease much faster than in the logarithmic cooling schedule, e.g., a square-root cooling schedule, while guaranteeing the global optima to be reached when the temperature tends to zero. The new algorithm has been tested on a few benchmark optimization problems, including feed-forward neural network training and protein-folding. The numerical results indicate that the new algorithm can significantly outperform simulated annealing and other competitors.« less

Adaptive control of stochastic linear systems with unknown parameters. M.S. Thesis

NASA Technical Reports Server (NTRS)

Ku, R. T.

1972-01-01

The problem of optimal control of linear discrete-time stochastic dynamical system with unknown and, possibly, stochastically varying parameters is considered on the basis of noisy measurements. It is desired to minimize the expected value of a quadratic cost functional. Since the simultaneous estimation of the state and plant parameters is a nonlinear filtering problem, the extended Kalman filter algorithm is used. Several qualitative and asymptotic properties of the open loop feedback optimal control and the enforced separation scheme are discussed. Simulation results via Monte Carlo method show that, in terms of the performance measure, for stable systems the open loop feedback optimal control system is slightly better than the enforced separation scheme, while for unstable systems the latter scheme is far better.

Intrinsic optimization using stochastic nanomagnets

PubMed Central

Sutton, Brian; Camsari, Kerem Yunus; Behin-Aein, Behtash; Datta, Supriyo

2017-01-01

This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic constituents are stochastic nanomagnets which switch randomly between the ±1 Ising states and can be monitored continuously with standard electronics. Their mutual interactions can be short or long range, and their strengths can be reconfigured as needed to solve specific problems and to anneal the system at room temperature. The natural laws of statistical mechanics guide the network of stochastic nanomagnets at GHz speeds through the collective states with an emphasis on the low energy states that represent optimal solutions. As proof-of-concept, we present simulation results for standard NP-complete examples including a 16-city traveling salesman problem using experimentally benchmarked models for spin-transfer torque driven stochastic nanomagnets. PMID:28295053

Intrinsic optimization using stochastic nanomagnets

NASA Astrophysics Data System (ADS)

Sutton, Brian; Camsari, Kerem Yunus; Behin-Aein, Behtash; Datta, Supriyo

2017-03-01

This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic constituents are stochastic nanomagnets which switch randomly between the ±1 Ising states and can be monitored continuously with standard electronics. Their mutual interactions can be short or long range, and their strengths can be reconfigured as needed to solve specific problems and to anneal the system at room temperature. The natural laws of statistical mechanics guide the network of stochastic nanomagnets at GHz speeds through the collective states with an emphasis on the low energy states that represent optimal solutions. As proof-of-concept, we present simulation results for standard NP-complete examples including a 16-city traveling salesman problem using experimentally benchmarked models for spin-transfer torque driven stochastic nanomagnets.

A quantile-based scenario analysis approach to biomass supply chain optimization under uncertainty

DOE PAGES

Zamar, David S.; Gopaluni, Bhushan; Sokhansanj, Shahab; ...

2016-11-21

Supply chain optimization for biomass-based power plants is an important research area due to greater emphasis on renewable power energy sources. Biomass supply chain design and operational planning models are often formulated and studied using deterministic mathematical models. While these models are beneficial for making decisions, their applicability to real world problems may be limited because they do not capture all the complexities in the supply chain, including uncertainties in the parameters. This study develops a statistically robust quantile-based approach for stochastic optimization under uncertainty, which builds upon scenario analysis. We apply and evaluate the performance of our approach tomore » address the problem of analyzing competing biomass supply chains subject to stochastic demand and supply. Finally, the proposed approach was found to outperform alternative methods in terms of computational efficiency and ability to meet the stochastic problem requirements.« less

A quantile-based scenario analysis approach to biomass supply chain optimization under uncertainty

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zamar, David S.; Gopaluni, Bhushan; Sokhansanj, Shahab

Supply chain optimization for biomass-based power plants is an important research area due to greater emphasis on renewable power energy sources. Biomass supply chain design and operational planning models are often formulated and studied using deterministic mathematical models. While these models are beneficial for making decisions, their applicability to real world problems may be limited because they do not capture all the complexities in the supply chain, including uncertainties in the parameters. This study develops a statistically robust quantile-based approach for stochastic optimization under uncertainty, which builds upon scenario analysis. We apply and evaluate the performance of our approach tomore » address the problem of analyzing competing biomass supply chains subject to stochastic demand and supply. Finally, the proposed approach was found to outperform alternative methods in terms of computational efficiency and ability to meet the stochastic problem requirements.« less

Price sensitive demand with random sales price - a newsboy problem

NASA Astrophysics Data System (ADS)

Sankar Sana, Shib

2012-03-01

Up to now, many newsboy problems have been considered in the stochastic inventory literature. Some assume that stochastic demand is independent of selling price (p) and others consider the demand as a function of stochastic shock factor and deterministic sales price. This article introduces a price-dependent demand with stochastic selling price into the classical Newsboy problem. The proposed model analyses the expected average profit for a general distribution function of p and obtains an optimal order size. Finally, the model is discussed for various appropriate distribution functions of p and illustrated with numerical examples.

Stochastic Optimization for an Analytical Model of Saltwater Intrusion in Coastal Aquifers

PubMed Central

Stratis, Paris N.; Karatzas, George P.; Papadopoulou, Elena P.; Zakynthinaki, Maria S.; Saridakis, Yiannis G.

2016-01-01

The present study implements a stochastic optimization technique to optimally manage freshwater pumping from coastal aquifers. Our simulations utilize the well-known sharp interface model for saltwater intrusion in coastal aquifers together with its known analytical solution. The objective is to maximize the total volume of freshwater pumped by the wells from the aquifer while, at the same time, protecting the aquifer from saltwater intrusion. In the direction of dealing with this problem in real time, the ALOPEX stochastic optimization method is used, to optimize the pumping rates of the wells, coupled with a penalty-based strategy that keeps the saltwater front at a safe distance from the wells. Several numerical optimization results, that simulate a known real aquifer case, are presented. The results explore the computational performance of the chosen stochastic optimization method as well as its abilities to manage freshwater pumping in real aquifer environments. PMID:27689362

A chance-constrained stochastic approach to intermodal container routing problems.

PubMed

Zhao, Yi; Liu, Ronghui; Zhang, Xi; Whiteing, Anthony

2018-01-01

We consider a container routing problem with stochastic time variables in a sea-rail intermodal transportation system. The problem is formulated as a binary integer chance-constrained programming model including stochastic travel times and stochastic transfer time, with the objective of minimising the expected total cost. Two chance constraints are proposed to ensure that the container service satisfies ship fulfilment and cargo on-time delivery with pre-specified probabilities. A hybrid heuristic algorithm is employed to solve the binary integer chance-constrained programming model. Two case studies are conducted to demonstrate the feasibility of the proposed model and to analyse the impact of stochastic variables and chance-constraints on the optimal solution and total cost.

A chance-constrained stochastic approach to intermodal container routing problems

PubMed Central

Zhao, Yi; Zhang, Xi; Whiteing, Anthony

2018-01-01

We consider a container routing problem with stochastic time variables in a sea-rail intermodal transportation system. The problem is formulated as a binary integer chance-constrained programming model including stochastic travel times and stochastic transfer time, with the objective of minimising the expected total cost. Two chance constraints are proposed to ensure that the container service satisfies ship fulfilment and cargo on-time delivery with pre-specified probabilities. A hybrid heuristic algorithm is employed to solve the binary integer chance-constrained programming model. Two case studies are conducted to demonstrate the feasibility of the proposed model and to analyse the impact of stochastic variables and chance-constraints on the optimal solution and total cost. PMID:29438389

A stochastic maximum principle for backward control systems with random default time

NASA Astrophysics Data System (ADS)

Shen, Yang; Kuen Siu, Tak

2013-05-01

This paper establishes a necessary and sufficient stochastic maximum principle for backward systems, where the state processes are governed by jump-diffusion backward stochastic differential equations with random default time. An application of the sufficient stochastic maximum principle to an optimal investment and capital injection problem in the presence of default risk is discussed.

Switching neuronal state: optimal stimuli revealed using a stochastically-seeded gradient algorithm.

PubMed

Chang, Joshua; Paydarfar, David

2014-12-01

Inducing a switch in neuronal state using energy optimal stimuli is relevant to a variety of problems in neuroscience. Analytical techniques from optimal control theory can identify such stimuli; however, solutions to the optimization problem using indirect variational approaches can be elusive in models that describe neuronal behavior. Here we develop and apply a direct gradient-based optimization algorithm to find stimulus waveforms that elicit a change in neuronal state while minimizing energy usage. We analyze standard models of neuronal behavior, the Hodgkin-Huxley and FitzHugh-Nagumo models, to show that the gradient-based algorithm: (1) enables automated exploration of a wide solution space, using stochastically generated initial waveforms that converge to multiple locally optimal solutions; and (2) finds optimal stimulus waveforms that achieve a physiological outcome condition, without a priori knowledge of the optimal terminal condition of all state variables. Analysis of biological systems using stochastically-seeded gradient methods can reveal salient dynamical mechanisms underlying the optimal control of system behavior. The gradient algorithm may also have practical applications in future work, for example, finding energy optimal waveforms for therapeutic neural stimulation that minimizes power usage and diminishes off-target effects and damage to neighboring tissue.

Fleet Assignment Using Collective Intelligence

NASA Technical Reports Server (NTRS)

Antoine, Nicolas E.; Bieniawski, Stefan R.; Kroo, Ilan M.; Wolpert, David H.

2004-01-01

Product distribution theory is a new collective intelligence-based framework for analyzing and controlling distributed systems. Its usefulness in distributed stochastic optimization is illustrated here through an airline fleet assignment problem. This problem involves the allocation of aircraft to a set of flights legs in order to meet passenger demand, while satisfying a variety of linear and non-linear constraints. Over the course of the day, the routing of each aircraft is determined in order to minimize the number of required flights for a given fleet. The associated flow continuity and aircraft count constraints have led researchers to focus on obtaining quasi-optimal solutions, especially at larger scales. In this paper, the authors propose the application of this new stochastic optimization algorithm to a non-linear objective cold start fleet assignment problem. Results show that the optimizer can successfully solve such highly-constrained problems (130 variables, 184 constraints).

Optimal Control via Self-Generated Stochasticity

NASA Technical Reports Server (NTRS)

Zak, Michail

2011-01-01

The problem of global maxima of functionals has been examined. Mathematical roots of local maxima are the same as those for a much simpler problem of finding global maximum of a multi-dimensional function. The second problem is instability even if an optimal trajectory is found, there is no guarantee that it is stable. As a result, a fundamentally new approach is introduced to optimal control based upon two new ideas. The first idea is to represent the functional to be maximized as a limit of a probability density governed by the appropriately selected Liouville equation. Then, the corresponding ordinary differential equations (ODEs) become stochastic, and that sample of the solution that has the largest value will have the highest probability to appear in ODE simulation. The main advantages of the stochastic approach are that it is not sensitive to local maxima, the function to be maximized must be only integrable but not necessarily differentiable, and global equality and inequality constraints do not cause any significant obstacles. The second idea is to remove possible instability of the optimal solution by equipping the control system with a self-stabilizing device. The applications of the proposed methodology will optimize the performance of NASA spacecraft, as well as robot performance.

Stochastic optimization model for order acceptance with multiple demand classes and uncertain demand/supply

NASA Astrophysics Data System (ADS)

Yang, Wen; Fung, Richard Y. K.

2014-06-01

This article considers an order acceptance problem in a make-to-stock manufacturing system with multiple demand classes in a finite time horizon. Demands in different periods are random variables and are independent of one another, and replenishments of inventory deviate from the scheduled quantities. The objective of this work is to maximize the expected net profit over the planning horizon by deciding the fraction of the demand that is going to be fulfilled. This article presents a stochastic order acceptance optimization model and analyses the existence of the optimal promising policies. An example of a discrete problem is used to illustrate the policies by applying the dynamic programming method. In order to solve the continuous problems, a heuristic algorithm based on stochastic approximation (HASA) is developed. Finally, the computational results of a case example illustrate the effectiveness and efficiency of the HASA approach, and make the application of the proposed model readily acceptable.

A Comparison Study of Stochastic- and Guaranteed- Service Approaches on Safety Stock Optimization for Multi Serial Systems

NASA Astrophysics Data System (ADS)

Li, Peng; Wu, Di

2018-01-01

Two competing approaches have been developed over the years for multi-echelon inventory system optimization, stochastic-service approach (SSA) and guaranteed-service approach (GSA). Although they solve the same inventory policy optimization problem in their core, they make different assumptions with regard to the role of safety stock. This paper provides a detailed comparison of the two approaches by considering operating flexibility costs in the optimization of (R, Q) policies for a continuous review serial inventory system. The results indicate the GSA model is more efficiency in solving the complicated inventory problem in terms of the computation time, and the cost difference of the two approaches is quite small.

Stochastic Control of Energy Efficient Buildings: A Semidefinite Programming Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ma, Xiao; Dong, Jin; Djouadi, Seddik M

2015-01-01

The key goal in energy efficient buildings is to reduce energy consumption of Heating, Ventilation, and Air- Conditioning (HVAC) systems while maintaining a comfortable temperature and humidity in the building. This paper proposes a novel stochastic control approach for achieving joint performance and power control of HVAC. We employ a constrained Stochastic Linear Quadratic Control (cSLQC) by minimizing a quadratic cost function with a disturbance assumed to be Gaussian. The problem is formulated to minimize the expected cost subject to a linear constraint and a probabilistic constraint. By using cSLQC, the problem is reduced to a semidefinite optimization problem, wheremore » the optimal control can be computed efficiently by Semidefinite programming (SDP). Simulation results are provided to demonstrate the effectiveness and power efficiency by utilizing the proposed control approach.« less

Stochastic modelling of turbulent combustion for design optimization of gas turbine combustors

NASA Astrophysics Data System (ADS)

Mehanna Ismail, Mohammed Ali

The present work covers the development and the implementation of an efficient algorithm for the design optimization of gas turbine combustors. The purpose is to explore the possibilities and indicate constructive suggestions for optimization techniques as alternative methods for designing gas turbine combustors. The algorithm is general to the extent that no constraints are imposed on the combustion phenomena or on the combustor configuration. The optimization problem is broken down into two elementary problems: the first is the optimum search algorithm, and the second is the turbulent combustion model used to determine the combustor performance parameters. These performance parameters constitute the objective and physical constraints in the optimization problem formulation. The examination of both turbulent combustion phenomena and the gas turbine design process suggests that the turbulent combustion model represents a crucial part of the optimization algorithm. The basic requirements needed for a turbulent combustion model to be successfully used in a practical optimization algorithm are discussed. In principle, the combustion model should comply with the conflicting requirements of high fidelity, robustness and computational efficiency. To that end, the problem of turbulent combustion is discussed and the current state of the art of turbulent combustion modelling is reviewed. According to this review, turbulent combustion models based on the composition PDF transport equation are found to be good candidates for application in the present context. However, these models are computationally expensive. To overcome this difficulty, two different models based on the composition PDF transport equation were developed: an improved Lagrangian Monte Carlo composition PDF algorithm and the generalized stochastic reactor model. Improvements in the Lagrangian Monte Carlo composition PDF model performance and its computational efficiency were achieved through the implementation of time splitting, variable stochastic fluid particle mass control, and a second order time accurate (predictor-corrector) scheme used for solving the stochastic differential equations governing the particles evolution. The model compared well against experimental data found in the literature for two different configurations: bluff body and swirl stabilized combustors. The generalized stochastic reactor is a newly developed model. This model relies on the generalization of the concept of the classical stochastic reactor theory in the sense that it accounts for both finite micro- and macro-mixing processes. (Abstract shortened by UMI.)

Optimization of Operations Resources via Discrete Event Simulation Modeling

NASA Technical Reports Server (NTRS)

Joshi, B.; Morris, D.; White, N.; Unal, R.

1996-01-01

The resource levels required for operation and support of reusable launch vehicles are typically defined through discrete event simulation modeling. Minimizing these resources constitutes an optimization problem involving discrete variables and simulation. Conventional approaches to solve such optimization problems involving integer valued decision variables are the pattern search and statistical methods. However, in a simulation environment that is characterized by search spaces of unknown topology and stochastic measures, these optimization approaches often prove inadequate. In this paper, we have explored the applicability of genetic algorithms to the simulation domain. Genetic algorithms provide a robust search strategy that does not require continuity and differentiability of the problem domain. The genetic algorithm successfully minimized the operation and support activities for a space vehicle, through a discrete event simulation model. The practical issues associated with simulation optimization, such as stochastic variables and constraints, were also taken into consideration.

Applications of Evolutionary Technology to Manufacturing and Logistics Systems : State-of-the Art Survey

NASA Astrophysics Data System (ADS)

Gen, Mitsuo; Lin, Lin

Many combinatorial optimization problems from industrial engineering and operations research in real-world are very complex in nature and quite hard to solve them by conventional techniques. Since the 1960s, there has been an increasing interest in imitating living beings to solve such kinds of hard combinatorial optimization problems. Simulating the natural evolutionary process of human beings results in stochastic optimization techniques called evolutionary algorithms (EAs), which can often outperform conventional optimization methods when applied to difficult real-world problems. In this survey paper, we provide a comprehensive survey of the current state-of-the-art in the use of EA in manufacturing and logistics systems. In order to demonstrate the EAs which are powerful and broadly applicable stochastic search and optimization techniques, we deal with the following engineering design problems: transportation planning models, layout design models and two-stage logistics models in logistics systems; job-shop scheduling, resource constrained project scheduling in manufacturing system.

Stochastic optimization for modeling physiological time series: application to the heart rate response to exercise

NASA Astrophysics Data System (ADS)

Zakynthinaki, M. S.; Stirling, J. R.

2007-01-01

Stochastic optimization is applied to the problem of optimizing the fit of a model to the time series of raw physiological (heart rate) data. The physiological response to exercise has been recently modeled as a dynamical system. Fitting the model to a set of raw physiological time series data is, however, not a trivial task. For this reason and in order to calculate the optimal values of the parameters of the model, the present study implements the powerful stochastic optimization method ALOPEX IV, an algorithm that has been proven to be fast, effective and easy to implement. The optimal parameters of the model, calculated by the optimization method for the particular athlete, are very important as they characterize the athlete's current condition. The present study applies the ALOPEX IV stochastic optimization to the modeling of a set of heart rate time series data corresponding to different exercises of constant intensity. An analysis of the optimization algorithm, together with an analytic proof of its convergence (in the absence of noise), is also presented.

Robust stochastic optimization for reservoir operation

NASA Astrophysics Data System (ADS)

Pan, Limeng; Housh, Mashor; Liu, Pan; Cai, Ximing; Chen, Xin

2015-01-01

Optimal reservoir operation under uncertainty is a challenging engineering problem. Application of classic stochastic optimization methods to large-scale problems is limited due to computational difficulty. Moreover, classic stochastic methods assume that the estimated distribution function or the sample inflow data accurately represents the true probability distribution, which may be invalid and the performance of the algorithms may be undermined. In this study, we introduce a robust optimization (RO) approach, Iterative Linear Decision Rule (ILDR), so as to provide a tractable approximation for a multiperiod hydropower generation problem. The proposed approach extends the existing LDR method by accommodating nonlinear objective functions. It also provides users with the flexibility of choosing the accuracy of ILDR approximations by assigning a desired number of piecewise linear segments to each uncertainty. The performance of the ILDR is compared with benchmark policies including the sampling stochastic dynamic programming (SSDP) policy derived from historical data. The ILDR solves both the single and multireservoir systems efficiently. The single reservoir case study results show that the RO method is as good as SSDP when implemented on the original historical inflows and it outperforms SSDP policy when tested on generated inflows with the same mean and covariance matrix as those in history. For the multireservoir case study, which considers water supply in addition to power generation, numerical results show that the proposed approach performs as well as in the single reservoir case study in terms of optimal value and distributional robustness.

Digital program for solving the linear stochastic optimal control and estimation problem

NASA Technical Reports Server (NTRS)

Geyser, L. C.; Lehtinen, B.

1975-01-01

A computer program is described which solves the linear stochastic optimal control and estimation (LSOCE) problem by using a time-domain formulation. The LSOCE problem is defined as that of designing controls for a linear time-invariant system which is disturbed by white noise in such a way as to minimize a performance index which is quadratic in state and control variables. The LSOCE problem and solution are outlined; brief descriptions are given of the solution algorithms, and complete descriptions of each subroutine, including usage information and digital listings, are provided. A test case is included, as well as information on the IBM 7090-7094 DCS time and storage requirements.

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less

Stochastic Averaging for Constrained Optimization With Application to Online Resource Allocation

NASA Astrophysics Data System (ADS)

Chen, Tianyi; Mokhtari, Aryan; Wang, Xin; Ribeiro, Alejandro; Giannakis, Georgios B.

2017-06-01

Existing approaches to resource allocation for nowadays stochastic networks are challenged to meet fast convergence and tolerable delay requirements. The present paper leverages online learning advances to facilitate stochastic resource allocation tasks. By recognizing the central role of Lagrange multipliers, the underlying constrained optimization problem is formulated as a machine learning task involving both training and operational modes, with the goal of learning the sought multipliers in a fast and efficient manner. To this end, an order-optimal offline learning approach is developed first for batch training, and it is then generalized to the online setting with a procedure termed learn-and-adapt. The novel resource allocation protocol permeates benefits of stochastic approximation and statistical learning to obtain low-complexity online updates with learning errors close to the statistical accuracy limits, while still preserving adaptation performance, which in the stochastic network optimization context guarantees queue stability. Analysis and simulated tests demonstrate that the proposed data-driven approach improves the delay and convergence performance of existing resource allocation schemes.

Control Improvement for Jump-Diffusion Processes with Applications to Finance

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baeuerle, Nicole, E-mail: nicole.baeuerle@kit.edu; Rieder, Ulrich, E-mail: ulrich.rieder@uni-ulm.de

2012-02-15

We consider stochastic control problems with jump-diffusion processes and formulate an algorithm which produces, starting from a given admissible control {pi}, a new control with a better value. If no improvement is possible, then {pi} is optimal. Such an algorithm is well-known for discrete-time Markov Decision Problems under the name Howard's policy improvement algorithm. The idea can be traced back to Bellman. Here we show with the help of martingale techniques that such an algorithm can also be formulated for stochastic control problems with jump-diffusion processes. As an application we derive some interesting results in financial portfolio optimization.

Inversion method based on stochastic optimization for particle sizing.

PubMed

Sánchez-Escobar, Juan Jaime; Barbosa-Santillán, Liliana Ibeth; Vargas-Ubera, Javier; Aguilar-Valdés, Félix

2016-08-01

A stochastic inverse method is presented based on a hybrid evolutionary optimization algorithm (HEOA) to retrieve a monomodal particle-size distribution (PSD) from the angular distribution of scattered light. By solving an optimization problem, the HEOA (with the Fraunhofer approximation) retrieves the PSD from an intensity pattern generated by Mie theory. The analyzed light-scattering pattern can be attributed to unimodal normal, gamma, or lognormal distribution of spherical particles covering the interval of modal size parameters 46≤α≤150. The HEOA ensures convergence to the near-optimal solution during the optimization of a real-valued objective function by combining the advantages of a multimember evolution strategy and locally weighted linear regression. The numerical results show that our HEOA can be satisfactorily applied to solve the inverse light-scattering problem.

Solving complex maintenance planning optimization problems using stochastic simulation and multi-criteria fuzzy decision making

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tahvili, Sahar; Österberg, Jonas; Silvestrov, Sergei

One of the most important factors in the operations of many cooperations today is to maximize profit and one important tool to that effect is the optimization of maintenance activities. Maintenance activities is at the largest level divided into two major areas, corrective maintenance (CM) and preventive maintenance (PM). When optimizing maintenance activities, by a maintenance plan or policy, we seek to find the best activities to perform at each point in time, be it PM or CM. We explore the use of stochastic simulation, genetic algorithms and other tools for solving complex maintenance planning optimization problems in terms ofmore » a suggested framework model based on discrete event simulation.« less

Design Tool Using a New Optimization Method Based on a Stochastic Process

NASA Astrophysics Data System (ADS)

Yoshida, Hiroaki; Yamaguchi, Katsuhito; Ishikawa, Yoshio

Conventional optimization methods are based on a deterministic approach since their purpose is to find out an exact solution. However, such methods have initial condition dependence and the risk of falling into local solution. In this paper, we propose a new optimization method based on the concept of path integrals used in quantum mechanics. The method obtains a solution as an expected value (stochastic average) using a stochastic process. The advantages of this method are that it is not affected by initial conditions and does not require techniques based on experiences. We applied the new optimization method to a hang glider design. In this problem, both the hang glider design and its flight trajectory were optimized. The numerical calculation results prove that performance of the method is sufficient for practical use.

Multiobjective optimization in structural design with uncertain parameters and stochastic processes

NASA Technical Reports Server (NTRS)

Rao, S. S.

1984-01-01

The application of multiobjective optimization techniques to structural design problems involving uncertain parameters and random processes is studied. The design of a cantilever beam with a tip mass subjected to a stochastic base excitation is considered for illustration. Several of the problem parameters are assumed to be random variables and the structural mass, fatigue damage, and negative of natural frequency of vibration are considered for minimization. The solution of this three-criteria design problem is found by using global criterion, utility function, game theory, goal programming, goal attainment, bounded objective function, and lexicographic methods. It is observed that the game theory approach is superior in finding a better optimum solution, assuming the proper balance of the various objective functions. The procedures used in the present investigation are expected to be useful in the design of general dynamic systems involving uncertain parameters, stochastic process, and multiple objectives.

A Novel Biobjective Risk-Based Model for Stochastic Air Traffic Network Flow Optimization Problem.

PubMed

Cai, Kaiquan; Jia, Yaoguang; Zhu, Yanbo; Xiao, Mingming

2015-01-01

Network-wide air traffic flow management (ATFM) is an effective way to alleviate demand-capacity imbalances globally and thereafter reduce airspace congestion and flight delays. The conventional ATFM models assume the capacities of airports or airspace sectors are all predetermined. However, the capacity uncertainties due to the dynamics of convective weather may make the deterministic ATFM measures impractical. This paper investigates the stochastic air traffic network flow optimization (SATNFO) problem, which is formulated as a weighted biobjective 0-1 integer programming model. In order to evaluate the effect of capacity uncertainties on ATFM, the operational risk is modeled via probabilistic risk assessment and introduced as an extra objective in SATNFO problem. Computation experiments using real-world air traffic network data associated with simulated weather data show that presented model has far less constraints compared to stochastic model with nonanticipative constraints, which means our proposed model reduces the computation complexity.

Stochastic Optimization For Water Resources Allocation

NASA Astrophysics Data System (ADS)

Yamout, G.; Hatfield, K.

2003-12-01

For more than 40 years, water resources allocation problems have been addressed using deterministic mathematical optimization. When data uncertainties exist, these methods could lead to solutions that are sub-optimal or even infeasible. While optimization models have been proposed for water resources decision-making under uncertainty, no attempts have been made to address the uncertainties in water allocation problems in an integrated approach. This paper presents an Integrated Dynamic, Multi-stage, Feedback-controlled, Linear, Stochastic, and Distributed parameter optimization approach to solve a problem of water resources allocation. It attempts to capture (1) the conflict caused by competing objectives, (2) environmental degradation produced by resource consumption, and finally (3) the uncertainty and risk generated by the inherently random nature of state and decision parameters involved in such a problem. A theoretical system is defined throughout its different elements. These elements consisting mainly of water resource components and end-users are described in terms of quantity, quality, and present and future associated risks and uncertainties. Models are identified, modified, and interfaced together to constitute an integrated water allocation optimization framework. This effort is a novel approach to confront the water allocation optimization problem while accounting for uncertainties associated with all its elements; thus resulting in a solution that correctly reflects the physical problem in hand.

Application of a stochastic inverse to the geophysical inverse problem

NASA Technical Reports Server (NTRS)

Jordan, T. H.; Minster, J. B.

1972-01-01

The inverse problem for gross earth data can be reduced to an undertermined linear system of integral equations of the first kind. A theory is discussed for computing particular solutions to this linear system based on the stochastic inverse theory presented by Franklin. The stochastic inverse is derived and related to the generalized inverse of Penrose and Moore. A Backus-Gilbert type tradeoff curve is constructed for the problem of estimating the solution to the linear system in the presence of noise. It is shown that the stochastic inverse represents an optimal point on this tradeoff curve. A useful form of the solution autocorrelation operator as a member of a one-parameter family of smoothing operators is derived.

Local Approximation and Hierarchical Methods for Stochastic Optimization

NASA Astrophysics Data System (ADS)

Cheng, Bolong

In this thesis, we present local and hierarchical approximation methods for two classes of stochastic optimization problems: optimal learning and Markov decision processes. For the optimal learning problem class, we introduce a locally linear model with radial basis function for estimating the posterior mean of the unknown objective function. The method uses a compact representation of the function which avoids storing the entire history, as is typically required by nonparametric methods. We derive a knowledge gradient policy with the locally parametric model, which maximizes the expected value of information. We show the policy is asymptotically optimal in theory, and experimental works suggests that the method can reliably find the optimal solution on a range of test functions. For the Markov decision processes problem class, we are motivated by an application where we want to co-optimize a battery for multiple revenue, in particular energy arbitrage and frequency regulation. The nature of this problem requires the battery to make charging and discharging decisions at different time scales while accounting for the stochastic information such as load demand, electricity prices, and regulation signals. Computing the exact optimal policy becomes intractable due to the large state space and the number of time steps. We propose two methods to circumvent the computation bottleneck. First, we propose a nested MDP model that structure the co-optimization problem into smaller sub-problems with reduced state space. This new model allows us to understand how the battery behaves down to the two-second dynamics (that of the frequency regulation market). Second, we introduce a low-rank value function approximation for backward dynamic programming. This new method only requires computing the exact value function for a small subset of the state space and approximate the entire value function via low-rank matrix completion. We test these methods on historical price data from the PJM Interconnect and show that it outperforms the baseline approach used in the industry.

Optimal harvesting of a stochastic delay logistic model with Lévy jumps

NASA Astrophysics Data System (ADS)

Qiu, Hong; Deng, Wenmin

2016-10-01

The optimal harvesting problem of a stochastic time delay logistic model with Lévy jumps is considered in this article. We first show that the model has a unique global positive solution and discuss the uniform boundedness of its pth moment with harvesting. Then we prove that the system is globally attractive and asymptotically stable in distribution under our assumptions. Furthermore, we obtain the existence of the optimal harvesting effort by the ergodic method, and then we give the explicit expression of the optimal harvesting policy and maximum yield.

Robust Consumption-Investment Problem on Infinite Horizon

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zawisza, Dariusz, E-mail: dariusz.zawisza@im.uj.edu.pl

In our paper we consider an infinite horizon consumption-investment problem under a model misspecification in a general stochastic factor model. We formulate the problem as a stochastic game and finally characterize the saddle point and the value function of that game using an ODE of semilinear type, for which we provide a proof of an existence and uniqueness theorem for its solution. Such equation is interested on its own right, since it generalizes many other equations arising in various infinite horizon optimization problems.

Strategic planning for disaster recovery with stochastic last mile distribution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bent, Russell Whitford; Van Hentenryck, Pascal; Coffrin, Carleton

2010-01-01

This paper considers the single commodity allocation problem (SCAP) for disaster recovery, a fundamental problem faced by all populated areas. SCAPs are complex stochastic optimization problems that combine resource allocation, warehouse routing, and parallel fleet routing. Moreover, these problems must be solved under tight runtime constraints to be practical in real-world disaster situations. This paper formalizes the specification of SCAPs and introduces a novel multi-stage hybrid-optimization algorithm that utilizes the strengths of mixed integer programming, constraint programming, and large neighborhood search. The algorithm was validated on hurricane disaster scenarios generated by Los Alamos National Laboratory using state-of-the-art disaster simulation toolsmore » and is deployed to aid federal organizations in the US.« less

Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bokanowski, Olivier, E-mail: boka@math.jussieu.fr; Picarelli, Athena, E-mail: athena.picarelli@inria.fr; Zidani, Hasnaa, E-mail: hasnaa.zidani@ensta.fr

2015-02-15

This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system ofmore » controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach.« less

A combined stochastic feedforward and feedback control design methodology with application to autoland design

NASA Technical Reports Server (NTRS)

Halyo, Nesim

1987-01-01

A combined stochastic feedforward and feedback control design methodology was developed. The objective of the feedforward control law is to track the commanded trajectory, whereas the feedback control law tries to maintain the plant state near the desired trajectory in the presence of disturbances and uncertainties about the plant. The feedforward control law design is formulated as a stochastic optimization problem and is embedded into the stochastic output feedback problem where the plant contains unstable and uncontrollable modes. An algorithm to compute the optimal feedforward is developed. In this approach, the use of error integral feedback, dynamic compensation, control rate command structures are an integral part of the methodology. An incremental implementation is recommended. Results on the eigenvalues of the implemented versus designed control laws are presented. The stochastic feedforward/feedback control methodology is used to design a digital automatic landing system for the ATOPS Research Vehicle, a Boeing 737-100 aircraft. The system control modes include localizer and glideslope capture and track, and flare to touchdown. Results of a detailed nonlinear simulation of the digital control laws, actuator systems, and aircraft aerodynamics are presented.

The Tool for Designing Engineering Systems Using a New Optimization Method Based on a Stochastic Process

NASA Astrophysics Data System (ADS)

Yoshida, Hiroaki; Yamaguchi, Katsuhito; Ishikawa, Yoshio

The conventional optimization methods were based on a deterministic approach, since their purpose is to find out an exact solution. However, these methods have initial condition dependence and risk of falling into local solution. In this paper, we propose a new optimization method based on a concept of path integral method used in quantum mechanics. The method obtains a solutions as an expected value (stochastic average) using a stochastic process. The advantages of this method are not to be affected by initial conditions and not to need techniques based on experiences. We applied the new optimization method to a design of the hang glider. In this problem, not only the hang glider design but also its flight trajectory were optimized. The numerical calculation results showed that the method has a sufficient performance.

Stochastic Optimal Prediction with Application to Averaged Euler Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bell, John; Chorin, Alexandre J.; Crutchfield, William

Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is approximated by its conditional expectation with respect to the invariant measure. In higher-order OP, unresolved information is approximated by a stochastic estimator, leading to a system of random or stochastic differential equations. We explain the ideas through a simple example, and then apply them to the solution of Averaged Euler equations in two space dimensions.

A stochastic optimization model under modeling uncertainty and parameter certainty for groundwater remediation design--part I. Model development.

PubMed

He, L; Huang, G H; Lu, H W

2010-04-15

Solving groundwater remediation optimization problems based on proxy simulators can usually yield optimal solutions differing from the "true" ones of the problem. This study presents a new stochastic optimization model under modeling uncertainty and parameter certainty (SOMUM) and the associated solution method for simultaneously addressing modeling uncertainty associated with simulator residuals and optimizing groundwater remediation processes. This is a new attempt different from the previous modeling efforts. The previous ones focused on addressing uncertainty in physical parameters (i.e. soil porosity) while this one aims to deal with uncertainty in mathematical simulator (arising from model residuals). Compared to the existing modeling approaches (i.e. only parameter uncertainty is considered), the model has the advantages of providing mean-variance analysis for contaminant concentrations, mitigating the effects of modeling uncertainties on optimal remediation strategies, offering confidence level of optimal remediation strategies to system designers, and reducing computational cost in optimization processes. 2009 Elsevier B.V. All rights reserved.

A supplier selection and order allocation problem with stochastic demands

NASA Astrophysics Data System (ADS)

Zhou, Yun; Zhao, Lei; Zhao, Xiaobo; Jiang, Jianhua

2011-08-01

We consider a system comprising a retailer and a set of candidate suppliers that operates within a finite planning horizon of multiple periods. The retailer replenishes its inventory from the suppliers and satisfies stochastic customer demands. At the beginning of each period, the retailer makes decisions on the replenishment quantity, supplier selection and order allocation among the selected suppliers. An optimisation problem is formulated to minimise the total expected system cost, which includes an outer level stochastic dynamic program for the optimal replenishment quantity and an inner level integer program for supplier selection and order allocation with a given replenishment quantity. For the inner level subproblem, we develop a polynomial algorithm to obtain optimal decisions. For the outer level subproblem, we propose an efficient heuristic for the system with integer-valued inventory, based on the structural properties of the system with real-valued inventory. We investigate the efficiency of the proposed solution approach, as well as the impact of parameters on the optimal replenishment decision with numerical experiments.

Development Optimization and Uncertainty Analysis Methods for Oil and Gas Reservoirs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ettehadtavakkol, Amin, E-mail: amin.ettehadtavakkol@ttu.edu; Jablonowski, Christopher; Lake, Larry

Uncertainty complicates the development optimization of oil and gas exploration and production projects, but methods have been devised to analyze uncertainty and its impact on optimal decision-making. This paper compares two methods for development optimization and uncertainty analysis: Monte Carlo (MC) simulation and stochastic programming. Two example problems for a gas field development and an oilfield development are solved and discussed to elaborate the advantages and disadvantages of each method. Development optimization involves decisions regarding the configuration of initial capital investment and subsequent operational decisions. Uncertainty analysis involves the quantification of the impact of uncertain parameters on the optimum designmore » concept. The gas field development problem is designed to highlight the differences in the implementation of the two methods and to show that both methods yield the exact same optimum design. The results show that both MC optimization and stochastic programming provide unique benefits, and that the choice of method depends on the goal of the analysis. While the MC method generates more useful information, along with the optimum design configuration, the stochastic programming method is more computationally efficient in determining the optimal solution. Reservoirs comprise multiple compartments and layers with multiphase flow of oil, water, and gas. We present a workflow for development optimization under uncertainty for these reservoirs, and solve an example on the design optimization of a multicompartment, multilayer oilfield development.« less

Optimal control of switching time in switched stochastic systems with multi-switching times and different costs

NASA Astrophysics Data System (ADS)

Liu, Xiaomei; Li, Shengtao; Zhang, Kanjian

2017-08-01

In this paper, we solve an optimal control problem for a class of time-invariant switched stochastic systems with multi-switching times, where the objective is to minimise a cost functional with different costs defined on the states. In particular, we focus on problems in which a pre-specified sequence of active subsystems is given and the switching times are the only control variables. Based on the calculus of variation, we derive the gradient of the cost functional with respect to the switching times on an especially simple form, which can be directly used in gradient descent algorithms to locate the optimal switching instants. Finally, a numerical example is given, highlighting the validity of the proposed methodology.

Stochastic Set-Based Particle Swarm Optimization Based on Local Exploration for Solving the Carpool Service Problem.

PubMed

Chou, Sheng-Kai; Jiau, Ming-Kai; Huang, Shih-Chia

2016-08-01

The growing ubiquity of vehicles has led to increased concerns about environmental issues. These concerns can be mitigated by implementing an effective carpool service. In an intelligent carpool system, an automated service process assists carpool participants in determining routes and matches. It is a discrete optimization problem that involves a system-wide condition as well as participants' expectations. In this paper, we solve the carpool service problem (CSP) to provide satisfactory ride matches. To this end, we developed a particle swarm carpool algorithm based on stochastic set-based particle swarm optimization (PSO). Our method introduces stochastic coding to augment traditional particles, and uses three terminologies to represent a particle: 1) particle position; 2) particle view; and 3) particle velocity. In this way, the set-based PSO (S-PSO) can be realized by local exploration. In the simulation and experiments, two kind of discrete PSOs-S-PSO and binary PSO (BPSO)-and a genetic algorithm (GA) are compared and examined using tested benchmarks that simulate a real-world metropolis. We observed that the S-PSO outperformed the BPSO and the GA thoroughly. Moreover, our method yielded the best result in a statistical test and successfully obtained numerical results for meeting the optimization objectives of the CSP.

Enhanced algorithms for stochastic programming

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krishna, Alamuru S.

1993-09-01

In this dissertation, we present some of the recent advances made in solving two-stage stochastic linear programming problems of large size and complexity. Decomposition and sampling are two fundamental components of techniques to solve stochastic optimization problems. We describe improvements to the current techniques in both these areas. We studied different ways of using importance sampling techniques in the context of Stochastic programming, by varying the choice of approximation functions used in this method. We have concluded that approximating the recourse function by a computationally inexpensive piecewise-linear function is highly efficient. This reduced the problem from finding the mean ofmore » a computationally expensive functions to finding that of a computationally inexpensive function. Then we implemented various variance reduction techniques to estimate the mean of a piecewise-linear function. This method achieved similar variance reductions in orders of magnitude less time than, when we directly applied variance-reduction techniques directly on the given problem. In solving a stochastic linear program, the expected value problem is usually solved before a stochastic solution and also to speed-up the algorithm by making use of the information obtained from the solution of the expected value problem. We have devised a new decomposition scheme to improve the convergence of this algorithm.« less

Horsetail matching: a flexible approach to optimization under uncertainty

NASA Astrophysics Data System (ADS)

Cook, L. W.; Jarrett, J. P.

2018-04-01

It is important to design engineering systems to be robust with respect to uncertainties in the design process. Often, this is done by considering statistical moments, but over-reliance on statistical moments when formulating a robust optimization can produce designs that are stochastically dominated by other feasible designs. This article instead proposes a formulation for optimization under uncertainty that minimizes the difference between a design's cumulative distribution function and a target. A standard target is proposed that produces stochastically non-dominated designs, but the formulation also offers enough flexibility to recover existing approaches for robust optimization. A numerical implementation is developed that employs kernels to give a differentiable objective function. The method is applied to algebraic test problems and a robust transonic airfoil design problem where it is compared to multi-objective, weighted-sum and density matching approaches to robust optimization; several advantages over these existing methods are demonstrated.

Kolkata Paise Restaurant Problem: An Introduction

NASA Astrophysics Data System (ADS)

Ghosh, Asim; Biswas, Soumyajyoti; Chatterjee, Arnab; Chakrabarti, Anindya Sundar; Naskar, Tapan; Mitra, Manipushpak; Chakrabarti, Bikas K.

We discuss several stochastic optimization strategies in games with many players having large number of choices (Kolkata Paise Restaurant Problem) and two choices (minority game problem). It is seen that a stochastic crowd avoiding strategy gives very efficient utilization in KPR problem. A slightly modified strategy in the minority game problem gives full utilization but the dynamics stops after reaching full efficiency, thereby making the utilization helpful for only about half of the population (those in minority). We further discuss the ways in which the dynamics may be continued and the utilization becomes effective for all the agents keeping fluctuation arbitrarily small.

A Framework for the Optimization of Discrete-Event Simulation Models

NASA Technical Reports Server (NTRS)

Joshi, B. D.; Unal, R.; White, N. H.; Morris, W. D.

1996-01-01

With the growing use of computer modeling and simulation, in all aspects of engineering, the scope of traditional optimization has to be extended to include simulation models. Some unique aspects have to be addressed while optimizing via stochastic simulation models. The optimization procedure has to explicitly account for the randomness inherent in the stochastic measures predicted by the model. This paper outlines a general purpose framework for optimization of terminating discrete-event simulation models. The methodology combines a chance constraint approach for problem formulation, together with standard statistical estimation and analyses techniques. The applicability of the optimization framework is illustrated by minimizing the operation and support resources of a launch vehicle, through a simulation model.

Optimal regulation in systems with stochastic time sampling

NASA Technical Reports Server (NTRS)

Montgomery, R. C.; Lee, P. S.

1980-01-01

An optimal control theory that accounts for stochastic variable time sampling in a distributed microprocessor based flight control system is presented. The theory is developed by using a linear process model for the airplane dynamics and the information distribution process is modeled as a variable time increment process where, at the time that information is supplied to the control effectors, the control effectors know the time of the next information update only in a stochastic sense. An optimal control problem is formulated and solved for the control law that minimizes the expected value of a quadratic cost function. The optimal cost obtained with a variable time increment Markov information update process where the control effectors know only the past information update intervals and the Markov transition mechanism is almost identical to that obtained with a known and uniform information update interval.

Optimization for Service Routes of Pallet Service Center Based on the Pallet Pool Mode

PubMed Central

He, Shiwei; Song, Rui

2016-01-01

Service routes optimization (SRO) of pallet service center should meet customers' demand firstly and then, through the reasonable method of lines organization, realize the shortest path of vehicle driving. The routes optimization of pallet service center is similar to the distribution problems of vehicle routing problem (VRP) and Chinese postman problem (CPP), but it has its own characteristics. Based on the relevant research results, the conditions of determining the number of vehicles, the one way of the route, the constraints of loading, and time windows are fully considered, and a chance constrained programming model with stochastic constraints is constructed taking the shortest path of all vehicles for a delivering (recycling) operation as an objective. For the characteristics of the model, a hybrid intelligent algorithm including stochastic simulation, neural network, and immune clonal algorithm is designed to solve the model. Finally, the validity and rationality of the optimization model and algorithm are verified by the case. PMID:27528865

Computationally efficient stochastic optimization using multiple realizations

NASA Astrophysics Data System (ADS)

Bayer, P.; Bürger, C. M.; Finkel, M.

2008-02-01

The presented study is concerned with computationally efficient methods for solving stochastic optimization problems involving multiple equally probable realizations of uncertain parameters. A new and straightforward technique is introduced that is based on dynamically ordering the stack of realizations during the search procedure. The rationale is that a small number of critical realizations govern the output of a reliability-based objective function. By utilizing a problem, which is typical to designing a water supply well field, several variants of this "stack ordering" approach are tested. The results are statistically assessed, in terms of optimality and nominal reliability. This study demonstrates that the simple ordering of a given number of 500 realizations while applying an evolutionary search algorithm can save about half of the model runs without compromising the optimization procedure. More advanced variants of stack ordering can, if properly configured, save up to more than 97% of the computational effort that would be required if the entire number of realizations were considered. The findings herein are promising for similar problems of water management and reliability-based design in general, and particularly for non-convex problems that require heuristic search techniques.

The ESPAT tool: a general-purpose DSS shell for solving stochastic optimization problems in complex river-aquifer systems

NASA Astrophysics Data System (ADS)

Macian-Sorribes, Hector; Pulido-Velazquez, Manuel; Tilmant, Amaury

2015-04-01

Stochastic programming methods are better suited to deal with the inherent uncertainty of inflow time series in water resource management. However, one of the most important hurdles in their use in practical implementations is the lack of generalized Decision Support System (DSS) shells, usually based on a deterministic approach. The purpose of this contribution is to present a general-purpose DSS shell, named Explicit Stochastic Programming Advanced Tool (ESPAT), able to build and solve stochastic programming problems for most water resource systems. It implements a hydro-economic approach, optimizing the total system benefits as the sum of the benefits obtained by each user. It has been coded using GAMS, and implements a Microsoft Excel interface with a GAMS-Excel link that allows the user to introduce the required data and recover the results. Therefore, no GAMS skills are required to run the program. The tool is divided into four modules according to its capabilities: 1) the ESPATR module, which performs stochastic optimization procedures in surface water systems using a Stochastic Dual Dynamic Programming (SDDP) approach; 2) the ESPAT_RA module, which optimizes coupled surface-groundwater systems using a modified SDDP approach; 3) the ESPAT_SDP module, capable of performing stochastic optimization procedures in small-size surface systems using a standard SDP approach; and 4) the ESPAT_DET module, which implements a deterministic programming procedure using non-linear programming, able to solve deterministic optimization problems in complex surface-groundwater river basins. The case study of the Mijares river basin (Spain) is used to illustrate the method. It consists in two reservoirs in series, one aquifer and four agricultural demand sites currently managed using historical (XIV century) rights, which give priority to the most traditional irrigation district over the XX century agricultural developments. Its size makes it possible to use either the SDP or the SDDP methods. The independent use of surface and groundwater can be examined with and without the aquifer. The ESPAT_DET, ESPATR and ESPAT_SDP modules were executed for the surface system, while the ESPAT_RA and the ESPAT_DET modules were run for the surface-groundwater system. The surface system's results show a similar performance between the ESPAT_SDP and ESPATR modules, with outperform the one showed by the current policies besides being outperformed by the ESPAT_DET results, which have the advantage of the perfect foresight. The surface-groundwater system's results show a robust situation in which the differences between the module's results and the current policies are lower due the use of pumped groundwater in the XX century crops when surface water is scarce. The results are realistic, with the deterministic optimization outperforming the stochastic one, which at the same time outperforms the current policies; showing that the tool is able to stochastically optimize river-aquifer water resources systems. We are currently working in the application of these tools in the analysis of changes in systems' operation under global change conditions. ACKNOWLEDGEMENT: This study has been partially supported by the IMPADAPT project (CGL2013-48424-C2-1-R) with Spanish MINECO (Ministerio de Economía y Competitividad) funds.

Investigation and appreciation of optimal output feedback. Volume 1: A convergent algorithm for the stochastic infinite-time discrete optimal output feedback problem

NASA Technical Reports Server (NTRS)

Halyo, N.; Broussard, J. R.

1984-01-01

The stochastic, infinite time, discrete output feedback problem for time invariant linear systems is examined. Two sets of sufficient conditions for the existence of a stable, globally optimal solution are presented. An expression for the total change in the cost function due to a change in the feedback gain is obtained. This expression is used to show that a sequence of gains can be obtained by an algorithm, so that the corresponding cost sequence is monotonically decreasing and the corresponding sequence of the cost gradient converges to zero. The algorithm is guaranteed to obtain a critical point of the cost function. The computational steps necessary to implement the algorithm on a computer are presented. The results are applied to a digital outer loop flight control problem. The numerical results for this 13th order problem indicate a rate of convergence considerably faster than two other algorithms used for comparison.

Dynamic, stochastic models for congestion pricing and congestion securities.

DOT National Transportation Integrated Search

2010-12-01

This research considers congestion pricing under demand uncertainty. In particular, a robust optimization (RO) approach is applied to optimal congestion pricing problems under user equilibrium. A mathematical model is developed and an analysis perfor...

Stochastic search in structural optimization - Genetic algorithms and simulated annealing

NASA Technical Reports Server (NTRS)

Hajela, Prabhat

1993-01-01

An account is given of illustrative applications of genetic algorithms and simulated annealing methods in structural optimization. The advantages of such stochastic search methods over traditional mathematical programming strategies are emphasized; it is noted that these methods offer a significantly higher probability of locating the global optimum in a multimodal design space. Both genetic-search and simulated annealing can be effectively used in problems with a mix of continuous, discrete, and integer design variables.

Asynchronous Incremental Stochastic Dual Descent Algorithm for Network Resource Allocation

NASA Astrophysics Data System (ADS)

Bedi, Amrit Singh; Rajawat, Ketan

2018-05-01

Stochastic network optimization problems entail finding resource allocation policies that are optimum on an average but must be designed in an online fashion. Such problems are ubiquitous in communication networks, where resources such as energy and bandwidth are divided among nodes to satisfy certain long-term objectives. This paper proposes an asynchronous incremental dual decent resource allocation algorithm that utilizes delayed stochastic {gradients} for carrying out its updates. The proposed algorithm is well-suited to heterogeneous networks as it allows the computationally-challenged or energy-starved nodes to, at times, postpone the updates. The asymptotic analysis of the proposed algorithm is carried out, establishing dual convergence under both, constant and diminishing step sizes. It is also shown that with constant step size, the proposed resource allocation policy is asymptotically near-optimal. An application involving multi-cell coordinated beamforming is detailed, demonstrating the usefulness of the proposed algorithm.

A shifted hyperbolic augmented Lagrangian-based artificial fish two-swarm algorithm with guaranteed convergence for constrained global optimization

NASA Astrophysics Data System (ADS)

Rocha, Ana Maria A. C.; Costa, M. Fernanda P.; Fernandes, Edite M. G. P.

2016-12-01

This article presents a shifted hyperbolic penalty function and proposes an augmented Lagrangian-based algorithm for non-convex constrained global optimization problems. Convergence to an ?-global minimizer is proved. At each iteration k, the algorithm requires the ?-global minimization of a bound constrained optimization subproblem, where ?. The subproblems are solved by a stochastic population-based metaheuristic that relies on the artificial fish swarm paradigm and a two-swarm strategy. To enhance the speed of convergence, the algorithm invokes the Nelder-Mead local search with a dynamically defined probability. Numerical experiments with benchmark functions and engineering design problems are presented. The results show that the proposed shifted hyperbolic augmented Lagrangian compares favorably with other deterministic and stochastic penalty-based methods.

Randomly Sampled-Data Control Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Han, Kuoruey

1990-01-01

The purpose is to solve the Linear Quadratic Regulator (LQR) problem with random time sampling. Such a sampling scheme may arise from imperfect instrumentation as in the case of sampling jitter. It can also model the stochastic information exchange among decentralized controllers to name just a few. A practical suboptimal controller is proposed with the nice property of mean square stability. The proposed controller is suboptimal in the sense that the control structure is limited to be linear. Because of i. i. d. assumption, this does not seem unreasonable. Once the control structure is fixed, the stochastic discrete optimal control problem is transformed into an equivalent deterministic optimal control problem with dynamics described by the matrix difference equation. The N-horizon control problem is solved using the Lagrange's multiplier method. The infinite horizon control problem is formulated as a classical minimization problem. Assuming existence of solution to the minimization problem, the total system is shown to be mean square stable under certain observability conditions. Computer simulations are performed to illustrate these conditions.

A Subspace Semi-Definite programming-based Underestimation (SSDU) method for stochastic global optimization in protein docking*

PubMed Central

Nan, Feng; Moghadasi, Mohammad; Vakili, Pirooz; Vajda, Sandor; Kozakov, Dima; Ch. Paschalidis, Ioannis

2015-01-01

We propose a new stochastic global optimization method targeting protein docking problems. The method is based on finding a general convex polynomial underestimator to the binding energy function in a permissive subspace that possesses a funnel-like structure. We use Principal Component Analysis (PCA) to determine such permissive subspaces. The problem of finding the general convex polynomial underestimator is reduced into the problem of ensuring that a certain polynomial is a Sum-of-Squares (SOS), which can be done via semi-definite programming. The underestimator is then used to bias sampling of the energy function in order to recover a deep minimum. We show that the proposed method significantly improves the quality of docked conformations compared to existing methods. PMID:25914440

Stochastic parameter estimation in nonlinear time-delayed vibratory systems with distributed delay

NASA Astrophysics Data System (ADS)

Torkamani, Shahab; Butcher, Eric A.

2013-07-01

The stochastic estimation of parameters and states in linear and nonlinear time-delayed vibratory systems with distributed delay is explored. The approach consists of first employing a continuous time approximation to approximate the delayed integro-differential system with a large set of ordinary differential equations having stochastic excitations. Then the problem of state and parameter estimation in the resulting stochastic ordinary differential system is represented as an optimal filtering problem using a state augmentation technique. By adapting the extended Kalman-Bucy filter to the augmented filtering problem, the unknown parameters of the time-delayed system are estimated from noise-corrupted, possibly incomplete measurements of the states. Similarly, the upper bound of the distributed delay can also be estimated by the proposed technique. As an illustrative example to a practical problem in vibrations, the parameter, delay upper bound, and state estimation from noise-corrupted measurements in a distributed force model widely used for modeling machine tool vibrations in the turning operation is investigated.

Inference of Stochastic Nonlinear Oscillators with Applications to Physiological Problems

NASA Technical Reports Server (NTRS)

Smelyanskiy, Vadim N.; Luchinsky, Dmitry G.

2004-01-01

A new method of inferencing of coupled stochastic nonlinear oscillators is described. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is robust in a broad range of dynamical models. We illustrate the main ideas of the technique by inferencing a model of five globally and locally coupled noisy oscillators. Specific modifications of the technique for inferencing hidden degrees of freedom of coupled nonlinear oscillators is discussed in the context of physiological applications.

A global stochastic programming approach for the optimal placement of gas detectors with nonuniform unavailabilities

DOE PAGES

Liu, Jianfeng; Laird, Carl Damon

2017-09-22

Optimal design of a gas detection systems is challenging because of the numerous sources of uncertainty, including weather and environmental conditions, leak location and characteristics, and process conditions. Rigorous CFD simulations of dispersion scenarios combined with stochastic programming techniques have been successfully applied to the problem of optimal gas detector placement; however, rigorous treatment of sensor failure and nonuniform unavailability has received less attention. To improve reliability of the design, this paper proposes a problem formulation that explicitly considers nonuniform unavailabilities and all backup detection levels. The resulting sensor placement problem is a large-scale mixed-integer nonlinear programming (MINLP) problem thatmore » requires a tailored solution approach for efficient solution. We have developed a multitree method which depends on iteratively solving a sequence of upper-bounding master problems and lower-bounding subproblems. The tailored global solution strategy is tested on a real data problem and the encouraging numerical results indicate that our solution framework is promising in solving sensor placement problems. This study was selected for the special issue in JLPPI from the 2016 International Symposium of the MKO Process Safety Center.« less

A global stochastic programming approach for the optimal placement of gas detectors with nonuniform unavailabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Jianfeng; Laird, Carl Damon

Optimal design of a gas detection systems is challenging because of the numerous sources of uncertainty, including weather and environmental conditions, leak location and characteristics, and process conditions. Rigorous CFD simulations of dispersion scenarios combined with stochastic programming techniques have been successfully applied to the problem of optimal gas detector placement; however, rigorous treatment of sensor failure and nonuniform unavailability has received less attention. To improve reliability of the design, this paper proposes a problem formulation that explicitly considers nonuniform unavailabilities and all backup detection levels. The resulting sensor placement problem is a large-scale mixed-integer nonlinear programming (MINLP) problem thatmore » requires a tailored solution approach for efficient solution. We have developed a multitree method which depends on iteratively solving a sequence of upper-bounding master problems and lower-bounding subproblems. The tailored global solution strategy is tested on a real data problem and the encouraging numerical results indicate that our solution framework is promising in solving sensor placement problems. This study was selected for the special issue in JLPPI from the 2016 International Symposium of the MKO Process Safety Center.« less

Low-complexity stochastic modeling of wall-bounded shear flows

NASA Astrophysics Data System (ADS)

Zare, Armin

Turbulent flows are ubiquitous in nature and they appear in many engineering applications. Transition to turbulence, in general, increases skin-friction drag in air/water vehicles compromising their fuel-efficiency and reduces the efficiency and longevity of wind turbines. While traditional flow control techniques combine physical intuition with costly experiments, their effectiveness can be significantly enhanced by control design based on low-complexity models and optimization. In this dissertation, we develop a theoretical and computational framework for the low-complexity stochastic modeling of wall-bounded shear flows. Part I of the dissertation is devoted to the development of a modeling framework which incorporates data-driven techniques to refine physics-based models. We consider the problem of completing partially known sample statistics in a way that is consistent with underlying stochastically driven linear dynamics. Neither the statistics nor the dynamics are precisely known. Thus, our objective is to reconcile the two in a parsimonious manner. To this end, we formulate optimization problems to identify the dynamics and directionality of input excitation in order to explain and complete available covariance data. For problem sizes that general-purpose solvers cannot handle, we develop customized optimization algorithms based on alternating direction methods. The solution to the optimization problem provides information about critical directions that have maximal effect in bringing model and statistics in agreement. In Part II, we employ our modeling framework to account for statistical signatures of turbulent channel flow using low-complexity stochastic dynamical models. We demonstrate that white-in-time stochastic forcing is not sufficient to explain turbulent flow statistics and develop models for colored-in-time forcing of the linearized Navier-Stokes equations. We also examine the efficacy of stochastically forced linearized NS equations and their parabolized equivalents in the receptivity analysis of velocity fluctuations to external sources of excitation as well as capturing the effect of the slowly-varying base flow on streamwise streaks and Tollmien-Schlichting waves. In Part III, we develop a model-based approach to design surface actuation of turbulent channel flow in the form of streamwise traveling waves. This approach is capable of identifying the drag reducing trends of traveling waves in a simulation-free manner. We also use the stochastically forced linearized NS equations to examine the Reynolds number independent effects of spanwise wall oscillations on drag reduction in turbulent channel flows. This allows us to extend the predictive capability of our simulation-free approach to high Reynolds numbers.

Stochastic control and the second law of thermodynamics

NASA Technical Reports Server (NTRS)

Brockett, R. W.; Willems, J. C.

1979-01-01

The second law of thermodynamics is studied from the point of view of stochastic control theory. We find that the feedback control laws which are of interest are those which depend only on average values, and not on sample path behavior. We are lead to a criterion which, when satisfied, permits one to assign a temperature to a stochastic system in such a way as to have Carnot cycles be the optimal trajectories of optimal control problems. Entropy is also defined and we are able to prove an equipartition of energy theorem using this definition of temperature. Our formulation allows one to treat irreversibility in a quite natural and completely precise way.

Optimal harvesting of a stochastic delay tri-trophic food-chain model with Lévy jumps

NASA Astrophysics Data System (ADS)

Qiu, Hong; Deng, Wenmin

2018-02-01

In this paper, the optimal harvesting of a stochastic delay tri-trophic food-chain model with Lévy jumps is considered. We introduce two kinds of environmental perturbations in this model. One is called white noise which is continuous and is described by a stochastic integral with respect to the standard Brownian motion. And the other one is jumping noise which is modeled by a Lévy process. Under some mild assumptions, the critical values between extinction and persistent in the mean of each species are established. The sufficient and necessary criteria for the existence of optimal harvesting policy are established and the optimal harvesting effort and the maximum of sustainable yield are also obtained. We utilize the ergodic method to discuss the optimal harvesting problem. The results show that white noises and Lévy noises significantly affect the optimal harvesting policy while time delays is harmless for the optimal harvesting strategy in some cases. At last, some numerical examples are introduced to show the validity of our results.

Multicriteria approaches for a private equity fund

NASA Astrophysics Data System (ADS)

Tammer, Christiane; Tannert, Johannes

2012-09-01

We develop a new model for a Private Equity Fund based on stochastic differential equations. In order to find efficient strategies for the fund manager we formulate a multicriteria optimization problem for a Private Equity Fund. Using the e-constraint method we solve this multicriteria optimization problem. Furthermore, a genetic algorithm is applied in order to get an approximation of the efficient frontier.

Event-triggered resilient filtering with stochastic uncertainties and successive packet dropouts via variance-constrained approach

NASA Astrophysics Data System (ADS)

Jia, Chaoqing; Hu, Jun; Chen, Dongyan; Liu, Yurong; Alsaadi, Fuad E.

2018-07-01

In this paper, we discuss the event-triggered resilient filtering problem for a class of time-varying systems subject to stochastic uncertainties and successive packet dropouts. The event-triggered mechanism is employed with hope to reduce the communication burden and save network resources. The stochastic uncertainties are considered to describe the modelling errors and the phenomenon of successive packet dropouts is characterized by a random variable obeying the Bernoulli distribution. The aim of the paper is to provide a resilient event-based filtering approach for addressed time-varying systems such that, for all stochastic uncertainties, successive packet dropouts and filter gain perturbation, an optimized upper bound of the filtering error covariance is obtained by designing the filter gain. Finally, simulations are provided to demonstrate the effectiveness of the proposed robust optimal filtering strategy.

Solving a Class of Stochastic Mixed-Integer Programs With Branch and Price

DTIC Science & Technology

2006-01-01

a two-dimensional knapsack problem, but for a given m, the objective value gi does not depend on the variance index v. This will be used in a final...optimization. Journal of Multicriteria Decision Analysis 11, 139–150 (2002) 29. Ford, L.R., Fulkerson, D.R.: A suggested computation for the maximal...for solution by a branch-and-price algorithm (B&P). We then survey a number of examples, and use a stochastic facility-location problem (SFLP) for a

Fast and Efficient Stochastic Optimization for Analytic Continuation

DOE PAGES

Bao, Feng; Zhang, Guannan; Webster, Clayton G; ...

2016-09-28

In this analytic continuation of imaginary-time quantum Monte Carlo data to extract real-frequency spectra remains a key problem in connecting theory with experiment. Here we present a fast and efficient stochastic optimization method (FESOM) as a more accessible variant of the stochastic optimization method introduced by Mishchenko et al. [Phys. Rev. B 62, 6317 (2000)], and we benchmark the resulting spectra with those obtained by the standard maximum entropy method for three representative test cases, including data taken from studies of the two-dimensional Hubbard model. Genearally, we find that our FESOM approach yields spectra similar to the maximum entropy results.more » In particular, while the maximum entropy method yields superior results when the quality of the data is strong, we find that FESOM is able to resolve fine structure with more detail when the quality of the data is poor. In addition, because of its stochastic nature, the method provides detailed information on the frequency-dependent uncertainty of the resulting spectra, while the maximum entropy method does so only for the spectral weight integrated over a finite frequency region. Therefore, we believe that this variant of the stochastic optimization approach provides a viable alternative to the routinely used maximum entropy method, especially for data of poor quality.« less

Better delivery/pick up routes in the presence of uncertainty.

DOT National Transportation Integrated Search

2007-08-01

We consider the Courier Delivery Problem, a variant of the Vehicle Routing Problem with : time windows in which customers appear probabilistically and their service times are uncertain. : We use scenario-based stochastic optimization with recourse fo...

Continuous-Time Public Good Contribution Under Uncertainty: A Stochastic Control Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ferrari, Giorgio, E-mail: giorgio.ferrari@uni-bielefeld.de; Riedel, Frank, E-mail: frank.riedel@uni-bielefeld.de; Steg, Jan-Henrik, E-mail: jsteg@uni-bielefeld.de

In this paper we study continuous-time stochastic control problems with both monotone and classical controls motivated by the so-called public good contribution problem. That is the problem of n economic agents aiming to maximize their expected utility allocating initial wealth over a given time period between private consumption and irreversible contributions to increase the level of some public good. We investigate the corresponding social planner problem and the case of strategic interaction between the agents, i.e. the public good contribution game. We show existence and uniqueness of the social planner’s optimal policy, we characterize it by necessary and sufficient stochasticmore » Kuhn–Tucker conditions and we provide its expression in terms of the unique optional solution of a stochastic backward equation. Similar stochastic first order conditions prove to be very useful for studying any Nash equilibria of the public good contribution game. In the symmetric case they allow us to prove (qualitative) uniqueness of the Nash equilibrium, which we again construct as the unique optional solution of a stochastic backward equation. We finally also provide a detailed analysis of the so-called free rider effect.« less

Numerical research of the optimal control problem in the semi-Markov inventory model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gorshenin, Andrey K.; Belousov, Vasily V.; Shnourkoff, Peter V.

2015-03-10

This paper is devoted to the numerical simulation of stochastic system for inventory management products using controlled semi-Markov process. The results of a special software for the system’s research and finding the optimal control are presented.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Malikopoulos, Andreas; Djouadi, Seddik M; Kuruganti, Teja

We consider the optimal stochastic control problem for home energy systems with solar and energy storage devices when the demand is realized from the grid. The demand is subject to Brownian motions with both drift and variance parameters modulated by a continuous-time Markov chain that represents the regime of electricity price. We model the systems as pure stochastic differential equation models, and then we follow the completing square technique to solve the stochastic home energy management problem. The effectiveness of the efficiency of the proposed approach is validated through a simulation example. For practical situations with constraints consistent to thosemore » studied here, our results imply the proposed framework could reduce the electricity cost from short-term purchase in peak hour market.« less

A stochastic discrete optimization model for designing container terminal facilities

NASA Astrophysics Data System (ADS)

Zukhruf, Febri; Frazila, Russ Bona; Burhani, Jzolanda Tsavalista

2017-11-01

As uncertainty essentially affect the total transportation cost, it remains important in the container terminal that incorporates several modes and transshipments process. This paper then presents a stochastic discrete optimization model for designing the container terminal, which involves the decision of facilities improvement action. The container terminal operation model is constructed by accounting the variation of demand and facilities performance. In addition, for illustrating the conflicting issue that practically raises in the terminal operation, the model also takes into account the possible increment delay of facilities due to the increasing number of equipment, especially the container truck. Those variations expectantly reflect the uncertainty issue in the container terminal operation. A Monte Carlo simulation is invoked to propagate the variations by following the observed distribution. The problem is constructed within the framework of the combinatorial optimization problem for investigating the optimal decision of facilities improvement. A new variant of glow-worm swarm optimization (GSO) is thus proposed for solving the optimization, which is rarely explored in the transportation field. The model applicability is tested by considering the actual characteristics of the container terminal.

Finite-Dimensional Representations for Controlled Diffusions with Delay

DOE Office of Scientific and Technical Information (OSTI.GOV)

Federico, Salvatore, E-mail: salvatore.federico@unimi.it; Tankov, Peter, E-mail: tankov@math.univ-paris-diderot.fr

2015-02-15

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which the solution of the SDDE and a linear path functional of it admit a finite-dimensional Markovian representation. As a second contribution, we show how approximate finite-dimensional Markovian representations may be constructed when these conditions are not satisfied, and provide an estimate of the error corresponding to these approximations. These results are applied to optimal control and optimal stopping problems for stochastic systems with delay.

Robust Path Planning and Feedback Design Under Stochastic Uncertainty

NASA Technical Reports Server (NTRS)

Blackmore, Lars

2008-01-01

Autonomous vehicles require optimal path planning algorithms to achieve mission goals while avoiding obstacles and being robust to uncertainties. The uncertainties arise from exogenous disturbances, modeling errors, and sensor noise, which can be characterized via stochastic models. Previous work defined a notion of robustness in a stochastic setting by using the concept of chance constraints. This requires that mission constraint violation can occur with a probability less than a prescribed value.In this paper we describe a novel method for optimal chance constrained path planning with feedback design. The approach optimizes both the reference trajectory to be followed and the feedback controller used to reject uncertainty. Our method extends recent results in constrained control synthesis based on convex optimization to solve control problems with nonconvex constraints. This extension is essential for path planning problems, which inherently have nonconvex obstacle avoidance constraints. Unlike previous approaches to chance constrained path planning, the new approach optimizes the feedback gain as wellas the reference trajectory.The key idea is to couple a fast, nonconvex solver that does not take into account uncertainty, with existing robust approaches that apply only to convex feasible regions. By alternating between robust and nonrobust solutions, the new algorithm guarantees convergence to a global optimum. We apply the new method to an unmanned aircraft and show simulation results that demonstrate the efficacy of the approach.

Optimal Budget Allocation for Sample Average Approximation

DTIC Science & Technology

2011-06-01

an optimization algorithm applied to the sample average problem. We examine the convergence rate of the estimator as the computing budget tends to...regime for the optimization algorithm . 1 Introduction Sample average approximation (SAA) is a frequently used approach to solving stochastic programs...appealing due to its simplicity and the fact that a large number of standard optimization algorithms are often available to optimize the resulting sample

Modeling and optimization of the multiobjective stochastic joint replenishment and delivery problem under supply chain environment.

PubMed

Wang, Lin; Qu, Hui; Liu, Shan; Dun, Cai-xia

2013-01-01

As a practical inventory and transportation problem, it is important to synthesize several objectives for the joint replenishment and delivery (JRD) decision. In this paper, a new multiobjective stochastic JRD (MSJRD) of the one-warehouse and n-retailer systems considering the balance of service level and total cost simultaneously is proposed. The goal of this problem is to decide the reasonable replenishment interval, safety stock factor, and traveling routing. Secondly, two approaches are designed to handle this complex multi-objective optimization problem. Linear programming (LP) approach converts the multi-objective to single objective, while a multi-objective evolution algorithm (MOEA) solves a multi-objective problem directly. Thirdly, three intelligent optimization algorithms, differential evolution algorithm (DE), hybrid DE (HDE), and genetic algorithm (GA), are utilized in LP-based and MOEA-based approaches. Results of the MSJRD with LP-based and MOEA-based approaches are compared by a contrastive numerical example. To analyses the nondominated solution of MOEA, a metric is also used to measure the distribution of the last generation solution. Results show that HDE outperforms DE and GA whenever LP or MOEA is adopted.

Modeling and Optimization of the Multiobjective Stochastic Joint Replenishment and Delivery Problem under Supply Chain Environment

PubMed Central

Dun, Cai-xia

2013-01-01

As a practical inventory and transportation problem, it is important to synthesize several objectives for the joint replenishment and delivery (JRD) decision. In this paper, a new multiobjective stochastic JRD (MSJRD) of the one-warehouse and n-retailer systems considering the balance of service level and total cost simultaneously is proposed. The goal of this problem is to decide the reasonable replenishment interval, safety stock factor, and traveling routing. Secondly, two approaches are designed to handle this complex multi-objective optimization problem. Linear programming (LP) approach converts the multi-objective to single objective, while a multi-objective evolution algorithm (MOEA) solves a multi-objective problem directly. Thirdly, three intelligent optimization algorithms, differential evolution algorithm (DE), hybrid DE (HDE), and genetic algorithm (GA), are utilized in LP-based and MOEA-based approaches. Results of the MSJRD with LP-based and MOEA-based approaches are compared by a contrastive numerical example. To analyses the nondominated solution of MOEA, a metric is also used to measure the distribution of the last generation solution. Results show that HDE outperforms DE and GA whenever LP or MOEA is adopted. PMID:24302880

PIPS-SBB: A Parallel Distributed-Memory Branch-and-Bound Algorithm for Stochastic Mixed-Integer Programs

DOE PAGES

Munguia, Lluis-Miquel; Oxberry, Geoffrey; Rajan, Deepak

2016-05-01

Stochastic mixed-integer programs (SMIPs) deal with optimization under uncertainty at many levels of the decision-making process. When solved as extensive formulation mixed- integer programs, problem instances can exceed available memory on a single workstation. In order to overcome this limitation, we present PIPS-SBB: a distributed-memory parallel stochastic MIP solver that takes advantage of parallelism at multiple levels of the optimization process. We also show promising results on the SIPLIB benchmark by combining methods known for accelerating Branch and Bound (B&B) methods with new ideas that leverage the structure of SMIPs. Finally, we expect the performance of PIPS-SBB to improve furthermore » as more functionality is added in the future.« less

Stochastic DG Placement for Conservation Voltage Reduction Based on Multiple Replications Procedure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Zhaoyu; Chen, Bokan; Wang, Jianhui

2015-06-01

Conservation voltage reduction (CVR) and distributed-generation (DG) integration are popular strategies implemented by utilities to improve energy efficiency. This paper investigates the interactions between CVR and DG placement to minimize load consumption in distribution networks, while keeping the lowest voltage level within the predefined range. The optimal placement of DG units is formulated as a stochastic optimization problem considering the uncertainty of DG outputs and load consumptions. A sample average approximation algorithm-based technique is developed to solve the formulated problem effectively. A multiple replications procedure is developed to test the stability of the solution and calculate the confidence interval ofmore » the gap between the candidate solution and optimal solution. The proposed method has been applied to the IEEE 37-bus distribution test system with different scenarios. The numerical results indicate that the implementations of CVR and DG, if combined, can achieve significant energy savings.« less

Novel Numerical Methods for Optimal Control Problems Involving Fractional-Order Differential Equations

DTIC Science & Technology

2018-03-14

pricing, Appl. Math . Comp. Vol.305, 174-187 (2017) 5. W. Li, S. Wang, Pricing European options with proportional transaction costs and stochastic...for fractional differential equation. Numer. Math . Theor. Methods Appl. 5, 229–241, 2012. [23] Kilbas A.A. and Marzan, S.A., Cauchy problem for...numerical technique for solving fractional optimal control problems, Comput. Math . Appl., 62, Issue 3, 1055–1067, 2011. [26] Lotfi A., Yousefi SA., Dehghan M

A framework for modeling and optimizing dynamic systems under uncertainty

DOE PAGES

Nicholson, Bethany; Siirola, John

2017-11-11

Algebraic modeling languages (AMLs) have drastically simplified the implementation of algebraic optimization problems. However, there are still many classes of optimization problems that are not easily represented in most AMLs. These classes of problems are typically reformulated before implementation, which requires significant effort and time from the modeler and obscures the original problem structure or context. In this work we demonstrate how the Pyomo AML can be used to represent complex optimization problems using high-level modeling constructs. We focus on the operation of dynamic systems under uncertainty and demonstrate the combination of Pyomo extensions for dynamic optimization and stochastic programming.more » We use a dynamic semibatch reactor model and a large-scale bubbling fluidized bed adsorber model as test cases.« less

A framework for modeling and optimizing dynamic systems under uncertainty

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nicholson, Bethany; Siirola, John

Algebraic modeling languages (AMLs) have drastically simplified the implementation of algebraic optimization problems. However, there are still many classes of optimization problems that are not easily represented in most AMLs. These classes of problems are typically reformulated before implementation, which requires significant effort and time from the modeler and obscures the original problem structure or context. In this work we demonstrate how the Pyomo AML can be used to represent complex optimization problems using high-level modeling constructs. We focus on the operation of dynamic systems under uncertainty and demonstrate the combination of Pyomo extensions for dynamic optimization and stochastic programming.more » We use a dynamic semibatch reactor model and a large-scale bubbling fluidized bed adsorber model as test cases.« less

A generic methodology for the optimisation of sewer systems using stochastic programming and self-optimizing control.

PubMed

Mauricio-Iglesias, Miguel; Montero-Castro, Ignacio; Mollerup, Ane L; Sin, Gürkan

2015-05-15

The design of sewer system control is a complex task given the large size of the sewer networks, the transient dynamics of the water flow and the stochastic nature of rainfall. This contribution presents a generic methodology for the design of a self-optimising controller in sewer systems. Such controller is aimed at keeping the system close to the optimal performance, thanks to an optimal selection of controlled variables. The definition of an optimal performance was carried out by a two-stage optimisation (stochastic and deterministic) to take into account both the overflow during the current rain event as well as the expected overflow given the probability of a future rain event. The methodology is successfully applied to design an optimising control strategy for a subcatchment area in Copenhagen. The results are promising and expected to contribute to the advance of the operation and control problem of sewer systems. Copyright © 2015 Elsevier Ltd. All rights reserved.

Using Stochastic Spiking Neural Networks on SpiNNaker to Solve Constraint Satisfaction Problems

PubMed Central

Fonseca Guerra, Gabriel A.; Furber, Steve B.

2017-01-01

Constraint satisfaction problems (CSP) are at the core of numerous scientific and technological applications. However, CSPs belong to the NP-complete complexity class, for which the existence (or not) of efficient algorithms remains a major unsolved question in computational complexity theory. In the face of this fundamental difficulty heuristics and approximation methods are used to approach instances of NP (e.g., decision and hard optimization problems). The human brain efficiently handles CSPs both in perception and behavior using spiking neural networks (SNNs), and recent studies have demonstrated that the noise embedded within an SNN can be used as a computational resource to solve CSPs. Here, we provide a software framework for the implementation of such noisy neural solvers on the SpiNNaker massively parallel neuromorphic hardware, further demonstrating their potential to implement a stochastic search that solves instances of P and NP problems expressed as CSPs. This facilitates the exploration of new optimization strategies and the understanding of the computational abilities of SNNs. We demonstrate the basic principles of the framework by solving difficult instances of the Sudoku puzzle and of the map color problem, and explore its application to spin glasses. The solver works as a stochastic dynamical system, which is attracted by the configuration that solves the CSP. The noise allows an optimal exploration of the space of configurations, looking for the satisfiability of all the constraints; if applied discontinuously, it can also force the system to leap to a new random configuration effectively causing a restart. PMID:29311791

Ordinal optimization and its application to complex deterministic problems

NASA Astrophysics Data System (ADS)

Yang, Mike Shang-Yu

1998-10-01

We present in this thesis a new perspective to approach a general class of optimization problems characterized by large deterministic complexities. Many problems of real-world concerns today lack analyzable structures and almost always involve high level of difficulties and complexities in the evaluation process. Advances in computer technology allow us to build computer models to simulate the evaluation process through numerical means, but the burden of high complexities remains to tax the simulation with an exorbitant computing cost for each evaluation. Such a resource requirement makes local fine-tuning of a known design difficult under most circumstances, let alone global optimization. Kolmogorov equivalence of complexity and randomness in computation theory is introduced to resolve this difficulty by converting the complex deterministic model to a stochastic pseudo-model composed of a simple deterministic component and a white-noise like stochastic term. The resulting randomness is then dealt with by a noise-robust approach called Ordinal Optimization. Ordinal Optimization utilizes Goal Softening and Ordinal Comparison to achieve an efficient and quantifiable selection of designs in the initial search process. The approach is substantiated by a case study in the turbine blade manufacturing process. The problem involves the optimization of the manufacturing process of the integrally bladed rotor in the turbine engines of U.S. Air Force fighter jets. The intertwining interactions among the material, thermomechanical, and geometrical changes makes the current FEM approach prohibitively uneconomical in the optimization process. The generalized OO approach to complex deterministic problems is applied here with great success. Empirical results indicate a saving of nearly 95% in the computing cost.

Continuous-time mean-variance portfolio selection with value-at-risk and no-shorting constraints

NASA Astrophysics Data System (ADS)

Yan, Wei

2012-01-01

An investment problem is considered with dynamic mean-variance(M-V) portfolio criterion under discontinuous prices which follow jump-diffusion processes according to the actual prices of stocks and the normality and stability of the financial market. The short-selling of stocks is prohibited in this mathematical model. Then, the corresponding stochastic Hamilton-Jacobi-Bellman(HJB) equation of the problem is presented and the solution of the stochastic HJB equation based on the theory of stochastic LQ control and viscosity solution is obtained. The efficient frontier and optimal strategies of the original dynamic M-V portfolio selection problem are also provided. And then, the effects on efficient frontier under the value-at-risk constraint are illustrated. Finally, an example illustrating the discontinuous prices based on M-V portfolio selection is presented.

Economic-Oriented Stochastic Optimization in Advanced Process Control of Chemical Processes

PubMed Central

Dobos, László; Király, András; Abonyi, János

2012-01-01

Finding the optimal operating region of chemical processes is an inevitable step toward improving economic performance. Usually the optimal operating region is situated close to process constraints related to product quality or process safety requirements. Higher profit can be realized only by assuring a relatively low frequency of violation of these constraints. A multilevel stochastic optimization framework is proposed to determine the optimal setpoint values of control loops with respect to predetermined risk levels, uncertainties, and costs of violation of process constraints. The proposed framework is realized as direct search-type optimization of Monte-Carlo simulation of the controlled process. The concept is illustrated throughout by a well-known benchmark problem related to the control of a linear dynamical system and the model predictive control of a more complex nonlinear polymerization process. PMID:23213298

Generating moment matching scenarios using optimization techniques

DOE PAGES

Mehrotra, Sanjay; Papp, Dávid

2013-05-16

An optimization based method is proposed to generate moment matching scenarios for numerical integration and its use in stochastic programming. The main advantage of the method is its flexibility: it can generate scenarios matching any prescribed set of moments of the underlying distribution rather than matching all moments up to a certain order, and the distribution can be defined over an arbitrary set. This allows for a reduction in the number of scenarios and allows the scenarios to be better tailored to the problem at hand. The method is based on a semi-infinite linear programming formulation of the problem thatmore » is shown to be solvable with polynomial iteration complexity. A practical column generation method is implemented. The column generation subproblems are polynomial optimization problems; however, they need not be solved to optimality. It is found that the columns in the column generation approach can be efficiently generated by random sampling. The number of scenarios generated matches a lower bound of Tchakaloff's. The rate of convergence of the approximation error is established for continuous integrands, and an improved bound is given for smooth integrands. Extensive numerical experiments are presented in which variants of the proposed method are compared to Monte Carlo and quasi-Monte Carlo methods on both numerical integration problems and stochastic optimization problems. The benefits of being able to match any prescribed set of moments, rather than all moments up to a certain order, is also demonstrated using optimization problems with 100-dimensional random vectors. Here, empirical results show that the proposed approach outperforms Monte Carlo and quasi-Monte Carlo based approaches on the tested problems.« less

Differential geometric methods in system theory.

NASA Technical Reports Server (NTRS)

Brockett, R. W.

1971-01-01

Discussion of certain problems in system theory which have been or might be solved using some basic concepts from differential geometry. The problems considered involve differential equations, controllability, optimal control, qualitative behavior, stochastic processes, and bilinear systems. The main goal is to extend the essentials of linear theory to some nonlinear classes of problems.

Machine learning for inverse lithography: using stochastic gradient descent for robust photomask synthesis

NASA Astrophysics Data System (ADS)

Jia, Ningning; Y Lam, Edmund

2010-04-01

Inverse lithography technology (ILT) synthesizes photomasks by solving an inverse imaging problem through optimization of an appropriate functional. Much effort on ILT is dedicated to deriving superior masks at a nominal process condition. However, the lower k1 factor causes the mask to be more sensitive to process variations. Robustness to major process variations, such as focus and dose variations, is desired. In this paper, we consider the focus variation as a stochastic variable, and treat the mask design as a machine learning problem. The stochastic gradient descent approach, which is a useful tool in machine learning, is adopted to train the mask design. Compared with previous work, simulation shows that the proposed algorithm is effective in producing robust masks.

Final Report---Optimization Under Nonconvexity and Uncertainty: Algorithms and Software

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jeff Linderoth

2011-11-06

the goal of this work was to develop new algorithmic techniques for solving large-scale numerical optimization problems, focusing on problems classes that have proven to be among the most challenging for practitioners: those involving uncertainty and those involving nonconvexity. This research advanced the state-of-the-art in solving mixed integer linear programs containing symmetry, mixed integer nonlinear programs, and stochastic optimization problems. The focus of the work done in the continuation was on Mixed Integer Nonlinear Programs (MINLP)s and Mixed Integer Linear Programs (MILP)s, especially those containing a great deal of symmetry.

Methods of sequential estimation for determining initial data in numerical weather prediction. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Cohn, S. E.

1982-01-01

Numerical weather prediction (NWP) is an initial-value problem for a system of nonlinear differential equations, in which initial values are known incompletely and inaccurately. Observational data available at the initial time must therefore be supplemented by data available prior to the initial time, a problem known as meteorological data assimilation. A further complication in NWP is that solutions of the governing equations evolve on two different time scales, a fast one and a slow one, whereas fast scale motions in the atmosphere are not reliably observed. This leads to the so called initialization problem: initial values must be constrained to result in a slowly evolving forecast. The theory of estimation of stochastic dynamic systems provides a natural approach to such problems. For linear stochastic dynamic models, the Kalman-Bucy (KB) sequential filter is the optimal data assimilation method, for linear models, the optimal combined data assimilation-initialization method is a modified version of the KB filter.

Guidance and Control strategies for aerospace vehicles

NASA Technical Reports Server (NTRS)

Hibey, J. L.; Naidu, D. S.; Charalambous, C. D.

1989-01-01

A neighboring optimal guidance scheme was devised for a nonlinear dynamic system with stochastic inputs and perfect measurements as applicable to fuel optimal control of an aeroassisted orbital transfer vehicle. For the deterministic nonlinear dynamic system describing the atmospheric maneuver, a nominal trajectory was determined. Then, a neighboring, optimal guidance scheme was obtained for open loop and closed loop control configurations. Taking modelling uncertainties into account, a linear, stochastic, neighboring optimal guidance scheme was devised. Finally, the optimal trajectory was approximated as the sum of the deterministic nominal trajectory and the stochastic neighboring optimal solution. Numerical results are presented for a typical vehicle. A fuel-optimal control problem in aeroassisted noncoplanar orbital transfer is also addressed. The equations of motion for the atmospheric maneuver are nonlinear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighboring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in reference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditions.

Pricing of swing options: A Monte Carlo simulation approach

NASA Astrophysics Data System (ADS)

Leow, Kai-Siong

We study the problem of pricing swing options, a class of multiple early exercise options that are traded in energy market, particularly in the electricity and natural gas markets. These contracts permit the option holder to periodically exercise the right to trade a variable amount of energy with a counterparty, subject to local volumetric constraints. In addition, the total amount of energy traded from settlement to expiration with the counterparty is restricted by a global volumetric constraint. Violation of this global volumetric constraint is allowed but would lead to penalty settled at expiration. The pricing problem is formulated as a stochastic optimal control problem in discrete time and state space. We present a stochastic dynamic programming algorithm which is based on piecewise linear concave approximation of value functions. This algorithm yields the value of the swing option under the assumption that the optimal exercise policy is applied by the option holder. We present a proof of an almost sure convergence that the algorithm generates the optimal exercise strategy as the number of iterations approaches to infinity. Finally, we provide a numerical example for pricing a natural gas swing call option.

A class of stochastic optimization problems with one quadratic & several linear objective functions and extended portfolio selection model

NASA Astrophysics Data System (ADS)

Xu, Jiuping; Li, Jun

2002-09-01

In this paper a class of stochastic multiple-objective programming problems with one quadratic, several linear objective functions and linear constraints has been introduced. The former model is transformed into a deterministic multiple-objective nonlinear programming model by means of the introduction of random variables' expectation. The reference direction approach is used to deal with linear objectives and results in a linear parametric optimization formula with a single linear objective function. This objective function is combined with the quadratic function using the weighted sums. The quadratic problem is transformed into a linear (parametric) complementary problem, the basic formula for the proposed approach. The sufficient and necessary conditions for (properly, weakly) efficient solutions and some construction characteristics of (weakly) efficient solution sets are obtained. An interactive algorithm is proposed based on reference direction and weighted sums. Varying the parameter vector on the right-hand side of the model, the DM can freely search the efficient frontier with the model. An extended portfolio selection model is formed when liquidity is considered as another objective to be optimized besides expectation and risk. The interactive approach is illustrated with a practical example.

Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pham, Huyên, E-mail: pham@math.univ-paris-diderot.fr; Wei, Xiaoli, E-mail: tyswxl@gmail.com

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.

Incorporating uncertainty and motion in Intensity Modulated Radiation Therapy treatment planning

NASA Astrophysics Data System (ADS)

Martin, Benjamin Charles

In radiation therapy, one seeks to destroy a tumor while minimizing the damage to surrounding healthy tissue. Intensity Modulated Radiation Therapy (IMRT) uses overlapping beams of x-rays that add up to a high dose within the target and a lower dose in the surrounding healthy tissue. IMRT relies on optimization techniques to create high quality treatments. Unfortunately, the possible conformality is limited by the need to ensure coverage even if there is organ movement or deformation. Currently, margins are added around the tumor to ensure coverage based on an assumed motion range. This approach does not ensure high quality treatments. In the standard IMRT optimization problem, an objective function measures the deviation of the dose from the clinical goals. The optimization then finds the beamlet intensities that minimize the objective function. When modeling uncertainty, the dose delivered from a given set of beamlet intensities is a random variable. Thus the objective function is also a random variable. In our stochastic formulation we minimize the expected value of this objective function. We developed a problem formulation that is both flexible and fast enough for use on real clinical cases. While working on accelerating the stochastic optimization, we developed a technique of voxel sampling. Voxel sampling is a randomized algorithms approach to a steepest descent problem based on estimating the gradient by only calculating the dose to a fraction of the voxels within the patient. When combined with an automatic sampling rate adaptation technique, voxel sampling produced an order of magnitude speed up in IMRT optimization. We also develop extensions of our results to Intensity Modulated Proton Therapy (IMPT). Due to the physics of proton beams the stochastic formulation yields visibly different and better plans than normal optimization. The results of our research have been incorporated into a software package OPT4D, which is an IMRT and IMPT optimization tool that we developed.

Online learning in optical tomography: a stochastic approach

NASA Astrophysics Data System (ADS)

Chen, Ke; Li, Qin; Liu, Jian-Guo

2018-07-01

We study the inverse problem of radiative transfer equation (RTE) using stochastic gradient descent method (SGD) in this paper. Mathematically, optical tomography amounts to recovering the optical parameters in RTE using the incoming–outgoing pair of light intensity. We formulate it as a PDE-constraint optimization problem, where the mismatch of computed and measured outgoing data is minimized with same initial data and RTE constraint. The memory and computation cost it requires, however, is typically prohibitive, especially in high dimensional space. Smart iterative solvers that only use partial information in each step is called for thereafter. Stochastic gradient descent method is an online learning algorithm that randomly selects data for minimizing the mismatch. It requires minimum memory and computation, and advances fast, therefore perfectly serves the purpose. In this paper we formulate the problem, in both nonlinear and its linearized setting, apply SGD algorithm and analyze the convergence performance.

Finite-time synchronization of stochastic coupled neural networks subject to Markovian switching and input saturation.

PubMed

Selvaraj, P; Sakthivel, R; Kwon, O M

2018-06-07

This paper addresses the problem of finite-time synchronization of stochastic coupled neural networks (SCNNs) subject to Markovian switching, mixed time delay, and actuator saturation. In addition, coupling strengths of the SCNNs are characterized by mutually independent random variables. By utilizing a simple linear transformation, the problem of stochastic finite-time synchronization of SCNNs is converted into a mean-square finite-time stabilization problem of an error system. By choosing a suitable mode dependent switched Lyapunov-Krasovskii functional, a new set of sufficient conditions is derived to guarantee the finite-time stability of the error system. Subsequently, with the help of anti-windup control scheme, the actuator saturation risks could be mitigated. Moreover, the derived conditions help to optimize estimation of the domain of attraction by enlarging the contractively invariant set. Furthermore, simulations are conducted to exhibit the efficiency of proposed control scheme. Copyright © 2018 Elsevier Ltd. All rights reserved.

Optimal Operation of Energy Storage in Power Transmission and Distribution

NASA Astrophysics Data System (ADS)

Akhavan Hejazi, Seyed Hossein

In this thesis, we investigate optimal operation of energy storage units in power transmission and distribution grids. At transmission level, we investigate the problem where an investor-owned independently-operated energy storage system seeks to offer energy and ancillary services in the day-ahead and real-time markets. We specifically consider the case where a significant portion of the power generated in the grid is from renewable energy resources and there exists significant uncertainty in system operation. In this regard, we formulate a stochastic programming framework to choose optimal energy and reserve bids for the storage units that takes into account the fluctuating nature of the market prices due to the randomness in the renewable power generation availability. At distribution level, we develop a comprehensive data set to model various stochastic factors on power distribution networks, with focus on networks that have high penetration of electric vehicle charging load and distributed renewable generation. Furthermore, we develop a data-driven stochastic model for energy storage operation at distribution level, where the distribution of nodal voltage and line power flow are modelled as stochastic functions of the energy storage unit's charge and discharge schedules. In particular, we develop new closed-form stochastic models for such key operational parameters in the system. Our approach is analytical and allows formulating tractable optimization problems. Yet, it does not involve any restricting assumption on the distribution of random parameters, hence, it results in accurate modeling of uncertainties. By considering the specific characteristics of random variables, such as their statistical dependencies and often irregularly-shaped probability distributions, we propose a non-parametric chance-constrained optimization approach to operate and plan energy storage units in power distribution girds. In the proposed stochastic optimization, we consider uncertainty from various elements, such as solar photovoltaic , electric vehicle chargers, and residential baseloads, in the form of discrete probability functions. In the last part of this thesis we address some other resources and concepts for enhancing the operation of power distribution and transmission systems. In particular, we proposed a new framework to determine the best sites, sizes, and optimal payment incentives under special contracts for committed-type DG projects to offset distribution network investment costs. In this framework, the aim is to allocate DGs such that the profit gained by the distribution company is maximized while each DG unit's individual profit is also taken into account to assure that private DG investment remains economical.

Energy Storage Sizing Taking Into Account Forecast Uncertainties and Receding Horizon Operation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baker, Kyri; Hug, Gabriela; Li, Xin

Energy storage systems (ESS) have the potential to be very beneficial for applications such as reducing the ramping of generators, peak shaving, and balancing not only the variability introduced by renewable energy sources, but also the uncertainty introduced by errors in their forecasts. Optimal usage of storage may result in reduced generation costs and an increased use of renewable energy. However, optimally sizing these devices is a challenging problem. This paper aims to provide the tools to optimally size an ESS under the assumption that it will be operated under a model predictive control scheme and that the forecast ofmore » the renewable energy resources include prediction errors. A two-stage stochastic model predictive control is formulated and solved, where the optimal usage of the storage is simultaneously determined along with the optimal generation outputs and size of the storage. Wind forecast errors are taken into account in the optimization problem via probabilistic constraints for which an analytical form is derived. This allows for the stochastic optimization problem to be solved directly, without using sampling-based approaches, and sizing the storage to account not only for a wide range of potential scenarios, but also for a wide range of potential forecast errors. In the proposed formulation, we account for the fact that errors in the forecast affect how the device is operated later in the horizon and that a receding horizon scheme is used in operation to optimally use the available storage.« less

Active stability augmentation of large space structures: A stochastic control problem

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1987-01-01

A problem in SCOLE is that of slewing an offset antenna on a long flexible beam-like truss attached to the space shuttle, with rather stringent pointing accuracy requirements. The relevant methodology aspects in robust feedback-control design for stability augmentation of the beam using on-board sensors is examined. It is framed as a stochastic control problem, boundary control of a distributed parameter system described by partial differential equations. While the framework is mathematical, the emphasis is still on an engineering solution. An abstract mathematical formulation is developed as a nonlinear wave equation in a Hilbert space. That the system is controllable is shown and a feedback control law that is robust in the sense that it does not require quantitative knowledge of system parameters is developed. The stochastic control problem that arises in instrumenting this law using appropriate sensors is treated. Using an engineering first approximation which is valid for small damping, formulas for optimal choice of the control gain are developed.

Constrained optimization via simulation models for new product innovation

NASA Astrophysics Data System (ADS)

Pujowidianto, Nugroho A.

2017-11-01

We consider the problem of constrained optimization where the decision makers aim to optimize the primary performance measure while constraining the secondary performance measures. This paper provides a brief overview of stochastically constrained optimization via discrete event simulation. Most review papers tend to be methodology-based. This review attempts to be problem-based as decision makers may have already decided on the problem formulation. We consider constrained optimization models as there are usually constraints on secondary performance measures as trade-off in new product development. It starts by laying out different possible methods and the reasons using constrained optimization via simulation models. It is then followed by the review of different simulation optimization approach to address constrained optimization depending on the number of decision variables, the type of constraints, and the risk preferences of the decision makers in handling uncertainties.

Optimization under variability and uncertainty: a case study for NOx emissions control for a gasification system.

PubMed

Chen, Jianjun; Frey, H Christopher

2004-12-15

Methods for optimization of process technologies considering the distinction between variability and uncertainty are developed and applied to case studies of NOx control for Integrated Gasification Combined Cycle systems. Existing methods of stochastic optimization (SO) and stochastic programming (SP) are demonstrated. A comparison of SO and SP results provides the value of collecting additional information to reduce uncertainty. For example, an expected annual benefit of 240,000 dollars is estimated if uncertainty can be reduced before a final design is chosen. SO and SP are typically applied to uncertainty. However, when applied to variability, the benefit of dynamic process control is obtained. For example, an annual savings of 1 million dollars could be achieved if the system is adjusted to changes in process conditions. When variability and uncertainty are treated distinctively, a coupled stochastic optimization and programming method and a two-dimensional stochastic programming method are demonstrated via a case study. For the case study, the mean annual benefit of dynamic process control is estimated to be 700,000 dollars, with a 95% confidence range of 500,000 dollars to 940,000 dollars. These methods are expected to be of greatest utility for problems involving a large commitment of resources, for which small differences in designs can produce large cost savings.

Mean-variance portfolio selection for defined-contribution pension funds with stochastic salary.

PubMed

Zhang, Chubing

2014-01-01

This paper focuses on a continuous-time dynamic mean-variance portfolio selection problem of defined-contribution pension funds with stochastic salary, whose risk comes from both financial market and nonfinancial market. By constructing a special Riccati equation as a continuous (actually a viscosity) solution to the HJB equation, we obtain an explicit closed form solution for the optimal investment portfolio as well as the efficient frontier.

Exploration of the Maximum Entropy/Optimal Projection Approach to Control Design Synthesis for Large Space Structures.

DTIC Science & Technology

1985-02-01

Energy Analysis , a branch of dynamic modal analysis developed for analyzing acoustic vibration problems, its present stage of development embodies a...Maximum Entropy Stochastic Modelling and Reduced-Order Design Synthesis is a rigorous new approach to this class of problems. Inspired by Statistical

Chance-Constrained Guidance With Non-Convex Constraints

NASA Technical Reports Server (NTRS)

Ono, Masahiro

2011-01-01

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

Stochastic search, optimization and regression with energy applications

NASA Astrophysics Data System (ADS)

Hannah, Lauren A.

Designing clean energy systems will be an important task over the next few decades. One of the major roadblocks is a lack of mathematical tools to economically evaluate those energy systems. However, solutions to these mathematical problems are also of interest to the operations research and statistical communities in general. This thesis studies three problems that are of interest to the energy community itself or provide support for solution methods: R&D portfolio optimization, nonparametric regression and stochastic search with an observable state variable. First, we consider the one stage R&D portfolio optimization problem to avoid the sequential decision process associated with the multi-stage. The one stage problem is still difficult because of a non-convex, combinatorial decision space and a non-convex objective function. We propose a heuristic solution method that uses marginal project values---which depend on the selected portfolio---to create a linear objective function. In conjunction with the 0-1 decision space, this new problem can be solved as a knapsack linear program. This method scales well to large decision spaces. We also propose an alternate, provably convergent algorithm that does not exploit problem structure. These methods are compared on a solid oxide fuel cell R&D portfolio problem. Next, we propose Dirichlet Process mixtures of Generalized Linear Models (DPGLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We prove conditions for the asymptotic unbiasedness of the DP-GLM regression mean function estimate. We also give examples for when those conditions hold, including models for compactly supported continuous distributions and a model with continuous covariates and categorical response. We empirically analyze the properties of the DP-GLM and why it provides better results than existing Dirichlet process mixture regression models. We evaluate DP-GLM on several data sets, comparing it to modern methods of nonparametric regression like CART, Bayesian trees and Gaussian processes. Compared to existing techniques, the DP-GLM provides a single model (and corresponding inference algorithms) that performs well in many regression settings. Finally, we study convex stochastic search problems where a noisy objective function value is observed after a decision is made. There are many stochastic search problems whose behavior depends on an exogenous state variable which affects the shape of the objective function. Currently, there is no general purpose algorithm to solve this class of problems. We use nonparametric density estimation to take observations from the joint state-outcome distribution and use them to infer the optimal decision for a given query state. We propose two solution methods that depend on the problem characteristics: function-based and gradient-based optimization. We examine two weighting schemes, kernel-based weights and Dirichlet process-based weights, for use with the solution methods. The weights and solution methods are tested on a synthetic multi-product newsvendor problem and the hour-ahead wind commitment problem. Our results show that in some cases Dirichlet process weights offer substantial benefits over kernel based weights and more generally that nonparametric estimation methods provide good solutions to otherwise intractable problems.

Application of Monte Carlo techniques to optimization of high-energy beam transport in a stochastic environment

NASA Technical Reports Server (NTRS)

Parrish, R. V.; Dieudonne, J. E.; Filippas, T. A.

1971-01-01

An algorithm employing a modified sequential random perturbation, or creeping random search, was applied to the problem of optimizing the parameters of a high-energy beam transport system. The stochastic solution of the mathematical model for first-order magnetic-field expansion allows the inclusion of state-variable constraints, and the inclusion of parameter constraints allowed by the method of algorithm application eliminates the possibility of infeasible solutions. The mathematical model and the algorithm were programmed for a real-time simulation facility; thus, two important features are provided to the beam designer: (1) a strong degree of man-machine communication (even to the extent of bypassing the algorithm and applying analog-matching techniques), and (2) extensive graphics for displaying information concerning both algorithm operation and transport-system behavior. Chromatic aberration was also included in the mathematical model and in the optimization process. Results presented show this method as yielding better solutions (in terms of resolutions) to the particular problem than those of a standard analog program as well as demonstrating flexibility, in terms of elements, constraints, and chromatic aberration, allowed by user interaction with both the algorithm and the stochastic model. Example of slit usage and a limited comparison of predicted results and actual results obtained with a 600 MeV cyclotron are given.

Multi-criteria multi-stakeholder decision analysis using a fuzzy-stochastic approach for hydrosystem management

NASA Astrophysics Data System (ADS)

Subagadis, Y. H.; Schütze, N.; Grundmann, J.

2014-09-01

The conventional methods used to solve multi-criteria multi-stakeholder problems are less strongly formulated, as they normally incorporate only homogeneous information at a time and suggest aggregating objectives of different decision-makers avoiding water-society interactions. In this contribution, Multi-Criteria Group Decision Analysis (MCGDA) using a fuzzy-stochastic approach has been proposed to rank a set of alternatives in water management decisions incorporating heterogeneous information under uncertainty. The decision making framework takes hydrologically, environmentally, and socio-economically motivated conflicting objectives into consideration. The criteria related to the performance of the physical system are optimized using multi-criteria simulation-based optimization, and fuzzy linguistic quantifiers have been used to evaluate subjective criteria and to assess stakeholders' degree of optimism. The proposed methodology is applied to find effective and robust intervention strategies for the management of a coastal hydrosystem affected by saltwater intrusion due to excessive groundwater extraction for irrigated agriculture and municipal use. Preliminary results show that the MCGDA based on a fuzzy-stochastic approach gives useful support for robust decision-making and is sensitive to the decision makers' degree of optimism.

Doubly stochastic radial basis function methods

NASA Astrophysics Data System (ADS)

Yang, Fenglian; Yan, Liang; Ling, Leevan

2018-06-01

We propose a doubly stochastic radial basis function (DSRBF) method for function recoveries. Instead of a constant, we treat the RBF shape parameters as stochastic variables whose distribution were determined by a stochastic leave-one-out cross validation (LOOCV) estimation. A careful operation count is provided in order to determine the ranges of all the parameters in our methods. The overhead cost for setting up the proposed DSRBF method is O (n2) for function recovery problems with n basis. Numerical experiments confirm that the proposed method not only outperforms constant shape parameter formulation (in terms of accuracy with comparable computational cost) but also the optimal LOOCV formulation (in terms of both accuracy and computational cost).

Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Han Yuecai; Hu Yaozhong; Song Jian, E-mail: jsong2@math.rutgers.edu

2013-04-15

We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter H>1/2). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential equation driven by both fractional Brownian motions and the corresponding underlying standard Brownian motions. In addition to this backward equation, the maximum principle also involves the Malliavin derivatives. Our approach is to use conditioning and Malliavin calculus. To arrive at our maximum principle we need tomore » develop some new results of stochastic analysis of the controlled systems driven by fractional Brownian motions via fractional calculus. Our approach of conditioning and Malliavin calculus is also applied to classical system driven by standard Brownian motions while the controller has only partial information. As a straightforward consequence, the classical maximum principle is also deduced in this more natural and simpler way.« less

Optimal route discovery for soft QOS provisioning in mobile ad hoc multimedia networks

NASA Astrophysics Data System (ADS)

Huang, Lei; Pan, Feng

2007-09-01

In this paper, we propose an optimal routing discovery algorithm for ad hoc multimedia networks whose resource keeps changing, First, we use stochastic models to measure the network resource availability, based on the information about the location and moving pattern of the nodes, as well as the link conditions between neighboring nodes. Then, for a certain multimedia packet flow to be transmitted from a source to a destination, we formulate the optimal soft-QoS provisioning problem as to find the best route that maximize the probability of satisfying its desired QoS requirements in terms of the maximum delay constraints. Based on the stochastic network resource model, we developed three approaches to solve the formulated problem: A centralized approach serving as the theoretical reference, a distributed approach that is more suitable to practical real-time deployment, and a distributed dynamic approach that utilizes the updated time information to optimize the routing for each individual packet. Examples of numerical results demonstrated that using the route discovered by our distributed algorithm in a changing network environment, multimedia applications could achieve better QoS statistically.

Stochastic correlative firing for figure-ground segregation.

PubMed

Chen, Zhe

2005-03-01

Segregation of sensory inputs into separate objects is a central aspect of perception and arises in all sensory modalities. The figure-ground segregation problem requires identifying an object of interest in a complex scene, in many cases given binaural auditory or binocular visual observations. The computations required for visual and auditory figure-ground segregation share many common features and can be cast within a unified framework. Sensory perception can be viewed as a problem of optimizing information transmission. Here we suggest a stochastic correlative firing mechanism and an associative learning rule for figure-ground segregation in several classic sensory perception tasks, including the cocktail party problem in binaural hearing, binocular fusion of stereo images, and Gestalt grouping in motion perception.

Algorithms for output feedback, multiple-model, and decentralized control problems

NASA Technical Reports Server (NTRS)

Halyo, N.; Broussard, J. R.

1984-01-01

The optimal stochastic output feedback, multiple-model, and decentralized control problems with dynamic compensation are formulated and discussed. Algorithms for each problem are presented, and their relationship to a basic output feedback algorithm is discussed. An aircraft control design problem is posed as a combined decentralized, multiple-model, output feedback problem. A control design is obtained using the combined algorithm. An analysis of the design is presented.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buckdahn, Rainer, E-mail: Rainer.Buckdahn@univ-brest.fr; Li, Juan, E-mail: juanli@sdu.edu.cn; Ma, Jin, E-mail: jinma@usc.edu

In this paper we study the optimal control problem for a class of general mean-field stochastic differential equations, in which the coefficients depend, nonlinearly, on both the state process as well as of its law. In particular, we assume that the control set is a general open set that is not necessary convex, and the coefficients are only continuous on the control variable without any further regularity or convexity. We validate the approach of Peng (SIAM J Control Optim 2(4):966–979, 1990) by considering the second order variational equations and the corresponding second order adjoint process in this setting, and wemore » extend the Stochastic Maximum Principle of Buckdahn et al. (Appl Math Optim 64(2):197–216, 2011) to this general case.« less

Extremal Optimization: Methods Derived from Co-Evolution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boettcher, S.; Percus, A.G.

1999-07-13

We describe a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organized critical models of co-evolution such as the Bak-Sneppen model. The method, called Extremal Optimization, successively eliminates extremely undesirable components of sub-optimal solutions, rather than ''breeding'' better components. In contrast to Genetic Algorithms which operate on an entire ''gene-pool'' of possible solutions, Extremal Optimization improves on a single candidate solution by treating each of its components as species co-evolving according to Darwinian principles. Unlike Simulated Annealing, its non-equilibrium approach effects an algorithm requiring few parameters to tune. With only one adjustable parameter, its performance provesmore » competitive with, and often superior to, more elaborate stochastic optimization procedures. We demonstrate it here on two classic hard optimization problems: graph partitioning and the traveling salesman problem.« less

A Semi-linear Backward Parabolic Cauchy Problem with Unbounded Coefficients of Hamilton–Jacobi–Bellman Type and Applications to Optimal Control

DOE Office of Scientific and Technical Information (OSTI.GOV)

Addona, Davide, E-mail: d.addona@campus.unimib.it

2015-08-15

We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a semi-linear backward parabolic Cauchy problem, where the differential equation is the Hamilton–Jacobi–Bellman equation of a suitable optimal control problem. Via backward stochastic differential equations, we show that the mild solution is indeed the value function of the controlled equation and that the feedback law is verified.

Joint pricing, inventory, and preservation decisions for deteriorating items with stochastic demand and promotional efforts

NASA Astrophysics Data System (ADS)

Soni, Hardik N.; Chauhan, Ashaba D.

2018-03-01

This study models a joint pricing, inventory, and preservation decision-making problem for deteriorating items subject to stochastic demand and promotional effort. The generalized price-dependent stochastic demand, time proportional deterioration, and partial backlogging rates are used to model the inventory system. The objective is to find the optimal pricing, replenishment, and preservation technology investment strategies while maximizing the total profit per unit time. Based on the partial backlogging and lost sale cases, we first deduce the criterion for optimal replenishment schedules for any given price and technology investment cost. Second, we show that, respectively, total profit per time unit is concave function of price and preservation technology cost. At the end, some numerical examples and the results of a sensitivity analysis are used to illustrate the features of the proposed model.

Stochastic scheduling on a repairable manufacturing system

NASA Astrophysics Data System (ADS)

Li, Wei; Cao, Jinhua

1995-08-01

In this paper, we consider some stochastic scheduling problems with a set of stochastic jobs on a manufacturing system with a single machine that is subject to multiple breakdowns and repairs. When the machine processing a job fails, the job processing must restart some time later when the machine is repaired. For this typical manufacturing system, we find the optimal policies that minimize the following objective functions: (1) the weighed sum of the completion times; (2) the weighed number of late jobs having constant due dates; (3) the weighted number of late jobs having random due dates exponentially distributed, which generalize some previous results.

Periodic Application of Stochastic Cost Optimization Methodology to Achieve Remediation Objectives with Minimized Life Cycle Cost

NASA Astrophysics Data System (ADS)

Kim, U.; Parker, J.

2016-12-01

Many dense non-aqueous phase liquid (DNAPL) contaminated sites in the U.S. are reported as "remediation in progress" (RIP). However, the cost to complete (CTC) remediation at these sites is highly uncertain and in many cases, the current remediation plan may need to be modified or replaced to achieve remediation objectives. This study evaluates the effectiveness of iterative stochastic cost optimization that incorporates new field data for periodic parameter recalibration to incrementally reduce prediction uncertainty and implement remediation design modifications as needed to minimize the life cycle cost (i.e., CTC). This systematic approach, using the Stochastic Cost Optimization Toolkit (SCOToolkit), enables early identification and correction of problems to stay on track for completion while minimizing the expected (i.e., probability-weighted average) CTC. This study considers a hypothetical site involving multiple DNAPL sources in an unconfined aquifer using thermal treatment for source reduction and electron donor injection for dissolved plume control. The initial design is based on stochastic optimization using model parameters and their joint uncertainty based on calibration to site characterization data. The model is periodically recalibrated using new monitoring data and performance data for the operating remediation systems. Projected future performance using the current remediation plan is assessed and reoptimization of operational variables for the current system or consideration of alternative designs are considered depending on the assessment results. We compare remediation duration and cost for the stepwise re-optimization approach with single stage optimization as well as with a non-optimized design based on typical engineering practice.

Flexible Demand Management under Time-Varying Prices

NASA Astrophysics Data System (ADS)

Liang, Yong

In this dissertation, the problem of flexible demand management under time-varying prices is studied. This generic problem has many applications, which usually have multiple periods in which decisions on satisfying demand need to be made, and prices in these periods are time-varying. Examples of such applications include multi-period procurement problem, operating room scheduling, and user-end demand scheduling in the Smart Grid, where the last application is used as the main motivating story throughout the dissertation. The current grid is experiencing an upgrade with lots of new designs. What is of particular interest is the idea of passing time-varying prices that reflect electricity market conditions to end users as incentives for load shifting. One key component, consequently, is the demand management system at the user-end. The objective of the system is to find the optimal trade-off between cost saving and discomfort increment resulted from load shifting. In this dissertation, we approach this problem from the following aspects: (1) construct a generic model, solve for Pareto optimal solutions, and analyze the robust solution that optimizes the worst-case payoffs, (2) extend to a distribution-free model for multiple types of demand (appliances), for which an approximate dynamic programming (ADP) approach is developed, and (3) design other efficient algorithms for practical purposes of the flexible demand management system. We first construct a novel multi-objective flexible demand management model, in which there are a finite number of periods with time-varying prices, and demand arrives in each period. In each period, the decision maker chooses to either satisfy or defer outstanding demand to minimize costs and discomfort over a certain number of periods. We consider both the deterministic model, models with stochastic demand or prices, and when only partial information about the stochastic demand or prices is known. We first analyze the stochastic optimization problem when the objective is to minimize the expected total cost and discomfort, then since the decision maker is likely to be risk-averse, and she wants to protect herself from price spikes, we study the robust optimization problem to address the risk-aversion of the decision maker. We conduct numerical studies to evaluate the price of robustness. Next, we present a detailed model that manages multiple types of flexible demand in the absence of knowledge regarding the distributions of related stochastic processes. Specifically, we consider the case in which time-varying prices with general structures are offered to users, and an energy management system for each household makes optimal energy usage, storage, and trading decisions according to the preferences of users. Because of the uncertainties associated with electricity prices, local generation, and the arrival processes of demand, we formulate a stochastic dynamic programming model, and outline a novel and tractable ADP approach to overcome the curses of dimensionality. Then, we perform numerical studies, whose results demonstrate the effectiveness of the ADP approach. At last, we propose another approximation approach based on Q-learning. In addition, we also develop another decentralization-based heuristic. Both the Q-learning approach and the heuristic make necessary assumptions on the knowledge of information, and each of them has unique advantages. We conduct numerical studies on a testing problem. The simulation results show that both the Q-learning and the decentralization based heuristic approaches work well. Lastly, we conclude the paper with some discussions on future extension directions.

Removing Barriers for Effective Deployment of Intermittent Renewable Generation

NASA Astrophysics Data System (ADS)

Arabali, Amirsaman

The stochastic nature of intermittent renewable resources is the main barrier to effective integration of renewable generation. This problem can be studied from feeder-scale and grid-scale perspectives. Two new stochastic methods are proposed to meet the feeder-scale controllable load with a hybrid renewable generation (including wind and PV) and energy storage system. For the first method, an optimization problem is developed whose objective function is the cost of the hybrid system including the cost of renewable generation and storage subject to constraints on energy storage and shifted load. A smart-grid strategy is developed to shift the load and match the renewable energy generation and controllable load. Minimizing the cost function guarantees minimum PV and wind generation installation, as well as storage capacity selection for supplying the controllable load. A confidence coefficient is allocated to each stochastic constraint which shows to what degree the constraint is satisfied. In the second method, a stochastic framework is developed for optimal sizing and reliability analysis of a hybrid power system including renewable resources (PV and wind) and energy storage system. The hybrid power system is optimally sized to satisfy the controllable load with a specified reliability level. A load-shifting strategy is added to provide more flexibility for the system and decrease the installation cost. Load shifting strategies and their potential impacts on the hybrid system reliability/cost analysis are evaluated trough different scenarios. Using a compromise-solution method, the best compromise between the reliability and cost will be realized for the hybrid system. For the second problem, a grid-scale stochastic framework is developed to examine the storage application and its optimal placement for the social cost and transmission congestion relief of wind integration. Storage systems are optimally placed and adequately sized to minimize the sum of operation and congestion costs over a scheduling period. A technical assessment framework is developed to enhance the efficiency of wind integration and evaluate the economics of storage technologies and conventional gas-fired alternatives. The proposed method is used to carry out a cost-benefit analysis for the IEEE 24-bus system and determine the most economical technology. In order to mitigate the financial and technical concerns of renewable energy integration into the power system, a stochastic framework is proposed for transmission grid reinforcement studies in a power system with wind generation. A multi-stage multi-objective transmission network expansion planning (TNEP) methodology is developed which considers the investment cost, absorption of private investment and reliability of the system as the objective functions. A Non-dominated Sorting Genetic Algorithm (NSGA II) optimization approach is used in combination with a probabilistic optimal power flow (POPF) to determine the Pareto optimal solutions considering the power system uncertainties. Using a compromise-solution method, the best final plan is then realized based on the decision maker preferences. The proposed methodology is applied to the IEEE 24-bus Reliability Tests System (RTS) to evaluate the feasibility and practicality of the developed planning strategy.

Stochastic noncooperative and cooperative evolutionary game strategies of a population of biological networks under natural selection.

PubMed

Chen, Bor-Sen; Yeh, Chin-Hsun

2017-12-01

We review current static and dynamic evolutionary game strategies of biological networks and discuss the lack of random genetic variations and stochastic environmental disturbances in these models. To include these factors, a population of evolving biological networks is modeled as a nonlinear stochastic biological system with Poisson-driven genetic variations and random environmental fluctuations (stimuli). To gain insight into the evolutionary game theory of stochastic biological networks under natural selection, the phenotypic robustness and network evolvability of noncooperative and cooperative evolutionary game strategies are discussed from a stochastic Nash game perspective. The noncooperative strategy can be transformed into an equivalent multi-objective optimization problem and is shown to display significantly improved network robustness to tolerate genetic variations and buffer environmental disturbances, maintaining phenotypic traits for longer than the cooperative strategy. However, the noncooperative case requires greater effort and more compromises between partly conflicting players. Global linearization is used to simplify the problem of solving nonlinear stochastic evolutionary games. Finally, a simple stochastic evolutionary model of a metabolic pathway is simulated to illustrate the procedure of solving for two evolutionary game strategies and to confirm and compare their respective characteristics in the evolutionary process. Copyright © 2017 Elsevier B.V. All rights reserved.

A method for minimum risk portfolio optimization under hybrid uncertainty

NASA Astrophysics Data System (ADS)

Egorova, Yu E.; Yazenin, A. V.

2018-03-01

In this paper, we investigate a minimum risk portfolio model under hybrid uncertainty when the profitability of financial assets is described by fuzzy random variables. According to Feng, the variance of a portfolio is defined as a crisp value. To aggregate fuzzy information the weakest (drastic) t-norm is used. We construct an equivalent stochastic problem of the minimum risk portfolio model and specify the stochastic penalty method for solving it.

Mean-Variance Portfolio Selection for Defined-Contribution Pension Funds with Stochastic Salary

PubMed Central

Zhang, Chubing

2014-01-01

This paper focuses on a continuous-time dynamic mean-variance portfolio selection problem of defined-contribution pension funds with stochastic salary, whose risk comes from both financial market and nonfinancial market. By constructing a special Riccati equation as a continuous (actually a viscosity) solution to the HJB equation, we obtain an explicit closed form solution for the optimal investment portfolio as well as the efficient frontier. PMID:24782667

Planning with Continuous Resources in Stochastic Domains

NASA Technical Reports Server (NTRS)

Mausam, Mausau; Benazera, Emmanuel; Brafman, Roneu; Hansen, Eric

2005-01-01

We consider the problem of optimal planning in stochastic domains with metric resource constraints. Our goal is to generate a policy whose expected sum of rewards is maximized for a given initial state. We consider a general formulation motivated by our application domain--planetary exploration--in which the choice of an action at each step may depend on the current resource levels. We adapt the forward search algorithm AO* to handle our continuous state space efficiently.

Understanding Innovation Engines: Automated Creativity and Improved Stochastic Optimization via Deep Learning.

PubMed

Nguyen, A; Yosinski, J; Clune, J

2016-01-01

The Achilles Heel of stochastic optimization algorithms is getting trapped on local optima. Novelty Search mitigates this problem by encouraging exploration in all interesting directions by replacing the performance objective with a reward for novel behaviors. This reward for novel behaviors has traditionally required a human-crafted, behavioral distance function. While Novelty Search is a major conceptual breakthrough and outperforms traditional stochastic optimization on certain problems, it is not clear how to apply it to challenging, high-dimensional problems where specifying a useful behavioral distance function is difficult. For example, in the space of images, how do you encourage novelty to produce hawks and heroes instead of endless pixel static? Here we propose a new algorithm, the Innovation Engine, that builds on Novelty Search by replacing the human-crafted behavioral distance with a Deep Neural Network (DNN) that can recognize interesting differences between phenotypes. The key insight is that DNNs can recognize similarities and differences between phenotypes at an abstract level, wherein novelty means interesting novelty. For example, a DNN-based novelty search in the image space does not explore in the low-level pixel space, but instead creates a pressure to create new types of images (e.g., churches, mosques, obelisks, etc.). Here, we describe the long-term vision for the Innovation Engine algorithm, which involves many technical challenges that remain to be solved. We then implement a simplified version of the algorithm that enables us to explore some of the algorithm's key motivations. Our initial results, in the domain of images, suggest that Innovation Engines could ultimately automate the production of endless streams of interesting solutions in any domain: for example, producing intelligent software, robot controllers, optimized physical components, and art.

Performance improvement of optical CDMA networks with stochastic artificial bee colony optimization technique

NASA Astrophysics Data System (ADS)

Panda, Satyasen

2018-05-01

This paper proposes a modified artificial bee colony optimization (ABC) algorithm based on levy flight swarm intelligence referred as artificial bee colony levy flight stochastic walk (ABC-LFSW) optimization for optical code division multiple access (OCDMA) network. The ABC-LFSW algorithm is used to solve asset assignment problem based on signal to noise ratio (SNR) optimization in OCDM networks with quality of service constraints. The proposed optimization using ABC-LFSW algorithm provides methods for minimizing various noises and interferences, regulating the transmitted power and optimizing the network design for improving the power efficiency of the optical code path (OCP) from source node to destination node. In this regard, an optical system model is proposed for improving the network performance with optimized input parameters. The detailed discussion and simulation results based on transmitted power allocation and power efficiency of OCPs are included. The experimental results prove the superiority of the proposed network in terms of power efficiency and spectral efficiency in comparison to networks without any power allocation approach.

Estimation for bilinear stochastic systems

NASA Technical Reports Server (NTRS)

Willsky, A. S.; Marcus, S. I.

1974-01-01

Three techniques for the solution of bilinear estimation problems are presented. First, finite dimensional optimal nonlinear estimators are presented for certain bilinear systems evolving on solvable and nilpotent lie groups. Then the use of harmonic analysis for estimation problems evolving on spheres and other compact manifolds is investigated. Finally, an approximate estimation technique utilizing cumulants is discussed.

Bidding strategy for microgrid in day-ahead market based on hybrid stochastic/robust optimization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Guodong; Xu, Yan; Tomsovic, Kevin

In this paper, we propose an optimal bidding strategy in the day-ahead market of a microgrid consisting of intermittent distributed generation (DG), storage, dispatchable DG and price responsive loads. The microgrid coordinates the energy consumption or production of its components and trades electricity in both the day-ahead and real-time markets to minimize its operating cost as a single entity. The bidding problem is challenging due to a variety of uncertainties, including power output of intermittent DG, load variation, day-ahead and real-time market prices. A hybrid stochastic/robust optimization model is proposed to minimize the expected net cost, i.e., expected total costmore » of operation minus total benefit of demand. This formulation can be solved by mixed integer linear programming. The uncertain output of intermittent DG and day-ahead market price are modeled via scenarios based on forecast results, while a robust optimization is proposed to limit the unbalanced power in real-time market taking account of the uncertainty of real-time market price. Numerical simulations on a microgrid consisting of a wind turbine, a PV panel, a fuel cell, a micro-turbine, a diesel generator, a battery and a responsive load show the advantage of stochastic optimization in addition to robust optimization.« less

Bidding strategy for microgrid in day-ahead market based on hybrid stochastic/robust optimization

DOE PAGES

Liu, Guodong; Xu, Yan; Tomsovic, Kevin

2016-01-01

In this paper, we propose an optimal bidding strategy in the day-ahead market of a microgrid consisting of intermittent distributed generation (DG), storage, dispatchable DG and price responsive loads. The microgrid coordinates the energy consumption or production of its components and trades electricity in both the day-ahead and real-time markets to minimize its operating cost as a single entity. The bidding problem is challenging due to a variety of uncertainties, including power output of intermittent DG, load variation, day-ahead and real-time market prices. A hybrid stochastic/robust optimization model is proposed to minimize the expected net cost, i.e., expected total costmore » of operation minus total benefit of demand. This formulation can be solved by mixed integer linear programming. The uncertain output of intermittent DG and day-ahead market price are modeled via scenarios based on forecast results, while a robust optimization is proposed to limit the unbalanced power in real-time market taking account of the uncertainty of real-time market price. Numerical simulations on a microgrid consisting of a wind turbine, a PV panel, a fuel cell, a micro-turbine, a diesel generator, a battery and a responsive load show the advantage of stochastic optimization in addition to robust optimization.« less

Opitmal Platform Strategies in the Smartphone Market

NASA Astrophysics Data System (ADS)

Unno, Masaru; Xu, Hua

In a smartphone market, smartphone makers encourage smartphone application providers (AP) to create more popular smartphone applications through making a revenue-sharing contract with AP and providing application-purchasing support to end users. In this paper, we study revenue-sharing and application-purchasing support problem between a risk-averse smartphone maker and a smartphone application provider. The problem is formulated as the smartphone makers's risk-sensitive stochastic control problem. The sufficient conditions for the existence of the optimal revenue-sharing strategy, the optimal application-purchasing support strategy and the incentive compatible effort recommended to AP are obtained. The effects of the smartphone makers's risk-sensitivity on the optimal strategies are also discussed. A numerical example is solved to show the computation aspects of the problem.

Multivariable optimization of an auto-thermal ammonia synthesis reactor using genetic algorithm

NASA Astrophysics Data System (ADS)

Anh-Nga, Nguyen T.; Tuan-Anh, Nguyen; Tien-Dung, Vu; Kim-Trung, Nguyen

2017-09-01

The ammonia synthesis system is an important chemical process used in the manufacture of fertilizers, chemicals, explosives, fibers, plastics, refrigeration. In the literature, many works approaching the modeling, simulation and optimization of an auto-thermal ammonia synthesis reactor can be found. However, they just focus on the optimization of the reactor length while keeping the others parameters constant. In this study, the other parameters are also considered in the optimization problem such as the temperature of feed gas enters the catalyst zone. The optimal problem requires the maximization of a multivariable objective function which subjects to a number of equality constraints involving the solution of coupled differential equations and also inequality constraints. The solution of an optimization problem can be found through, among others, deterministic or stochastic approaches. The stochastic methods, such as evolutionary algorithm (EA), which is based on natural phenomenon, can overcome the drawbacks such as the requirement of the derivatives of the objective function and/or constraints, or being not efficient in non-differentiable or discontinuous problems. Genetic algorithm (GA) which is a class of EA, exceptionally simple, robust at numerical optimization and is more likely to find a true global optimum. In this study, the genetic algorithm is employed to find the optimum profit of the process. The inequality constraints were treated using penalty method. The coupled differential equations system was solved using Runge-Kutta 4th order method. The results showed that the presented numerical method could be applied to model the ammonia synthesis reactor. The optimum economic profit obtained from this study are also compared to the results from the literature. It suggests that the process should be operated at higher temperature of feed gas in catalyst zone and the reactor length is slightly longer.

Stochastic Multi-Commodity Facility Location Based on a New Scenario Generation Technique

NASA Astrophysics Data System (ADS)

Mahootchi, M.; Fattahi, M.; Khakbazan, E.

2011-11-01

This paper extends two models for stochastic multi-commodity facility location problem. The problem is formulated as two-stage stochastic programming. As a main point of this study, a new algorithm is applied to efficiently generate scenarios for uncertain correlated customers' demands. This algorithm uses Latin Hypercube Sampling (LHS) and a scenario reduction approach. The relation between customer satisfaction level and cost are considered in model I. The risk measure using Conditional Value-at-Risk (CVaR) is embedded into the optimization model II. Here, the structure of the network contains three facility layers including plants, distribution centers, and retailers. The first stage decisions are the number, locations, and the capacity of distribution centers. In the second stage, the decisions are the amount of productions, the volume of transportation between plants and customers.

Bi-Objective Flexible Job-Shop Scheduling Problem Considering Energy Consumption under Stochastic Processing Times.

PubMed

Yang, Xin; Zeng, Zhenxiang; Wang, Ruidong; Sun, Xueshan

2016-01-01

This paper presents a novel method on the optimization of bi-objective Flexible Job-shop Scheduling Problem (FJSP) under stochastic processing times. The robust counterpart model and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) are used to solve the bi-objective FJSP with consideration of the completion time and the total energy consumption under stochastic processing times. The case study on GM Corporation verifies that the NSGA-II used in this paper is effective and has advantages to solve the proposed model comparing with HPSO and PSO+SA. The idea and method of the paper can be generalized widely in the manufacturing industry, because it can reduce the energy consumption of the energy-intensive manufacturing enterprise with less investment when the new approach is applied in existing systems.

Bi-Objective Flexible Job-Shop Scheduling Problem Considering Energy Consumption under Stochastic Processing Times

PubMed Central

Zeng, Zhenxiang; Wang, Ruidong; Sun, Xueshan

2016-01-01

This paper presents a novel method on the optimization of bi-objective Flexible Job-shop Scheduling Problem (FJSP) under stochastic processing times. The robust counterpart model and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) are used to solve the bi-objective FJSP with consideration of the completion time and the total energy consumption under stochastic processing times. The case study on GM Corporation verifies that the NSGA-II used in this paper is effective and has advantages to solve the proposed model comparing with HPSO and PSO+SA. The idea and method of the paper can be generalized widely in the manufacturing industry, because it can reduce the energy consumption of the energy-intensive manufacturing enterprise with less investment when the new approach is applied in existing systems. PMID:27907163

An Approach to Economic Dispatch with Multiple Fuels Based on Particle Swarm Optimization

NASA Astrophysics Data System (ADS)

Sriyanyong, Pichet

2011-06-01

Particle Swarm Optimization (PSO), a stochastic optimization technique, shows superiority to other evolutionary computation techniques in terms of less computation time, easy implementation with high quality solution, stable convergence characteristic and independent from initialization. For this reason, this paper proposes the application of PSO to the Economic Dispatch (ED) problem, which occurs in the operational planning of power systems. In this study, ED problem can be categorized according to the different characteristics of its cost function that are ED problem with smooth cost function and ED problem with multiple fuels. Taking the multiple fuels into account will make the problem more realistic. The experimental results show that the proposed PSO algorithm is more efficient than previous approaches under consideration as well as highly promising in real world applications.

Maximum Entropy/Optimal Projection (MEOP) control design synthesis: Optimal quantification of the major design tradeoffs

NASA Technical Reports Server (NTRS)

Hyland, D. C.; Bernstein, D. S.

1987-01-01

The underlying philosophy and motivation of the optimal projection/maximum entropy (OP/ME) stochastic modeling and reduced control design methodology for high order systems with parameter uncertainties are discussed. The OP/ME design equations for reduced-order dynamic compensation including the effect of parameter uncertainties are reviewed. The application of the methodology to several Large Space Structures (LSS) problems of representative complexity is illustrated.

Modeling and Computation of Transboundary Industrial Pollution with Emission Permits Trading by Stochastic Differential Game

PubMed Central

2015-01-01

Transboundary industrial pollution requires international actions to control its formation and effects. In this paper, we present a stochastic differential game to model the transboundary industrial pollution problems with emission permits trading. More generally, the process of emission permits price is assumed to be stochastic and to follow a geometric Brownian motion (GBM). We make use of stochastic optimal control theory to derive the system of Hamilton-Jacobi-Bellman (HJB) equations satisfied by the value functions for the cooperative and the noncooperative games, respectively, and then propose a so-called fitted finite volume method to solve it. The efficiency and the usefulness of this method are illustrated by the numerical experiments. The two regions’ cooperative and noncooperative optimal emission paths, which maximize the regions’ discounted streams of the net revenues, together with the value functions, are obtained. Additionally, we can also obtain the threshold conditions for the two regions to decide whether they cooperate or not in different cases. The effects of parameters in the established model on the results have been also examined. All the results demonstrate that the stochastic emission permits prices can motivate the players to make more flexible strategic decisions in the games. PMID:26402322

Modeling and Computation of Transboundary Industrial Pollution with Emission Permits Trading by Stochastic Differential Game.

PubMed

Chang, Shuhua; Wang, Xinyu; Wang, Zheng

2015-01-01

Transboundary industrial pollution requires international actions to control its formation and effects. In this paper, we present a stochastic differential game to model the transboundary industrial pollution problems with emission permits trading. More generally, the process of emission permits price is assumed to be stochastic and to follow a geometric Brownian motion (GBM). We make use of stochastic optimal control theory to derive the system of Hamilton-Jacobi-Bellman (HJB) equations satisfied by the value functions for the cooperative and the noncooperative games, respectively, and then propose a so-called fitted finite volume method to solve it. The efficiency and the usefulness of this method are illustrated by the numerical experiments. The two regions' cooperative and noncooperative optimal emission paths, which maximize the regions' discounted streams of the net revenues, together with the value functions, are obtained. Additionally, we can also obtain the threshold conditions for the two regions to decide whether they cooperate or not in different cases. The effects of parameters in the established model on the results have been also examined. All the results demonstrate that the stochastic emission permits prices can motivate the players to make more flexible strategic decisions in the games.

Random search optimization based on genetic algorithm and discriminant function

NASA Technical Reports Server (NTRS)

Kiciman, M. O.; Akgul, M.; Erarslanoglu, G.

1990-01-01

The general problem of optimization with arbitrary merit and constraint functions, which could be convex, concave, monotonic, or non-monotonic, is treated using stochastic methods. To improve the efficiency of the random search methods, a genetic algorithm for the search phase and a discriminant function for the constraint-control phase were utilized. The validity of the technique is demonstrated by comparing the results to published test problem results. Numerical experimentation indicated that for cases where a quick near optimum solution is desired, a general, user-friendly optimization code can be developed without serious penalties in both total computer time and accuracy.

A finite state, finite memory minimum principle, part 2. [a discussion of game theory, signaling, stochastic processes, and control theory

NASA Technical Reports Server (NTRS)

Sandell, N. R., Jr.; Athans, M.

1975-01-01

The development of the theory of the finite - state, finite - memory (FSFM) stochastic control problem is discussed. The sufficiency of the FSFM minimum principle (which is in general only a necessary condition) was investigated. By introducing the notion of a signaling strategy as defined in the literature on games, conditions under which the FSFM minimum principle is sufficient were determined. This result explicitly interconnects the information structure of the FSFM problem with its optimality conditions. The min-H algorithm for the FSFM problem was studied. It is demonstrated that a version of the algorithm always converges to a particular type of local minimum termed a person - by - person extremal.

Revenue Share between Layers and Investment Incentive for ISP in the Internet Market

NASA Astrophysics Data System (ADS)

Unno, Masaru; Xu, Hua

In this paper, we consider a revenue-sharing and network investment problem between an Internet service provider (ISP) and a content provider (CP) by applying the dynamic agency theory. We formulate the problem as the principal-agent problem where the ISP is the principal and the CP is the agent. The principal-agent problem is transformed to a stochastic optimal control problem in which the objectives of ISP are to find an optimal revenue-sharing strategy and a network investment strategy, and to advise an incentive compatible effort level to the CP. The sufficient conditions for the existence of the optimal revenue-sharing strategy, the optimal investment strategy and the incentive compatible effort to the CP are obtained. A numerical example is solved to show the existence of such strategies. The practical implications of the results obtained in the paper will also be discussed.

The isolation limits of stochastic vibration

NASA Technical Reports Server (NTRS)

Knopse, C. R.; Allaire, P. E.

1993-01-01

The vibration isolation problem is formulated as a 1D kinematic problem. The geometry of the stochastic wall trajectories arising from the stroke constraint is defined in terms of their significant extrema. An optimal control solution for the minimum acceleration return path determines a lower bound on platform mean square acceleration. This bound is expressed in terms of the probability density function on the significant maxima and the conditional fourth moment of the first passage time inverse. The first of these is found analytically while the second is found using a Monte Carlo simulation. The rms acceleration lower bound as a function of available space is then determined through numerical quadrature.

Stochastic control of inertial sea wave energy converter.

PubMed

Raffero, Mattia; Martini, Michele; Passione, Biagio; Mattiazzo, Giuliana; Giorcelli, Ermanno; Bracco, Giovanni

2015-01-01

The ISWEC (inertial sea wave energy converter) is presented, its control problems are stated, and an optimal control strategy is introduced. As the aim of the device is energy conversion, the mean absorbed power by ISWEC is calculated for a plane 2D irregular sea state. The response of the WEC (wave energy converter) is driven by the sea-surface elevation, which is modeled by a stationary and homogeneous zero mean Gaussian stochastic process. System equations are linearized thus simplifying the numerical model of the device. The resulting response is obtained as the output of the coupled mechanic-hydrodynamic model of the device. A stochastic suboptimal controller, derived from optimal control theory, is defined and applied to ISWEC. Results of this approach have been compared with the ones obtained with a linear spring-damper controller, highlighting the capability to obtain a higher value of mean extracted power despite higher power peaks.

Stochastic Control of Inertial Sea Wave Energy Converter

PubMed Central

Mattiazzo, Giuliana; Giorcelli, Ermanno

2015-01-01

The ISWEC (inertial sea wave energy converter) is presented, its control problems are stated, and an optimal control strategy is introduced. As the aim of the device is energy conversion, the mean absorbed power by ISWEC is calculated for a plane 2D irregular sea state. The response of the WEC (wave energy converter) is driven by the sea-surface elevation, which is modeled by a stationary and homogeneous zero mean Gaussian stochastic process. System equations are linearized thus simplifying the numerical model of the device. The resulting response is obtained as the output of the coupled mechanic-hydrodynamic model of the device. A stochastic suboptimal controller, derived from optimal control theory, is defined and applied to ISWEC. Results of this approach have been compared with the ones obtained with a linear spring-damper controller, highlighting the capability to obtain a higher value of mean extracted power despite higher power peaks. PMID:25874267

Fault tolerant filtering and fault detection for quantum systems driven by fields in single photon states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gao, Qing, E-mail: qing.gao.chance@gmail.com; Dong, Daoyi, E-mail: daoyidong@gmail.com; Petersen, Ian R., E-mail: i.r.petersen@gmai.com

The purpose of this paper is to solve the fault tolerant filtering and fault detection problem for a class of open quantum systems driven by a continuous-mode bosonic input field in single photon states when the systems are subject to stochastic faults. Optimal estimates of both the system observables and the fault process are simultaneously calculated and characterized by a set of coupled recursive quantum stochastic differential equations.

Optimal Protocols and Optimal Transport in Stochastic Thermodynamics

NASA Astrophysics Data System (ADS)

Aurell, Erik; Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo

2011-06-01

Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a nonequilibrium transition in finite time is solved by the Burgers equation and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.

Optimal protocols and optimal transport in stochastic thermodynamics.

PubMed

Aurell, Erik; Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo

2011-06-24

Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a nonequilibrium transition in finite time is solved by the Burgers equation and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.

A Two-Stage Stochastic Mixed-Integer Programming Approach to the Smart House Scheduling Problem

NASA Astrophysics Data System (ADS)

Ozoe, Shunsuke; Tanaka, Yoichi; Fukushima, Masao

A “Smart House” is a highly energy-optimized house equipped with photovoltaic systems (PV systems), electric battery systems, fuel cell cogeneration systems (FC systems), electric vehicles (EVs) and so on. Smart houses are attracting much attention recently thanks to their enhanced ability to save energy by making full use of renewable energy and by achieving power grid stability despite an increased power draw for installed PV systems. Yet running a smart house's power system, with its multiple power sources and power storages, is no simple task. In this paper, we consider the problem of power scheduling for a smart house with a PV system, an FC system and an EV. We formulate the problem as a mixed integer programming problem, and then extend it to a stochastic programming problem involving recourse costs to cope with uncertain electricity demand, heat demand and PV power generation. Using our method, we seek to achieve the optimal power schedule running at the minimum expected operation cost. We present some results of numerical experiments with data on real-life demands and PV power generation to show the effectiveness of our method.

Coupled stochastic soil moisture simulation-optimization model of deficit irrigation

NASA Astrophysics Data System (ADS)

Alizadeh, Hosein; Mousavi, S. Jamshid

2013-07-01

This study presents an explicit stochastic optimization-simulation model of short-term deficit irrigation management for large-scale irrigation districts. The model which is a nonlinear nonconvex program with an economic objective function is built on an agrohydrological simulation component. The simulation component integrates (1) an explicit stochastic model of soil moisture dynamics of the crop-root zone considering interaction of stochastic rainfall and irrigation with shallow water table effects, (2) a conceptual root zone salt balance model, and 3) the FAO crop yield model. Particle Swarm Optimization algorithm, linked to the simulation component, solves the resulting nonconvex program with a significantly better computational performance compared to a Monte Carlo-based implicit stochastic optimization model. The model has been tested first by applying it in single-crop irrigation problems through which the effects of the severity of water deficit on the objective function (net benefit), root-zone water balance, and irrigation water needs have been assessed. Then, the model has been applied in Dasht-e-Abbas and Ein-khosh Fakkeh Irrigation Districts (DAID and EFID) of the Karkheh Basin in southwest of Iran. While the maximum net benefit has been obtained for a stress-avoidance (SA) irrigation policy, the highest water profitability has been resulted when only about 60% of the water used in the SA policy is applied. The DAID with respectively 33% of total cultivated area and 37% of total applied water has produced only 14% of the total net benefit due to low-valued crops and adverse soil and shallow water table conditions.

An inventory-theory-based interval-parameter two-stage stochastic programming model for water resources management

NASA Astrophysics Data System (ADS)

Suo, M. Q.; Li, Y. P.; Huang, G. H.

2011-09-01

In this study, an inventory-theory-based interval-parameter two-stage stochastic programming (IB-ITSP) model is proposed through integrating inventory theory into an interval-parameter two-stage stochastic optimization framework. This method can not only address system uncertainties with complex presentation but also reflect transferring batch (the transferring quantity at once) and period (the corresponding cycle time) in decision making problems. A case of water allocation problems in water resources management planning is studied to demonstrate the applicability of this method. Under different flow levels, different transferring measures are generated by this method when the promised water cannot be met. Moreover, interval solutions associated with different transferring costs also have been provided. They can be used for generating decision alternatives and thus help water resources managers to identify desired policies. Compared with the ITSP method, the IB-ITSP model can provide a positive measure for solving water shortage problems and afford useful information for decision makers under uncertainty.

Application of tabu search to deterministic and stochastic optimization problems

NASA Astrophysics Data System (ADS)

Gurtuna, Ozgur

During the past two decades, advances in computer science and operations research have resulted in many new optimization methods for tackling complex decision-making problems. One such method, tabu search, forms the basis of this thesis. Tabu search is a very versatile optimization heuristic that can be used for solving many different types of optimization problems. Another research area, real options, has also gained considerable momentum during the last two decades. Real options analysis is emerging as a robust and powerful method for tackling decision-making problems under uncertainty. Although the theoretical foundations of real options are well-established and significant progress has been made in the theory side, applications are lagging behind. A strong emphasis on practical applications and a multidisciplinary approach form the basic rationale of this thesis. The fundamental concepts and ideas behind tabu search and real options are investigated in order to provide a concise overview of the theory supporting both of these two fields. This theoretical overview feeds into the design and development of algorithms that are used to solve three different problems. The first problem examined is a deterministic one: finding the optimal servicing tours that minimize energy and/or duration of missions for servicing satellites around Earth's orbit. Due to the nature of the space environment, this problem is modeled as a time-dependent, moving-target optimization problem. Two solution methods are developed: an exhaustive method for smaller problem instances, and a method based on tabu search for larger ones. The second and third problems are related to decision-making under uncertainty. In the second problem, tabu search and real options are investigated together within the context of a stochastic optimization problem: option valuation. By merging tabu search and Monte Carlo simulation, a new method for studying options, Tabu Search Monte Carlo (TSMC) method, is developed. The theoretical underpinnings of the TSMC method and the flow of the algorithm are explained. Its performance is compared to other existing methods for financial option valuation. In the third, and final, problem, TSMC method is used to determine the conditions of feasibility for hybrid electric vehicles and fuel cell vehicles. There are many uncertainties related to the technologies and markets associated with new generation passenger vehicles. These uncertainties are analyzed in order to determine the conditions in which new generation vehicles can compete with established technologies.

Optimal and centralized reservoir management for drought and flood protection via Stochastic Dual Dynamic Programming on the Upper Seine-Aube River system

NASA Astrophysics Data System (ADS)

Chiavico, Mattia; Raso, Luciano; Dorchies, David; Malaterre, Pierre-Olivier

2015-04-01

Seine river region is an extremely important logistic and economic junction for France and Europe. The hydraulic protection of most part of the region relies on four controlled reservoirs, managed by EPTB Seine-Grands Lacs. Presently, reservoirs operation is not centrally coordinated, and release rules are based on empirical filling curves. In this study, we analyze how a centralized release policy can face flood and drought risks, optimizing water system efficiency. The optimal and centralized decisional problem is solved by Stochastic Dual Dynamic Programming (SDDP) method, minimizing an operational indicator for each planning objective. SDDP allows us to include into the system: 1) the hydrological discharge, specifically a stochastic semi-distributed auto-regressive model, 2) the hydraulic transfer model, represented by a linear lag and route model, and 3) reservoirs and diversions. The novelty of this study lies on the combination of reservoir and hydraulic models in SDDP for flood and drought protection problems. The study case covers the Seine basin until the confluence with Aube River: this system includes two reservoirs, the city of Troyes, and the Nuclear power plant of Nogent-Sur-Seine. The conflict between the interests of flood protection, drought protection, water use and ecology leads to analyze the environmental system in a Multi-Objective perspective.

Portable parallel portfolio optimization in the Aurora Financial Management System

NASA Astrophysics Data System (ADS)

Laure, Erwin; Moritsch, Hans

2001-07-01

Financial planning problems are formulated as large scale, stochastic, multiperiod, tree structured optimization problems. An efficient technique for solving this kind of problems is the nested Benders decomposition method. In this paper we present a parallel, portable, asynchronous implementation of this technique. To achieve our portability goals we elected the programming language Java for our implementation and used a high level Java based framework, called OpusJava, for expressing the parallelism potential as well as synchronization constraints. Our implementation is embedded within a modular decision support tool for portfolio and asset liability management, the Aurora Financial Management System.

An Approach for Dynamic Optimization of Prevention Program Implementation in Stochastic Environments

NASA Astrophysics Data System (ADS)

Kang, Yuncheol; Prabhu, Vittal

The science of preventing youth problems has significantly advanced in developing evidence-based prevention program (EBP) by using randomized clinical trials. Effective EBP can reduce delinquency, aggression, violence, bullying and substance abuse among youth. Unfortunately the outcomes of EBP implemented in natural settings usually tend to be lower than in clinical trials, which has motivated the need to study EBP implementations. In this paper we propose to model EBP implementations in natural settings as stochastic dynamic processes. Specifically, we propose Markov Decision Process (MDP) for modeling and dynamic optimization of such EBP implementations. We illustrate these concepts using simple numerical examples and discuss potential challenges in using such approaches in practice.

Stochastic optimal control as non-equilibrium statistical mechanics: calculus of variations over density and current

NASA Astrophysics Data System (ADS)

Chernyak, Vladimir Y.; Chertkov, Michael; Bierkens, Joris; Kappen, Hilbert J.

2014-01-01

In stochastic optimal control (SOC) one minimizes the average cost-to-go, that consists of the cost-of-control (amount of efforts), cost-of-space (where one wants the system to be) and the target cost (where one wants the system to arrive), for a system participating in forced and controlled Langevin dynamics. We extend the SOC problem by introducing an additional cost-of-dynamics, characterized by a vector potential. We propose derivation of the generalized gauge-invariant Hamilton-Jacobi-Bellman equation as a variation over density and current, suggest hydrodynamic interpretation and discuss examples, e.g., ergodic control of a particle-within-a-circle, illustrating non-equilibrium space-time complexity.

Stochastic control of smart home energy management with plug-in electric vehicle battery energy storage and photovoltaic array

NASA Astrophysics Data System (ADS)

Wu, Xiaohua; Hu, Xiaosong; Moura, Scott; Yin, Xiaofeng; Pickert, Volker

2016-11-01

Energy management strategies are instrumental in the performance and economy of smart homes integrating renewable energy and energy storage. This article focuses on stochastic energy management of a smart home with PEV (plug-in electric vehicle) energy storage and photovoltaic (PV) array. It is motivated by the challenges associated with sustainable energy supplies and the local energy storage opportunity provided by vehicle electrification. This paper seeks to minimize a consumer's energy charges under a time-of-use tariff, while satisfying home power demand and PEV charging requirements, and accommodating the variability of solar power. First, the random-variable models are developed, including Markov Chain model of PEV mobility, as well as predictive models of home power demand and PV power supply. Second, a stochastic optimal control problem is mathematically formulated for managing the power flow among energy sources in the smart home. Finally, based on time-varying electricity price, we systematically examine the performance of the proposed control strategy. As a result, the electric cost is 493.6% less for a Tesla Model S with optimal stochastic dynamic programming (SDP) control relative to the no optimal control case, and it is by 175.89% for a Nissan Leaf.

Foraging on the potential energy surface: a swarm intelligence-based optimizer for molecular geometry.

PubMed

Wehmeyer, Christoph; Falk von Rudorff, Guido; Wolf, Sebastian; Kabbe, Gabriel; Schärf, Daniel; Kühne, Thomas D; Sebastiani, Daniel

2012-11-21

We present a stochastic, swarm intelligence-based optimization algorithm for the prediction of global minima on potential energy surfaces of molecular cluster structures. Our optimization approach is a modification of the artificial bee colony (ABC) algorithm which is inspired by the foraging behavior of honey bees. We apply our modified ABC algorithm to the problem of global geometry optimization of molecular cluster structures and show its performance for clusters with 2-57 particles and different interatomic interaction potentials.

Foraging on the potential energy surface: A swarm intelligence-based optimizer for molecular geometry

NASA Astrophysics Data System (ADS)

Wehmeyer, Christoph; Falk von Rudorff, Guido; Wolf, Sebastian; Kabbe, Gabriel; Schärf, Daniel; Kühne, Thomas D.; Sebastiani, Daniel

2012-11-01

We present a stochastic, swarm intelligence-based optimization algorithm for the prediction of global minima on potential energy surfaces of molecular cluster structures. Our optimization approach is a modification of the artificial bee colony (ABC) algorithm which is inspired by the foraging behavior of honey bees. We apply our modified ABC algorithm to the problem of global geometry optimization of molecular cluster structures and show its performance for clusters with 2-57 particles and different interatomic interaction potentials.

Scenario generation for stochastic optimization problems via the sparse grid method

DOE PAGES

Chen, Michael; Mehrotra, Sanjay; Papp, David

2015-04-19

We study the use of sparse grids in the scenario generation (or discretization) problem in stochastic programming problems where the uncertainty is modeled using a continuous multivariate distribution. We show that, under a regularity assumption on the random function involved, the sequence of optimal objective function values of the sparse grid approximations converges to the true optimal objective function values as the number of scenarios increases. The rate of convergence is also established. We treat separately the special case when the underlying distribution is an affine transform of a product of univariate distributions, and show how the sparse grid methodmore » can be adapted to the distribution by the use of quadrature formulas tailored to the distribution. We numerically compare the performance of the sparse grid method using different quadrature rules with classic quasi-Monte Carlo (QMC) methods, optimal rank-one lattice rules, and Monte Carlo (MC) scenario generation, using a series of utility maximization problems with up to 160 random variables. The results show that the sparse grid method is very efficient, especially if the integrand is sufficiently smooth. In such problems the sparse grid scenario generation method is found to need several orders of magnitude fewer scenarios than MC and QMC scenario generation to achieve the same accuracy. As a result, it is indicated that the method scales well with the dimension of the distribution--especially when the underlying distribution is an affine transform of a product of univariate distributions, in which case the method appears scalable to thousands of random variables.« less

Review: Optimization methods for groundwater modeling and management

NASA Astrophysics Data System (ADS)

Yeh, William W.-G.

2015-09-01

Optimization methods have been used in groundwater modeling as well as for the planning and management of groundwater systems. This paper reviews and evaluates the various optimization methods that have been used for solving the inverse problem of parameter identification (estimation), experimental design, and groundwater planning and management. Various model selection criteria are discussed, as well as criteria used for model discrimination. The inverse problem of parameter identification concerns the optimal determination of model parameters using water-level observations. In general, the optimal experimental design seeks to find sampling strategies for the purpose of estimating the unknown model parameters. A typical objective of optimal conjunctive-use planning of surface water and groundwater is to minimize the operational costs of meeting water demand. The optimization methods include mathematical programming techniques such as linear programming, quadratic programming, dynamic programming, stochastic programming, nonlinear programming, and the global search algorithms such as genetic algorithms, simulated annealing, and tabu search. Emphasis is placed on groundwater flow problems as opposed to contaminant transport problems. A typical two-dimensional groundwater flow problem is used to explain the basic formulations and algorithms that have been used to solve the formulated optimization problems.

Optimizing decentralized production-distribution planning problem in a multi-period supply chain network under uncertainty

NASA Astrophysics Data System (ADS)

Nourifar, Raheleh; Mahdavi, Iraj; Mahdavi-Amiri, Nezam; Paydar, Mohammad Mahdi

2017-09-01

Decentralized supply chain management is found to be significantly relevant in today's competitive markets. Production and distribution planning is posed as an important optimization problem in supply chain networks. Here, we propose a multi-period decentralized supply chain network model with uncertainty. The imprecision related to uncertain parameters like demand and price of the final product is appropriated with stochastic and fuzzy numbers. We provide mathematical formulation of the problem as a bi-level mixed integer linear programming model. Due to problem's convolution, a structure to solve is developed that incorporates a novel heuristic algorithm based on Kth-best algorithm, fuzzy approach and chance constraint approach. Ultimately, a numerical example is constructed and worked through to demonstrate applicability of the optimization model. A sensitivity analysis is also made.

Stochastic Differential Games with Complexity Constrained Strategies.

DTIC Science & Technology

1982-03-01

Stochastic Differential Game ..... . 39 2.-1 A b.mp.C mcamp e ..... .... ................ . ..... qu CHAPTER 3 - PROBLEM OF STATE ESTDAATION IN TWO...similar to that used vith the differential game , e vould find that the optimal K has the form K T[T* + ( 2.58) This is not a surprising ansver in viev...Examle Example: Discrete-time, one-stage scalar game Transition equation: Y X + U - V P-offtfuntinl: J E + {5 2 CV Cc~ c>a> 0 Observation equations: Z x

A duality framework for stochastic optimal control of complex systems

DOE PAGES

Malikopoulos, Andreas A.

2016-01-01

In this study, we address the problem of minimizing the long-run expected average cost of a complex system consisting of interactive subsystems. We formulate a multiobjective optimization problem of the one-stage expected costs of the subsystems and provide a duality framework to prove that the control policy yielding the Pareto optimal solution minimizes the average cost criterion of the system. We provide the conditions of existence and a geometric interpretation of the solution. For practical situations having constraints consistent with those studied here, our results imply that the Pareto control policy may be of value when we seek to derivemore » online the optimal control policy in complex systems.« less

Solving geosteering inverse problems by stochastic Hybrid Monte Carlo method

DOE PAGES

Shen, Qiuyang; Wu, Xuqing; Chen, Jiefu; ...

2017-11-20

The inverse problems arise in almost all fields of science where the real-world parameters are extracted from a set of measured data. The geosteering inversion plays an essential role in the accurate prediction of oncoming strata as well as a reliable guidance to adjust the borehole position on the fly to reach one or more geological targets. This mathematical treatment is not easy to solve, which requires finding an optimum solution among a large solution space, especially when the problem is non-linear and non-convex. Nowadays, a new generation of logging-while-drilling (LWD) tools has emerged on the market. The so-called azimuthalmore » resistivity LWD tools have azimuthal sensitivity and a large depth of investigation. Hence, the associated inverse problems become much more difficult since the earth model to be inverted will have more detailed structures. The conventional deterministic methods are incapable to solve such a complicated inverse problem, where they suffer from the local minimum trap. Alternatively, stochastic optimizations are in general better at finding global optimal solutions and handling uncertainty quantification. In this article, we investigate the Hybrid Monte Carlo (HMC) based statistical inversion approach and suggest that HMC based inference is more efficient in dealing with the increased complexity and uncertainty faced by the geosteering problems.« less

Estimation and Analysis of Nonlinear Stochastic Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Marcus, S. I.

1975-01-01

The algebraic and geometric structures of certain classes of nonlinear stochastic systems were exploited in order to obtain useful stability and estimation results. The class of bilinear stochastic systems (or linear systems with multiplicative noise) was discussed. The stochastic stability of bilinear systems driven by colored noise was considered. Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups were discussed. Two classes of estimation problems involving bilinear systems were considered. It was proved that, for systems described by certain types of Volterra series expansions or by certain bilinear equations evolving on nilpotent or solvable Lie groups, the optimal conditional mean estimator consists of a finite dimensional nonlinear set of equations. The theory of harmonic analysis was used to derive suboptimal estimators for bilinear systems driven by white noise which evolve on compact Lie groups or homogeneous spaces.

Improved Stability and Stabilization Results for Stochastic Synchronization of Continuous-Time Semi-Markovian Jump Neural Networks With Time-Varying Delay.

PubMed

Wei, Yanling; Park, Ju H; Karimi, Hamid Reza; Tian, Yu-Chu; Jung, Hoyoul; Yanling Wei; Park, Ju H; Karimi, Hamid Reza; Yu-Chu Tian; Hoyoul Jung; Tian, Yu-Chu; Wei, Yanling; Jung, Hoyoul; Karimi, Hamid Reza; Park, Ju H

2018-06-01

Continuous-time semi-Markovian jump neural networks (semi-MJNNs) are those MJNNs whose transition rates are not constant but depend on the random sojourn time. Addressing stochastic synchronization of semi-MJNNs with time-varying delay, an improved stochastic stability criterion is derived in this paper to guarantee stochastic synchronization of the response systems with the drive systems. This is achieved through constructing a semi-Markovian Lyapunov-Krasovskii functional together as well as making use of a novel integral inequality and the characteristics of cumulative distribution functions. Then, with a linearization procedure, controller synthesis is carried out for stochastic synchronization of the drive-response systems. The desired state-feedback controller gains can be determined by solving a linear matrix inequality-based optimization problem. Simulation studies are carried out to demonstrate the effectiveness and less conservatism of the presented approach.

A Stochastic Inversion Method for Potential Field Data: Ant Colony Optimization

NASA Astrophysics Data System (ADS)

Liu, Shuang; Hu, Xiangyun; Liu, Tianyou

2014-07-01

Simulating natural ants' foraging behavior, the ant colony optimization (ACO) algorithm performs excellently in combinational optimization problems, for example the traveling salesman problem and the quadratic assignment problem. However, the ACO is seldom used to inverted for gravitational and magnetic data. On the basis of the continuous and multi-dimensional objective function for potential field data optimization inversion, we present the node partition strategy ACO (NP-ACO) algorithm for inversion of model variables of fixed shape and recovery of physical property distributions of complicated shape models. We divide the continuous variables into discrete nodes and ants directionally tour the nodes by use of transition probabilities. We update the pheromone trails by use of Gaussian mapping between the objective function value and the quantity of pheromone. It can analyze the search results in real time and promote the rate of convergence and precision of inversion. Traditional mapping, including the ant-cycle system, weaken the differences between ant individuals and lead to premature convergence. We tested our method by use of synthetic data and real data from scenarios involving gravity and magnetic anomalies. The inverted model variables and recovered physical property distributions were in good agreement with the true values. The ACO algorithm for binary representation imaging and full imaging can recover sharper physical property distributions than traditional linear inversion methods. The ACO has good optimization capability and some excellent characteristics, for example robustness, parallel implementation, and portability, compared with other stochastic metaheuristics.

Optimal estimation of recurrence structures from time series

NASA Astrophysics Data System (ADS)

beim Graben, Peter; Sellers, Kristin K.; Fröhlich, Flavio; Hutt, Axel

2016-05-01

Recurrent temporal dynamics is a phenomenon observed frequently in high-dimensional complex systems and its detection is a challenging task. Recurrence quantification analysis utilizing recurrence plots may extract such dynamics, however it still encounters an unsolved pertinent problem: the optimal selection of distance thresholds for estimating the recurrence structure of dynamical systems. The present work proposes a stochastic Markov model for the recurrent dynamics that allows for the analytical derivation of a criterion for the optimal distance threshold. The goodness of fit is assessed by a utility function which assumes a local maximum for that threshold reflecting the optimal estimate of the system's recurrence structure. We validate our approach by means of the nonlinear Lorenz system and its linearized stochastic surrogates. The final application to neurophysiological time series obtained from anesthetized animals illustrates the method and reveals novel dynamic features of the underlying system. We propose the number of optimal recurrence domains as a statistic for classifying an animals' state of consciousness.

Comparison of Traditional Design Nonlinear Programming Optimization and Stochastic Methods for Structural Design

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Pai, Shantaram S.; Coroneos, Rula M.

2010-01-01

Structural design generated by traditional method, optimization method and the stochastic design concept are compared. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions were produced by all the three methods. The variation in the weight calculated by the methods was modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliabilitytraced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.

Using a derivative-free optimization method for multiple solutions of inverse transport problems

DOE PAGES

Armstrong, Jerawan C.; Favorite, Jeffrey A.

2016-01-14

Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a meshmore » adaptive direct search (MADS) algorithm is incorporated into the local phase. Furthermore, numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.« less

Adaptive grid based multi-objective Cauchy differential evolution for stochastic dynamic economic emission dispatch with wind power uncertainty

PubMed Central

Lei, Xiaohui; Wang, Chao; Yue, Dong; Xie, Xiangpeng

2017-01-01

Since wind power is integrated into the thermal power operation system, dynamic economic emission dispatch (DEED) has become a new challenge due to its uncertain characteristics. This paper proposes an adaptive grid based multi-objective Cauchy differential evolution (AGB-MOCDE) for solving stochastic DEED with wind power uncertainty. To properly deal with wind power uncertainty, some scenarios are generated to simulate those possible situations by dividing the uncertainty domain into different intervals, the probability of each interval can be calculated using the cumulative distribution function, and a stochastic DEED model can be formulated under different scenarios. For enhancing the optimization efficiency, Cauchy mutation operation is utilized to improve differential evolution by adjusting the population diversity during the population evolution process, and an adaptive grid is constructed for retaining diversity distribution of Pareto front. With consideration of large number of generated scenarios, the reduction mechanism is carried out to decrease the scenarios number with covariance relationships, which can greatly decrease the computational complexity. Moreover, the constraint-handling technique is also utilized to deal with the system load balance while considering transmission loss among thermal units and wind farms, all the constraint limits can be satisfied under the permitted accuracy. After the proposed method is simulated on three test systems, the obtained results reveal that in comparison with other alternatives, the proposed AGB-MOCDE can optimize the DEED problem while handling all constraint limits, and the optimal scheme of stochastic DEED can decrease the conservation of interval optimization, which can provide a more valuable optimal scheme for real-world applications. PMID:28961262

Method for using global optimization to the estimation of surface-consistent residual statics

DOEpatents

Reister, David B.; Barhen, Jacob; Oblow, Edward M.

2001-01-01

An efficient method for generating residual statics corrections to compensate for surface-consistent static time shifts in stacked seismic traces. The method includes a step of framing the residual static corrections as a global optimization problem in a parameter space. The method also includes decoupling the global optimization problem involving all seismic traces into several one-dimensional problems. The method further utilizes a Stochastic Pijavskij Tunneling search to eliminate regions in the parameter space where a global minimum is unlikely to exist so that the global minimum may be quickly discovered. The method finds the residual statics corrections by maximizing the total stack power. The stack power is a measure of seismic energy transferred from energy sources to receivers.

Issues and Strategies in Solving Multidisciplinary Optimization Problems

NASA Technical Reports Server (NTRS)

Patnaik, Surya

2013-01-01

Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. The accumulated multidisciplinary design activity is collected under a testbed entitled COMETBOARDS. Several issues were encountered during the solution of the problems. Four issues and the strategies adapted for their resolution are discussed. This is followed by a discussion on analytical methods that is limited to structural design application. An optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. Optimum solutions obtained were infeasible for aircraft and airbreathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through a set of problems: Design of an engine component, Synthesis of a subsonic aircraft, Operation optimization of a supersonic engine, Design of a wave-rotor-topping device, Profile optimization of a cantilever beam, and Design of a cylindrical shell. This chapter provides a cursory account of the issues. Cited references provide detailed discussion on the topics. Design of a structure can also be generated by traditional method and the stochastic design concept. Merits and limitations of the three methods (traditional method, optimization method and stochastic concept) are illustrated. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions can be produced by all the three methods. The variation in the weight calculated by the methods was found to be modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliability traced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.

Stochastic dynamics and combinatorial optimization

NASA Astrophysics Data System (ADS)

Ovchinnikov, Igor V.; Wang, Kang L.

2017-11-01

Natural dynamics is often dominated by sudden nonlinear processes such as neuroavalanches, gamma-ray bursts, solar flares, etc., that exhibit scale-free statistics much in the spirit of the logarithmic Ritcher scale for earthquake magnitudes. On phase diagrams, stochastic dynamical systems (DSs) exhibiting this type of dynamics belong to the finite-width phase (N-phase for brevity) that precedes ordinary chaotic behavior and that is known under such names as noise-induced chaos, self-organized criticality, dynamical complexity, etc. Within the recently proposed supersymmetric theory of stochastic dynamics, the N-phase can be roughly interpreted as the noise-induced “overlap” between integrable and chaotic deterministic dynamics. As a result, the N-phase dynamics inherits the properties of the both. Here, we analyze this unique set of properties and conclude that the N-phase DSs must naturally be the most efficient optimizers: on one hand, N-phase DSs have integrable flows with well-defined attractors that can be associated with candidate solutions and, on the other hand, the noise-induced attractor-to-attractor dynamics in the N-phase is effectively chaotic or aperiodic so that a DS must avoid revisiting solutions/attractors thus accelerating the search for the best solution. Based on this understanding, we propose a method for stochastic dynamical optimization using the N-phase DSs. This method can be viewed as a hybrid of the simulated and chaotic annealing methods. Our proposition can result in a new generation of hardware devices for efficient solution of various search and/or combinatorial optimization problems.

Adaptive Decision Making Using Probabilistic Programming and Stochastic Optimization

DTIC Science & Technology

2018-01-01

world optimization problems (and hence 16 Approved for Public Release (PA); Distribution Unlimited Pred. demand (uncertain; discrete ...simplify the setting, we further assume that the demands are discrete , taking on values d1, . . . , dk with probabilities (conditional on x) (pθ)i ≡ p...Tyrrell Rockafellar. Implicit functions and solution mappings. Springer Monogr. Math ., 2009. Anthony V Fiacco and Yo Ishizuka. Sensitivity and stability

Fuel management optimization using genetic algorithms and code independence

DOE Office of Scientific and Technical Information (OSTI.GOV)

DeChaine, M.D.; Feltus, M.A.

1994-12-31

Fuel management optimization is a hard problem for traditional optimization techniques. Loading pattern optimization is a large combinatorial problem without analytical derivative information. Therefore, methods designed for continuous functions, such as linear programming, do not always work well. Genetic algorithms (GAs) address these problems and, therefore, appear ideal for fuel management optimization. They do not require derivative information and work well with combinatorial. functions. The GAs are a stochastic method based on concepts from biological genetics. They take a group of candidate solutions, called the population, and use selection, crossover, and mutation operators to create the next generation of bettermore » solutions. The selection operator is a {open_quotes}survival-of-the-fittest{close_quotes} operation and chooses the solutions for the next generation. The crossover operator is analogous to biological mating, where children inherit a mixture of traits from their parents, and the mutation operator makes small random changes to the solutions.« less

Planning and Scheduling for Fleets of Earth Observing Satellites

NASA Technical Reports Server (NTRS)

Frank, Jeremy; Jonsson, Ari; Morris, Robert; Smith, David E.; Norvig, Peter (Technical Monitor)

2001-01-01

We address the problem of scheduling observations for a collection of earth observing satellites. This scheduling task is a difficult optimization problem, potentially involving many satellites, hundreds of requests, constraints on when and how to service each request, and resources such as instruments, recording devices, transmitters, and ground stations. High-fidelity models are required to ensure the validity of schedules; at the same time, the size and complexity of the problem makes it unlikely that systematic optimization search methods will be able to solve them in a reasonable time. This paper presents a constraint-based approach to solving the Earth Observing Satellites (EOS) scheduling problem, and proposes a stochastic heuristic search method for solving it.

Solving multistage stochastic programming models of portfolio selection with outstanding liabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Edirisinghe, C.

1994-12-31

Models for portfolio selection in the presence of an outstanding liability have received significant attention, for example, models for pricing options. The problem may be described briefly as follows: given a set of risky securities (and a riskless security such as a bond), and given a set of cash flows, i.e., outstanding liability, to be met at some future date, determine an initial portfolio and a dynamic trading strategy for the underlying securities such that the initial cost of the portfolio is within a prescribed wealth level and the expected cash surpluses arising from trading is maximized. While the tradingmore » strategy should be self-financing, there may also be other restrictions such as leverage and short-sale constraints. Usually the treatment is limited to binomial evolution of uncertainty (of stock price), with possible extensions for developing computational bounds for multinomial generalizations. Posing as stochastic programming models of decision making, we investigate alternative efficient solution procedures under continuous evolution of uncertainty, for discrete time economies. We point out an important moment problem arising in the portfolio selection problem, the solution (or bounds) on which provides the basis for developing efficient computational algorithms. While the underlying stochastic program may be computationally tedious even for a modest number of trading opportunities (i.e., time periods), the derived algorithms may used to solve problems whose sizes are beyond those considered within stochastic optimization.« less

A stochastic algorithm for global optimization and for best populations: A test case of side chains in proteins

PubMed Central

Glick, Meir; Rayan, Anwar; Goldblum, Amiram

2002-01-01

The problem of global optimization is pivotal in a variety of scientific fields. Here, we present a robust stochastic search method that is able to find the global minimum for a given cost function, as well as, in most cases, any number of best solutions for very large combinatorial “explosive” systems. The algorithm iteratively eliminates variable values that contribute consistently to the highest end of a cost function's spectrum of values for the full system. Values that have not been eliminated are retained for a full, exhaustive search, allowing the creation of an ordered population of best solutions, which includes the global minimum. We demonstrate the ability of the algorithm to explore the conformational space of side chains in eight proteins, with 54 to 263 residues, to reproduce a population of their low energy conformations. The 1,000 lowest energy solutions are identical in the stochastic (with two different seed numbers) and full, exhaustive searches for six of eight proteins. The others retain the lowest 141 and 213 (of 1,000) conformations, depending on the seed number, and the maximal difference between stochastic and exhaustive is only about 0.15 Kcal/mol. The energy gap between the lowest and highest of the 1,000 low-energy conformers in eight proteins is between 0.55 and 3.64 Kcal/mol. This algorithm offers real opportunities for solving problems of high complexity in structural biology and in other fields of science and technology. PMID:11792838

a Stochastic Approach to Multiobjective Optimization of Large-Scale Water Reservoir Networks

NASA Astrophysics Data System (ADS)

Bottacin-Busolin, A.; Worman, A. L.

2013-12-01

A main challenge for the planning and management of water resources is the development of multiobjective strategies for operation of large-scale water reservoir networks. The optimal sequence of water releases from multiple reservoirs depends on the stochastic variability of correlated hydrologic inflows and on various processes that affect water demand and energy prices. Although several methods have been suggested, large-scale optimization problems arising in water resources management are still plagued by the high dimensional state space and by the stochastic nature of the hydrologic inflows. In this work, the optimization of reservoir operation is approached using approximate dynamic programming (ADP) with policy iteration and function approximators. The method is based on an off-line learning process in which operating policies are evaluated for a number of stochastic inflow scenarios, and the resulting value functions are used to design new, improved policies until convergence is attained. A case study is presented of a multi-reservoir system in the Dalälven River, Sweden, which includes 13 interconnected reservoirs and 36 power stations. Depending on the late spring and summer peak discharges, the lowlands adjacent to Dalälven can often be flooded during the summer period, and the presence of stagnating floodwater during the hottest months of the year is the cause of a large proliferation of mosquitos, which is a major problem for the people living in the surroundings. Chemical pesticides are currently being used as a preventive countermeasure, which do not provide an effective solution to the problem and have adverse environmental impacts. In this study, ADP was used to analyze the feasibility of alternative operating policies for reducing the flood risk at a reasonable economic cost for the hydropower companies. To this end, mid-term operating policies were derived by combining flood risk reduction with hydropower production objectives. The performance of the resulting policies was evaluated by simulating the online operating process for historical inflow scenarios and synthetic inflow forecasts. The simulations are based on a combined mid- and short-term planning model in which the value function derived in the mid-term planning phase provides the value of the policy at the end of the short-term operating horizon. While a purely deterministic linear analysis provided rather optimistic results, the stochastic model allowed for a more accurate evaluation of trade-offs and limitations of alternative operating strategies for the Dalälven reservoir network.

Minimizing Uncertainties Impact in Decision Making with an Applicability Study for Economic Power Dispatch

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Hong; Wang, Shaobu; Fan, Rui

This report summaries the work performed under the LDRD project on the preliminary study on knowledge automation, where specific focus has been made on the investigation of the impact of uncertainties of human decision making onto the optimization of the process operation. At first the statistics on signals from the Brain-Computing Interface (BCI) is analyzed so as to obtain the uncertainties characterization of human operators during the decision making phase using the electroencephalogram (EEG) signals. This is then followed by the discussions of an architecture that reveals the equivalence between optimization and closed loop feedback control design, where it hasmore » been shown that all the optimization problems can be transferred into the control design problem for closed loop systems. This has led to a “closed loop” framework, where the structure of the decision making is shown to be subjected to both process disturbances and controller’s uncertainties. The latter can well represent the uncertainties or randomness occurred during human decision making phase. As a result, a stochastic optimization problem has been formulated and a novel solution has been proposed using probability density function (PDF) shaping for both the cost function and the constraints using stochastic distribution control concept. A sufficient condition has been derived that guarantees the convergence of the optimal solution and discussions have been made for both the total probabilistic solution and chanced constrained optimization which have been well-studied in optimal power flows (OPF) area. A simple case study has been carried out for the economic dispatch of powers for a grid system when there are distributed energy resources (DERs) in the system, and encouraging results have been obtained showing that a significant savings on the generation cost can be expected.« less

Adaptiveness in monotone pseudo-Boolean optimization and stochastic neural computation.

PubMed

Grossi, Giuliano

2009-08-01

Hopfield neural network (HNN) is a nonlinear computational model successfully applied in finding near-optimal solutions of several difficult combinatorial problems. In many cases, the network energy function is obtained through a learning procedure so that its minima are states falling into a proper subspace (feasible region) of the search space. However, because of the network nonlinearity, a number of undesirable local energy minima emerge from the learning procedure, significantly effecting the network performance. In the neural model analyzed here, we combine both a penalty and a stochastic process in order to enhance the performance of a binary HNN. The penalty strategy allows us to gradually lead the search towards states representing feasible solutions, so avoiding oscillatory behaviors or asymptotically instable convergence. Presence of stochastic dynamics potentially prevents the network to fall into shallow local minima of the energy function, i.e., quite far from global optimum. Hence, for a given fixed network topology, the desired final distribution on the states can be reached by carefully modulating such process. The model uses pseudo-Boolean functions both to express problem constraints and cost function; a combination of these two functions is then interpreted as energy of the neural network. A wide variety of NP-hard problems fall in the class of problems that can be solved by the model at hand, particularly those having a monotonic quadratic pseudo-Boolean function as constraint function. That is, functions easily derived by closed algebraic expressions representing the constraint structure and easy (polynomial time) to maximize. We show the asymptotic convergence properties of this model characterizing its state space distribution at thermal equilibrium in terms of Markov chain and give evidence of its ability to find high quality solutions on benchmarks and randomly generated instances of two specific problems taken from the computational graph theory.

Scenario-based modeling for multiple allocation hub location problem under disruption risk: multiple cuts Benders decomposition approach

NASA Astrophysics Data System (ADS)

Yahyaei, Mohsen; Bashiri, Mahdi

2017-12-01

The hub location problem arises in a variety of domains such as transportation and telecommunication systems. In many real-world situations, hub facilities are subject to disruption. This paper deals with the multiple allocation hub location problem in the presence of facilities failure. To model the problem, a two-stage stochastic formulation is developed. In the proposed model, the number of scenarios grows exponentially with the number of facilities. To alleviate this issue, two approaches are applied simultaneously. The first approach is to apply sample average approximation to approximate the two stochastic problem via sampling. Then, by applying the multiple cuts Benders decomposition approach, computational performance is enhanced. Numerical studies show the effective performance of the SAA in terms of optimality gap for small problem instances with numerous scenarios. Moreover, performance of multi-cut Benders decomposition is assessed through comparison with the classic version and the computational results reveal the superiority of the multi-cut approach regarding the computational time and number of iterations.

Stochastic Control Synthesis of Systems with Structured Uncertainty

NASA Technical Reports Server (NTRS)

Padula, Sharon L. (Technical Monitor); Crespo, Luis G.

2003-01-01

This paper presents a study on the design of robust controllers by using random variables to model structured uncertainty for both SISO and MIMO feedback systems. Once the parameter uncertainty is prescribed with probability density functions, its effects are propagated through the analysis leading to stochastic metrics for the system's output. Control designs that aim for satisfactory performances while guaranteeing robust closed loop stability are attained by solving constrained non-linear optimization problems in the frequency domain. This approach permits not only to quantify the probability of having unstable and unfavorable responses for a particular control design but also to search for controls while favoring the values of the parameters with higher chance of occurrence. In this manner, robust optimality is achieved while the characteristic conservatism of conventional robust control methods is eliminated. Examples that admit closed form expressions for the probabilistic metrics of the output are used to elucidate the nature of the problem at hand and validate the proposed formulations.

Condition-dependent mate choice: A stochastic dynamic programming approach.

PubMed

Frame, Alicia M; Mills, Alex F

2014-09-01

We study how changing female condition during the mating season and condition-dependent search costs impact female mate choice, and what strategies a female could employ in choosing mates to maximize her own fitness. We address this problem via a stochastic dynamic programming model of mate choice. In the model, a female encounters males sequentially and must choose whether to mate or continue searching. As the female searches, her own condition changes stochastically, and she incurs condition-dependent search costs. The female attempts to maximize the quality of the offspring, which is a function of the female's condition at mating and the quality of the male with whom she mates. The mating strategy that maximizes the female's net expected reward is a quality threshold. We compare the optimal policy with other well-known mate choice strategies, and we use simulations to examine how well the optimal policy fares under imperfect information. Copyright © 2014 Elsevier Inc. All rights reserved.

Stochastic modelling of slow-progressing tumors: Analysis and applications to the cell interplay and control of low grade gliomas

NASA Astrophysics Data System (ADS)

Rodríguez, Clara Rojas; Fernández Calvo, Gabriel; Ramis-Conde, Ignacio; Belmonte-Beitia, Juan

2017-08-01

Tumor-normal cell interplay defines the course of a neoplastic malignancy. The outcome of this dual relation is the ultimate prevailing of one of the cells and the death or retreat of the other. In this paper we study the mathematical principles that underlay one important scenario: that of slow-progressing cancers. For this, we develop, within a stochastic framework, a mathematical model to account for tumor-normal cell interaction in such a clinically relevant situation and derive a number of deterministic approximations from the stochastic model. We consider in detail the existence and uniqueness of the solutions of the deterministic model and study the stability analysis. We then focus our model to the specific case of low grade gliomas, where we introduce an optimal control problem for different objective functionals under the administration of chemotherapy. We derive the conditions for which singular and bang-bang control exist and calculate the optimal control and states.

Medical resource inventory model for emergency preparation with uncertain demand and stochastic occurrence time under considering different risk preferences at the airport

PubMed Central

Pan, Wei; Guo, Ying; Jin, Lei; Liao, ShuJie

2017-01-01

With the high accident rate of civil aviation, medical resource inventory becomes more important for emergency management at the airport. Meanwhile, medical products usually are time-sensitive and short lifetime. Moreover, we find that the optimal medical resource inventory depends on multiple factors such as different risk preferences, the material shelf life and so on. Thus, it becomes very complex in a real-life environment. According to this situation, we construct medical resource inventory decision model for emergency preparation at the airport. Our model is formulated in such a way as to simultaneously consider uncertain demand, stochastic occurrence time and different risk preferences. For solving this problem, a new programming is developed. Finally, a numerical example is presented to illustrate the proposed method. The results show that it is effective for determining the optimal medical resource inventory for emergency preparation with uncertain demand and stochastic occurrence time under considering different risk preferences at the airport. PMID:28931007

Medical resource inventory model for emergency preparation with uncertain demand and stochastic occurrence time under considering different risk preferences at the airport.

PubMed

Pan, Wei; Guo, Ying; Jin, Lei; Liao, ShuJie

2017-01-01

With the high accident rate of civil aviation, medical resource inventory becomes more important for emergency management at the airport. Meanwhile, medical products usually are time-sensitive and short lifetime. Moreover, we find that the optimal medical resource inventory depends on multiple factors such as different risk preferences, the material shelf life and so on. Thus, it becomes very complex in a real-life environment. According to this situation, we construct medical resource inventory decision model for emergency preparation at the airport. Our model is formulated in such a way as to simultaneously consider uncertain demand, stochastic occurrence time and different risk preferences. For solving this problem, a new programming is developed. Finally, a numerical example is presented to illustrate the proposed method. The results show that it is effective for determining the optimal medical resource inventory for emergency preparation with uncertain demand and stochastic occurrence time under considering different risk preferences at the airport.

Energy-optimal path planning by stochastic dynamically orthogonal level-set optimization

NASA Astrophysics Data System (ADS)

Subramani, Deepak N.; Lermusiaux, Pierre F. J.

2016-04-01

A stochastic optimization methodology is formulated for computing energy-optimal paths from among time-optimal paths of autonomous vehicles navigating in a dynamic flow field. Based on partial differential equations, the methodology rigorously leverages the level-set equation that governs time-optimal reachability fronts for a given relative vehicle-speed function. To set up the energy optimization, the relative vehicle-speed and headings are considered to be stochastic and new stochastic Dynamically Orthogonal (DO) level-set equations are derived. Their solution provides the distribution of time-optimal reachability fronts and corresponding distribution of time-optimal paths. An optimization is then performed on the vehicle's energy-time joint distribution to select the energy-optimal paths for each arrival time, among all stochastic time-optimal paths for that arrival time. Numerical schemes to solve the reduced stochastic DO level-set equations are obtained, and accuracy and efficiency considerations are discussed. These reduced equations are first shown to be efficient at solving the governing stochastic level-sets, in part by comparisons with direct Monte Carlo simulations. To validate the methodology and illustrate its accuracy, comparisons with semi-analytical energy-optimal path solutions are then completed. In particular, we consider the energy-optimal crossing of a canonical steady front and set up its semi-analytical solution using a energy-time nested nonlinear double-optimization scheme. We then showcase the inner workings and nuances of the energy-optimal path planning, considering different mission scenarios. Finally, we study and discuss results of energy-optimal missions in a wind-driven barotropic quasi-geostrophic double-gyre ocean circulation.

Feasibility of Stochastic Voltage/VAr Optimization Considering Renewable Energy Resources for Smart Grid

NASA Astrophysics Data System (ADS)

Momoh, James A.; Salkuti, Surender Reddy

2016-06-01

This paper proposes a stochastic optimization technique for solving the Voltage/VAr control problem including the load demand and Renewable Energy Resources (RERs) variation. The RERs often take along some inputs like stochastic behavior. One of the important challenges i. e., Voltage/VAr control is a prime source for handling power system complexity and reliability, hence it is the fundamental requirement for all the utility companies. There is a need for the robust and efficient Voltage/VAr optimization technique to meet the peak demand and reduction of system losses. The voltages beyond the limit may damage costly sub-station devices and equipments at consumer end as well. Especially, the RERs introduces more disturbances and some of the RERs are not even capable enough to meet the VAr demand. Therefore, there is a strong need for the Voltage/VAr control in RERs environment. This paper aims at the development of optimal scheme for Voltage/VAr control involving RERs. In this paper, Latin Hypercube Sampling (LHS) method is used to cover full range of variables by maximally satisfying the marginal distribution. Here, backward scenario reduction technique is used to reduce the number of scenarios effectively and maximally retain the fitting accuracy of samples. The developed optimization scheme is tested on IEEE 24 bus Reliability Test System (RTS) considering the load demand and RERs variation.

Combinational Optimal Stopping Problems

DTIC Science & Technology

2016-04-01

such as final, technical, interim, memorandum, master’s thesis, progress, quarterly, research , special, group study, etc. 3. DATES COVERED...Vinel, A. and P. Krokhmal (2015) Certainty equivalent measures of risk, Annals of Operations Research , DOI:10.1007/s10479-015-1801-0. [3] Chernikov...Operations Research , 50(3):415–423, 2002. [16] I. Ljubi, P. Mutzel, and B. Zey. Stochastic survivable network design problems. Electronic Notes in Discrete

Stochastic Adaptive Estimation and Control.

DTIC Science & Technology

1994-10-26

Marcus, "Language Stability and Stabilizability of Discrete Event Dynamical Systems ," SIAM Journal on Control and Optimization, 31, September 1993...in the hierarchical control of flexible manufacturing systems ; in this problem, the model involves a hybrid process in continuous time whose state is...of the average cost control problem for discrete- time Markov processes. Our exposition covers from finite to Borel state and action spaces and

Output-Feedback Control of Unknown Linear Discrete-Time Systems With Stochastic Measurement and Process Noise via Approximate Dynamic Programming.

PubMed

Wang, Jun-Sheng; Yang, Guang-Hong

2017-07-25

This paper studies the optimal output-feedback control problem for unknown linear discrete-time systems with stochastic measurement and process noise. A dithered Bellman equation with the innovation covariance matrix is constructed via the expectation operator given in the form of a finite summation. On this basis, an output-feedback-based approximate dynamic programming method is developed, where the terms depending on the innovation covariance matrix are available with the aid of the innovation covariance matrix identified beforehand. Therefore, by iterating the Bellman equation, the resulting value function can converge to the optimal one in the presence of the aforementioned noise, and the nearly optimal control laws are delivered. To show the effectiveness and the advantages of the proposed approach, a simulation example and a velocity control experiment on a dc machine are employed.

Efficient computation of optimal actions.

PubMed

Todorov, Emanuel

2009-07-14

Optimal choice of actions is a fundamental problem relevant to fields as diverse as neuroscience, psychology, economics, computer science, and control engineering. Despite this broad relevance the abstract setting is similar: we have an agent choosing actions over time, an uncertain dynamical system whose state is affected by those actions, and a performance criterion that the agent seeks to optimize. Solving problems of this kind remains hard, in part, because of overly generic formulations. Here, we propose a more structured formulation that greatly simplifies the construction of optimal control laws in both discrete and continuous domains. An exhaustive search over actions is avoided and the problem becomes linear. This yields algorithms that outperform Dynamic Programming and Reinforcement Learning, and thereby solve traditional problems more efficiently. Our framework also enables computations that were not possible before: composing optimal control laws by mixing primitives, applying deterministic methods to stochastic systems, quantifying the benefits of error tolerance, and inferring goals from behavioral data via convex optimization. Development of a general class of easily solvable problems tends to accelerate progress--as linear systems theory has done, for example. Our framework may have similar impact in fields where optimal choice of actions is relevant.

Developing a new stochastic competitive model regarding inventory and price

NASA Astrophysics Data System (ADS)

Rashid, Reza; Bozorgi-Amiri, Ali; Seyedhoseini, S. M.

2015-09-01

Within the competition in today's business environment, the design of supply chains becomes more complex than before. This paper deals with the retailer's location problem when customers choose their vendors, and inventory costs have been considered for retailers. In a competitive location problem, price and location of facilities affect demands of customers; consequently, simultaneous optimization of the location and inventory system is needed. To prepare a realistic model, demand and lead time have been assumed as stochastic parameters, and queuing theory has been used to develop a comprehensive mathematical model. Due to complexity of the problem, a branch and bound algorithm has been developed, and its performance has been validated in several numerical examples, which indicated effectiveness of the algorithm. Also, a real case has been prepared to demonstrate performance of the model for real world.

Topology optimization under stochastic stiffness

NASA Astrophysics Data System (ADS)

Asadpoure, Alireza

Topology optimization is a systematic computational tool for optimizing the layout of materials within a domain for engineering design problems. It allows variation of structural boundaries and connectivities. This freedom in the design space often enables discovery of new, high performance designs. However, solutions obtained by performing the optimization in a deterministic setting may be impractical or suboptimal when considering real-world engineering conditions with inherent variabilities including (for example) variabilities in fabrication processes and operating conditions. The aim of this work is to provide a computational methodology for topology optimization in the presence of uncertainties associated with structural stiffness, such as uncertain material properties and/or structural geometry. Existing methods for topology optimization under deterministic conditions are first reviewed. Modifications are then proposed to improve the numerical performance of the so-called Heaviside Projection Method (HPM) in continuum domains. Next, two approaches, perturbation and Polynomial Chaos Expansion (PCE), are proposed to account for uncertainties in the optimization procedure. These approaches are intrusive, allowing tight and efficient coupling of the uncertainty quantification with the optimization sensitivity analysis. The work herein develops a robust topology optimization framework aimed at reducing the sensitivity of optimized solutions to uncertainties. The perturbation-based approach combines deterministic topology optimization with a perturbation method for the quantification of uncertainties. The use of perturbation transforms the problem of topology optimization under uncertainty to an augmented deterministic topology optimization problem. The PCE approach combines the spectral stochastic approach for the representation and propagation of uncertainties with an existing deterministic topology optimization technique. The resulting compact representations for the response quantities allow for efficient and accurate calculation of sensitivities of response statistics with respect to the design variables. The proposed methods are shown to be successful at generating robust optimal topologies. Examples from topology optimization in continuum and discrete domains (truss structures) under uncertainty are presented. It is also shown that proposed methods lead to significant computational savings when compared to Monte Carlo-based optimization which involve multiple formations and inversions of the global stiffness matrix and that results obtained from the proposed method are in excellent agreement with those obtained from a Monte Carlo-based optimization algorithm.

Modeling Limited Foresight in Water Management Systems

NASA Astrophysics Data System (ADS)

Howitt, R.

2005-12-01

The inability to forecast future water supplies means that their management inevitably occurs under situations of limited foresight. Three modeling problems arise, first what type of objective function is a manager with limited foresight optimizing? Second how can we measure these objectives? Third can objective functions that incorporate uncertainty be integrated within the structure of optimizing water management models? The paper reviews the concepts of relative risk aversion and intertemporal substitution that underlie stochastic dynamic preference functions. Some initial results from the estimation of such functions for four different dam operations in northern California are presented and discussed. It appears that the path of previous water decisions and states influences the decision-makers willingness to trade off water supplies between periods. A compromise modeling approach that incorporates carry-over value functions under limited foresight within a broader net work optimal water management model is developed. The approach uses annual carry-over value functions derived from small dimension stochastic dynamic programs embedded within a larger dimension water allocation network. The disaggregation of the carry-over value functions to the broader network is extended using the space rule concept. Initial results suggest that the solution of such annual nonlinear network optimizations is comparable to, or faster than, the solution of linear network problems over long time series.

A New Method for Global Optimization Based on Stochastic Differential Equations.

DTIC Science & Technology

1984-12-01

Optimizacion Global de Funciones, Universidad Nacional Autonoma de M~xico, Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, Report...SIGMA package and its usage are described in full de - tail in Annex A5; the complete listing of the FORTRAN code is in Annex A6. 5. Test problems Since...software implemen- tation on a number of test problems: and therefore a collection of test problems naturally began to build up during project de - velopment

Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems

PubMed Central

Rodriguez-Fernandez, Maria; Egea, Jose A; Banga, Julio R

2006-01-01

Background We consider the problem of parameter estimation (model calibration) in nonlinear dynamic models of biological systems. Due to the frequent ill-conditioning and multi-modality of many of these problems, traditional local methods usually fail (unless initialized with very good guesses of the parameter vector). In order to surmount these difficulties, global optimization (GO) methods have been suggested as robust alternatives. Currently, deterministic GO methods can not solve problems of realistic size within this class in reasonable computation times. In contrast, certain types of stochastic GO methods have shown promising results, although the computational cost remains large. Rodriguez-Fernandez and coworkers have presented hybrid stochastic-deterministic GO methods which could reduce computation time by one order of magnitude while guaranteeing robustness. Our goal here was to further reduce the computational effort without loosing robustness. Results We have developed a new procedure based on the scatter search methodology for nonlinear optimization of dynamic models of arbitrary (or even unknown) structure (i.e. black-box models). In this contribution, we describe and apply this novel metaheuristic, inspired by recent developments in the field of operations research, to a set of complex identification problems and we make a critical comparison with respect to the previous (above mentioned) successful methods. Conclusion Robust and efficient methods for parameter estimation are of key importance in systems biology and related areas. The new metaheuristic presented in this paper aims to ensure the proper solution of these problems by adopting a global optimization approach, while keeping the computational effort under reasonable values. This new metaheuristic was applied to a set of three challenging parameter estimation problems of nonlinear dynamic biological systems, outperforming very significantly all the methods previously used for these benchmark problems. PMID:17081289

Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems.

PubMed

Rodriguez-Fernandez, Maria; Egea, Jose A; Banga, Julio R

2006-11-02

We consider the problem of parameter estimation (model calibration) in nonlinear dynamic models of biological systems. Due to the frequent ill-conditioning and multi-modality of many of these problems, traditional local methods usually fail (unless initialized with very good guesses of the parameter vector). In order to surmount these difficulties, global optimization (GO) methods have been suggested as robust alternatives. Currently, deterministic GO methods can not solve problems of realistic size within this class in reasonable computation times. In contrast, certain types of stochastic GO methods have shown promising results, although the computational cost remains large. Rodriguez-Fernandez and coworkers have presented hybrid stochastic-deterministic GO methods which could reduce computation time by one order of magnitude while guaranteeing robustness. Our goal here was to further reduce the computational effort without loosing robustness. We have developed a new procedure based on the scatter search methodology for nonlinear optimization of dynamic models of arbitrary (or even unknown) structure (i.e. black-box models). In this contribution, we describe and apply this novel metaheuristic, inspired by recent developments in the field of operations research, to a set of complex identification problems and we make a critical comparison with respect to the previous (above mentioned) successful methods. Robust and efficient methods for parameter estimation are of key importance in systems biology and related areas. The new metaheuristic presented in this paper aims to ensure the proper solution of these problems by adopting a global optimization approach, while keeping the computational effort under reasonable values. This new metaheuristic was applied to a set of three challenging parameter estimation problems of nonlinear dynamic biological systems, outperforming very significantly all the methods previously used for these benchmark problems.

Optimality, stochasticity, and variability in motor behavior

PubMed Central

Guigon, Emmanuel; Baraduc, Pierre; Desmurget, Michel

2008-01-01

Recent theories of motor control have proposed that the nervous system acts as a stochastically optimal controller, i.e. it plans and executes motor behaviors taking into account the nature and statistics of noise. Detrimental effects of noise are converted into a principled way of controlling movements. Attractive aspects of such theories are their ability to explain not only characteristic features of single motor acts, but also statistical properties of repeated actions. Here, we present a critical analysis of stochastic optimality in motor control which reveals several difficulties with this hypothesis. We show that stochastic control may not be necessary to explain the stochastic nature of motor behavior, and we propose an alternative framework, based on the action of a deterministic controller coupled with an optimal state estimator, which relieves drawbacks of stochastic optimality and appropriately explains movement variability. PMID:18202922

Optimisation in radiotherapy. III: Stochastic optimisation algorithms and conclusions.

PubMed

Ebert, M

1997-12-01

This is the final article in a three part examination of optimisation in radiotherapy. Previous articles have established the bases and form of the radiotherapy optimisation problem, and examined certain types of optimisation algorithm, namely, those which perform some form of ordered search of the solution space (mathematical programming), and those which attempt to find the closest feasible solution to the inverse planning problem (deterministic inversion). The current paper examines algorithms which search the space of possible irradiation strategies by stochastic methods. The resulting iterative search methods move about the solution space by sampling random variates, which gradually become more constricted as the algorithm converges upon the optimal solution. This paper also discusses the implementation of optimisation in radiotherapy practice.

An Efficient Method Coupling Kernel Principal Component Analysis with Adjoint-Based Optimal Control and Its Goal-Oriented Extensions

NASA Astrophysics Data System (ADS)

Thimmisetty, C.; Talbot, C.; Tong, C. H.; Chen, X.

2016-12-01

The representativeness of available data poses a significant fundamental challenge to the quantification of uncertainty in geophysical systems. Furthermore, the successful application of machine learning methods to geophysical problems involving data assimilation is inherently constrained by the extent to which obtainable data represent the problem considered. We show how the adjoint method, coupled with optimization based on methods of machine learning, can facilitate the minimization of an objective function defined on a space of significantly reduced dimension. By considering uncertain parameters as constituting a stochastic process, the Karhunen-Loeve expansion and its nonlinear extensions furnish an optimal basis with respect to which optimization using L-BFGS can be carried out. In particular, we demonstrate that kernel PCA can be coupled with adjoint-based optimal control methods to successfully determine the distribution of material parameter values for problems in the context of channelized deformable media governed by the equations of linear elasticity. Since certain subsets of the original data are characterized by different features, the convergence rate of the method in part depends on, and may be limited by, the observations used to furnish the kernel principal component basis. By determining appropriate weights for realizations of the stochastic random field, then, one may accelerate the convergence of the method. To this end, we present a formulation of Weighted PCA combined with a gradient-based means using automatic differentiation to iteratively re-weight observations concurrent with the determination of an optimal reduced set control variables in the feature space. We demonstrate how improvements in the accuracy and computational efficiency of the weighted linear method can be achieved over existing unweighted kernel methods, and discuss nonlinear extensions of the algorithm.

Implications of Preference and Problem Formulation on the Operating Policies of Complex Multi-Reservoir Systems

NASA Astrophysics Data System (ADS)

Quinn, J.; Reed, P. M.; Giuliani, M.; Castelletti, A.

2016-12-01

Optimizing the operations of multi-reservoir systems poses several challenges: 1) the high dimension of the problem's states and controls, 2) the need to balance conflicting multi-sector objectives, and 3) understanding how uncertainties impact system performance. These difficulties motivated the development of the Evolutionary Multi-Objective Direct Policy Search (EMODPS) framework, in which multi-reservoir operating policies are parameterized in a given family of functions and then optimized for multiple objectives through simulation over a set of stochastic inputs. However, properly framing these objectives remains a severe challenge and a neglected source of uncertainty. Here, we use EMODPS to optimize operating policies for a 4-reservoir system in the Red River Basin in Vietnam, exploring the consequences of optimizing to different sets of objectives related to 1) hydropower production, 2) meeting multi-sector water demands, and 3) providing flood protection to the capital city of Hanoi. We show how coordinated operation of the reservoirs can differ markedly depending on how decision makers weigh these concerns. Moreover, we illustrate how formulation choices that emphasize the mean, tail, or variability of performance across objective combinations must be evaluated carefully. Our results show that these choices can significantly improve attainable system performance, or yield severe unintended consequences. Finally, we show that satisfactory validation of the operating policies on a set of out-of-sample stochastic inputs depends as much or more on the formulation of the objectives as on effective optimization of the policies. These observations highlight the importance of carefully considering how we abstract stakeholders' objectives and of iteratively optimizing and visualizing multiple problem formulation hypotheses to ensure that we capture the most important tradeoffs that emerge from different stakeholder preferences.

A path following algorithm for the graph matching problem.

PubMed

Zaslavskiy, Mikhail; Bach, Francis; Vert, Jean-Philippe

2009-12-01

We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We, therefore, construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore, perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four data sets: simulated graphs, QAPLib, retina vessel images, and handwritten Chinese characters. In all cases, the results are competitive with the state of the art.

Capacity improvement using simulation optimization approaches: A case study in the thermotechnology industry

NASA Astrophysics Data System (ADS)

Yelkenci Köse, Simge; Demir, Leyla; Tunalı, Semra; Türsel Eliiyi, Deniz

2015-02-01

In manufacturing systems, optimal buffer allocation has a considerable impact on capacity improvement. This study presents a simulation optimization procedure to solve the buffer allocation problem in a heat exchanger production plant so as to improve the capacity of the system. For optimization, three metaheuristic-based search algorithms, i.e. a binary-genetic algorithm (B-GA), a binary-simulated annealing algorithm (B-SA) and a binary-tabu search algorithm (B-TS), are proposed. These algorithms are integrated with the simulation model of the production line. The simulation model, which captures the stochastic and dynamic nature of the production line, is used as an evaluation function for the proposed metaheuristics. The experimental study with benchmark problem instances from the literature and the real-life problem show that the proposed B-TS algorithm outperforms B-GA and B-SA in terms of solution quality.

Improving stability margins in discrete-time LQG controllers

NASA Technical Reports Server (NTRS)

Oranc, B. Tarik; Phillips, Charles L.

1987-01-01

Some of the problems are discussed which are encountered in the design of discrete-time stochastic controllers for problems that may adequately be described by the Linear Quadratic Gaussian (LQG) assumptions; namely, the problems of obtaining acceptable relative stability, robustness, and disturbance rejection properties. A dynamic compensator is proposed to replace the optimal full state feedback regulator gains at steady state, provided that all states are measurable. The compensator increases the stability margins at the plant input, which may possibly be inadequate in practical applications. Though the optimal regulator has desirable properties the observer based controller as implemented with a Kalman filter, in a noisy environment, has inadequate stability margins. The proposed compensator is designed to match the return difference matrix at the plant input to that of the optimal regulator while maintaining the optimality of the state estimates as directed by the measurement noise characteristics.

Computing Optimal Stochastic Portfolio Execution Strategies: A Parametric Approach Using Simulations

NASA Astrophysics Data System (ADS)

Moazeni, Somayeh; Coleman, Thomas F.; Li, Yuying

2010-09-01

Computing optimal stochastic portfolio execution strategies under appropriate risk consideration presents great computational challenge. We investigate a parametric approach for computing optimal stochastic strategies using Monte Carlo simulations. This approach allows reduction in computational complexity by computing coefficients for a parametric representation of a stochastic dynamic strategy based on static optimization. Using this technique, constraints can be similarly handled using appropriate penalty functions. We illustrate the proposed approach to minimize the expected execution cost and Conditional Value-at-Risk (CVaR).

Uncertainty Reduction for Stochastic Processes on Complex Networks

NASA Astrophysics Data System (ADS)

Radicchi, Filippo; Castellano, Claudio

2018-05-01

Many real-world systems are characterized by stochastic dynamical rules where a complex network of interactions among individual elements probabilistically determines their state. Even with full knowledge of the network structure and of the stochastic rules, the ability to predict system configurations is generally characterized by a large uncertainty. Selecting a fraction of the nodes and observing their state may help to reduce the uncertainty about the unobserved nodes. However, choosing these points of observation in an optimal way is a highly nontrivial task, depending on the nature of the stochastic process and on the structure of the underlying interaction pattern. In this paper, we introduce a computationally efficient algorithm to determine quasioptimal solutions to the problem. The method leverages network sparsity to reduce computational complexity from exponential to almost quadratic, thus allowing the straightforward application of the method to mid-to-large-size systems. Although the method is exact only for equilibrium stochastic processes defined on trees, it turns out to be effective also for out-of-equilibrium processes on sparse loopy networks.

Optimal control of hydroelectric facilities

NASA Astrophysics Data System (ADS)

Zhao, Guangzhi

This thesis considers a simple yet realistic model of pump-assisted hydroelectric facilities operating in a market with time-varying but deterministic power prices. Both deterministic and stochastic water inflows are considered. The fluid mechanical and engineering details of the facility are described by a model containing several parameters. We present a dynamic programming algorithm for optimizing either the total energy produced or the total cash generated by these plants. The algorithm allows us to give the optimal control strategy as a function of time and to see how this strategy, and the associated plant value, varies with water inflow and electricity price. We investigate various cases. For a single pumped storage facility experiencing deterministic power prices and water inflows, we investigate the varying behaviour for an oversimplified constant turbine- and pump-efficiency model with simple reservoir geometries. We then generalize this simple model to include more realistic turbine efficiencies, situations with more complicated reservoir geometry, and the introduction of dissipative switching costs between various control states. We find many results which reinforce our physical intuition about this complicated system as well as results which initially challenge, though later deepen, this intuition. One major lesson of this work is that the optimal control strategy does not differ much between two differing objectives of maximizing energy production and maximizing its cash value. We then turn our attention to the case of stochastic water inflows. We present a stochastic dynamic programming algorithm which can find an on-average optimal control in the face of this randomness. As the operator of a facility must be more cautious when inflows are random, the randomness destroys facility value. Following this insight we quantify exactly how much a perfect hydrological inflow forecast would be worth to a dam operator. In our final chapter we discuss the challenging problem of optimizing a sequence of two hydro dams sharing the same river system. The complexity of this problem is magnified and we just scratch its surface here. The thesis concludes with suggestions for future work in this fertile area. Keywords: dynamic programming, hydroelectric facility, optimization, optimal control, switching cost, turbine efficiency.

Leveraging human decision making through the optimal management of centralized resources

NASA Astrophysics Data System (ADS)

Hyden, Paul; McGrath, Richard G.

2016-05-01

Combining results from mixed integer optimization, stochastic modeling and queuing theory, we will advance the interdisciplinary problem of efficiently and effectively allocating centrally managed resources. Academia currently fails to address this, as the esoteric demands of each of these large research areas limits work across traditional boundaries. The commercial space does not currently address these challenges due to the absence of a profit metric. By constructing algorithms that explicitly use inputs across boundaries, we are able to incorporate the advantages of using human decision makers. Key improvements in the underlying algorithms are made possible by aligning decision maker goals with the feedback loops introduced between the core optimization step and the modeling of the overall stochastic process of supply and demand. A key observation is that human decision-makers must be explicitly included in the analysis for these approaches to be ultimately successful. Transformative access gives warfighters and mission owners greater understanding of global needs and allows for relationships to guide optimal resource allocation decisions. Mastery of demand processes and optimization bottlenecks reveals long term maximum marginal utility gaps in capabilities.

Volatile decision dynamics: experiments, stochastic description, intermittency control and traffic optimization

NASA Astrophysics Data System (ADS)

Helbing, Dirk; Schönhof, Martin; Kern, Daniel

2002-06-01

The coordinated and efficient distribution of limited resources by individual decisions is a fundamental, unsolved problem. When individuals compete for road capacities, time, space, money, goods, etc, they normally make decisions based on aggregate rather than complete information, such as TV news or stock market indices. In related experiments, we have observed a volatile decision dynamics and far-from-optimal payoff distributions. We have also identified methods of information presentation that can considerably improve the overall performance of the system. In order to determine optimal strategies of decision guidance by means of user-specific recommendations, a stochastic behavioural description is developed. These strategies manage to increase the adaptibility to changing conditions and to reduce the deviation from the time-dependent user equilibrium, thereby enhancing the average and individual payoffs. Hence, our guidance strategies can increase the performance of all users by reducing overreaction and stabilizing the decision dynamics. These results are highly significant for predicting decision behaviour, for reaching optimal behavioural distributions by decision support systems and for information service providers. One of the promising fields of application is traffic optimization.

Control system estimation and design for aerospace vehicles with time delay

NASA Technical Reports Server (NTRS)

Allgaier, G. R.; Williams, T. L.

1972-01-01

The problems of estimation and control of discrete, linear, time-varying systems are considered. Previous solutions to these problems involved either approximate techniques, open-loop control solutions, or results which required excessive computation. The estimation problem is solved by two different methods, both of which yield the identical algorithm for determining the optimal filter. The partitioned results achieve a substantial reduction in computation time and storage requirements over the expanded solution, however. The results reduce to the Kalman filter when no delays are present in the system. The control problem is also solved by two different methods, both of which yield identical algorithms for determining the optimal control gains. The stochastic control is shown to be identical to the deterministic control, thus extending the separation principle to time delay systems. The results obtained reduce to the familiar optimal control solution when no time delays are present in the system.

Fully probabilistic control design in an adaptive critic framework.

PubMed

Herzallah, Randa; Kárný, Miroslav

2011-12-01

Optimal stochastic controller pushes the closed-loop behavior as close as possible to the desired one. The fully probabilistic design (FPD) uses probabilistic description of the desired closed loop and minimizes Kullback-Leibler divergence of the closed-loop description to the desired one. Practical exploitation of the fully probabilistic design control theory continues to be hindered by the computational complexities involved in numerically solving the associated stochastic dynamic programming problem; in particular, very hard multivariate integration and an approximate interpolation of the involved multivariate functions. This paper proposes a new fully probabilistic control algorithm that uses the adaptive critic methods to circumvent the need for explicitly evaluating the optimal value function, thereby dramatically reducing computational requirements. This is a main contribution of this paper. Copyright © 2011 Elsevier Ltd. All rights reserved.

Energy Optimal Path Planning: Integrating Coastal Ocean Modelling with Optimal Control

NASA Astrophysics Data System (ADS)

Subramani, D. N.; Haley, P. J., Jr.; Lermusiaux, P. F. J.

2016-02-01

A stochastic optimization methodology is formulated for computing energy-optimal paths from among time-optimal paths of autonomous vehicles navigating in a dynamic flow field. To set up the energy optimization, the relative vehicle speed and headings are considered to be stochastic, and new stochastic Dynamically Orthogonal (DO) level-set equations that govern their stochastic time-optimal reachability fronts are derived. Their solution provides the distribution of time-optimal reachability fronts and corresponding distribution of time-optimal paths. An optimization is then performed on the vehicle's energy-time joint distribution to select the energy-optimal paths for each arrival time, among all stochastic time-optimal paths for that arrival time. The accuracy and efficiency of the DO level-set equations for solving the governing stochastic level-set reachability fronts are quantitatively assessed, including comparisons with independent semi-analytical solutions. Energy-optimal missions are studied in wind-driven barotropic quasi-geostrophic double-gyre circulations, and in realistic data-assimilative re-analyses of multiscale coastal ocean flows. The latter re-analyses are obtained from multi-resolution 2-way nested primitive-equation simulations of tidal-to-mesoscale dynamics in the Middle Atlantic Bight and Shelbreak Front region. The effects of tidal currents, strong wind events, coastal jets, and shelfbreak fronts on the energy-optimal paths are illustrated and quantified. Results showcase the opportunities for longer-duration missions that intelligently utilize the ocean environment to save energy, rigorously integrating ocean forecasting with optimal control of autonomous vehicles.

Competitive Facility Location with Random Demands

NASA Astrophysics Data System (ADS)

Uno, Takeshi; Katagiri, Hideki; Kato, Kosuke

2009-10-01

This paper proposes a new location problem of competitive facilities, e.g. shops and stores, with uncertain demands in the plane. By representing the demands for facilities as random variables, the location problem is formulated to a stochastic programming problem, and for finding its solution, three deterministic programming problems: expectation maximizing problem, probability maximizing problem, and satisfying level maximizing problem are considered. After showing that one of their optimal solutions can be found by solving 0-1 programming problems, their solution method is proposed by improving the tabu search algorithm with strategic vibration. Efficiency of the solution method is shown by applying to numerical examples of the facility location problems.

Genetic evolutionary taboo search for optimal marker placement in infrared patient setup

NASA Astrophysics Data System (ADS)

Riboldi, M.; Baroni, G.; Spadea, M. F.; Tagaste, B.; Garibaldi, C.; Cambria, R.; Orecchia, R.; Pedotti, A.

2007-09-01

In infrared patient setup adequate selection of the external fiducial configuration is required for compensating inner target displacements (target registration error, TRE). Genetic algorithms (GA) and taboo search (TS) were applied in a newly designed approach to optimal marker placement: the genetic evolutionary taboo search (GETS) algorithm. In the GETS paradigm, multiple solutions are simultaneously tested in a stochastic evolutionary scheme, where taboo-based decision making and adaptive memory guide the optimization process. The GETS algorithm was tested on a group of ten prostate patients, to be compared to standard optimization and to randomly selected configurations. The changes in the optimal marker configuration, when TRE is minimized for OARs, were specifically examined. Optimal GETS configurations ensured a 26.5% mean decrease in the TRE value, versus 19.4% for conventional quasi-Newton optimization. Common features in GETS marker configurations were highlighted in the dataset of ten patients, even when multiple runs of the stochastic algorithm were performed. Including OARs in TRE minimization did not considerably affect the spatial distribution of GETS marker configurations. In conclusion, the GETS algorithm proved to be highly effective in solving the optimal marker placement problem. Further work is needed to embed site-specific deformation models in the optimization process.

A stochastic equilibrium model for the North American natural gas market

NASA Astrophysics Data System (ADS)

Zhuang, Jifang

This dissertation is an endeavor in the field of energy modeling for the North American natural gas market using a mixed complementarity formulation combined with the stochastic programming. The genesis of the stochastic equilibrium model presented in this dissertation is the deterministic market equilibrium model developed in [Gabriel, Kiet and Zhuang, 2005]. Based on some improvements that we made to this model, including proving new existence and uniqueness results, we present a multistage stochastic equilibrium model with uncertain demand for the deregulated North American natural gas market using the recourse method of the stochastic programming. The market participants considered by the model are pipeline operators, producers, storage operators, peak gas operators, marketers and consumers. Pipeline operators are described with regulated tariffs but also involve "congestion pricing" as a mechanism to allocate scarce pipeline capacity. Marketers are modeled as Nash-Cournot players in sales to the residential and commercial sectors but price-takers in all other aspects. Consumers are represented by demand functions in the marketers' problem. Producers, storage operators and peak gas operators are price-takers consistent with perfect competition. Also, two types of the natural gas markets are included: the long-term and spot markets. Market participants make both high-level planning decisions (first-stage decisions) in the long-term market and daily operational decisions (recourse decisions) in the spot market subject to their engineering, resource and political constraints, resource constraints as well as market constraints on both the demand and the supply side, so as to simultaneously maximize their expected profits given others' decisions. The model is shown to be an instance of a mixed complementarity problem (MiCP) under minor conditions. The MiCP formulation is derived from applying the Karush-Kuhn-Tucker optimality conditions of the optimization problems faced by the market participants. Some theoretical results regarding the market prices in both markets are shown. We also illustrate the model on a representative, sample network of two production nodes, two consumption nodes with discretely distributed end-user demand and three seasons using four cases.

Solving Constraint Satisfaction Problems with Networks of Spiking Neurons

PubMed Central

Jonke, Zeno; Habenschuss, Stefan; Maass, Wolfgang

2016-01-01

Network of neurons in the brain apply—unlike processors in our current generation of computer hardware—an event-based processing strategy, where short pulses (spikes) are emitted sparsely by neurons to signal the occurrence of an event at a particular point in time. Such spike-based computations promise to be substantially more power-efficient than traditional clocked processing schemes. However, it turns out to be surprisingly difficult to design networks of spiking neurons that can solve difficult computational problems on the level of single spikes, rather than rates of spikes. We present here a new method for designing networks of spiking neurons via an energy function. Furthermore, we show how the energy function of a network of stochastically firing neurons can be shaped in a transparent manner by composing the networks of simple stereotypical network motifs. We show that this design approach enables networks of spiking neurons to produce approximate solutions to difficult (NP-hard) constraint satisfaction problems from the domains of planning/optimization and verification/logical inference. The resulting networks employ noise as a computational resource. Nevertheless, the timing of spikes plays an essential role in their computations. Furthermore, networks of spiking neurons carry out for the Traveling Salesman Problem a more efficient stochastic search for good solutions compared with stochastic artificial neural networks (Boltzmann machines) and Gibbs sampling. PMID:27065785

Mum, why do you keep on growing? Impacts of environmental variability on optimal growth and reproduction allocation strategies of annual plants.

PubMed

De Lara, Michel

2006-05-01

In their 1990 paper Optimal reproductive efforts and the timing of reproduction of annual plants in randomly varying environments, Amir and Cohen considered stochastic environments consisting of i.i.d. sequences in an optimal allocation discrete-time model. We suppose here that the sequence of environmental factors is more generally described by a Markov chain. Moreover, we discuss the connection between the time interval of the discrete-time dynamic model and the ability of the plant to rebuild completely its vegetative body (from reserves). We formulate a stochastic optimization problem covering the so-called linear and logarithmic fitness (corresponding to variation within and between years), which yields optimal strategies. For "linear maximizers'', we analyse how optimal strategies depend upon the environmental variability type: constant, random stationary, random i.i.d., random monotonous. We provide general patterns in terms of targets and thresholds, including both determinate and indeterminate growth. We also provide a partial result on the comparison between ;"linear maximizers'' and "log maximizers''. Numerical simulations are provided, allowing to give a hint at the effect of different mathematical assumptions.

BBPH: Using progressive hedging within branch and bound to solve multi-stage stochastic mixed integer programs

DOE PAGES

Barnett, Jason; Watson, Jean -Paul; Woodruff, David L.

2016-11-27

Progressive hedging, though an effective heuristic for solving stochastic mixed integer programs (SMIPs), is not guaranteed to converge in this case. Here, we describe BBPH, a branch and bound algorithm that uses PH at each node in the search tree such that, given sufficient time, it will always converge to a globally optimal solution. Additionally, to providing a theoretically convergent “wrapper” for PH applied to SMIPs, computational results demonstrate that for some difficult problem instances branch and bound can find improved solutions after exploring only a few nodes.

Multistage Stochastic Programming and its Applications in Energy Systems Modeling and Optimization

NASA Astrophysics Data System (ADS)

Golari, Mehdi

Electric energy constitutes one of the most crucial elements to almost every aspect of life of people. The modern electric power systems face several challenges such as efficiency, economics, sustainability, and reliability. Increase in electrical energy demand, distributed generations, integration of uncertain renewable energy resources, and demand side management are among the main underlying reasons of such growing complexity. Additionally, the elements of power systems are often vulnerable to failures because of many reasons, such as system limits, weak conditions, unexpected events, hidden failures, human errors, terrorist attacks, and natural disasters. One common factor complicating the operation of electrical power systems is the underlying uncertainties from the demands, supplies and failures of system components. Stochastic programming provides a mathematical framework for decision making under uncertainty. It enables a decision maker to incorporate some knowledge of the intrinsic uncertainty into the decision making process. In this dissertation, we focus on application of two-stage and multistage stochastic programming approaches to electric energy systems modeling and optimization. Particularly, we develop models and algorithms addressing the sustainability and reliability issues in power systems. First, we consider how to improve the reliability of power systems under severe failures or contingencies prone to cascading blackouts by so called islanding operations. We present a two-stage stochastic mixed-integer model to find optimal islanding operations as a powerful preventive action against cascading failures in case of extreme contingencies. Further, we study the properties of this problem and propose efficient solution methods to solve this problem for large-scale power systems. We present the numerical results showing the effectiveness of the model and investigate the performance of the solution methods. Next, we address the sustainability issue considering the integration of renewable energy resources into production planning of energy-intensive manufacturing industries. Recently, a growing number of manufacturing companies are considering renewable energies to meet their energy requirements to move towards green manufacturing as well as decreasing their energy costs. However, the intermittent nature of renewable energies imposes several difficulties in long term planning of how to efficiently exploit renewables. In this study, we propose a scheme for manufacturing companies to use onsite and grid renewable energies provided by their own investments and energy utilities as well as conventional grid energy to satisfy their energy requirements. We propose a multistage stochastic programming model and study an efficient solution method to solve this problem. We examine the proposed framework on a test case simulated based on a real-world semiconductor company. Moreover, we evaluate long-term profitability of such scheme via so called value of multistage stochastic programming.

Path optimization method for the sign problem

NASA Astrophysics Data System (ADS)

Ohnishi, Akira; Mori, Yuto; Kashiwa, Kouji

2018-03-01

We propose a path optimization method (POM) to evade the sign problem in the Monte-Carlo calculations for complex actions. Among many approaches to the sign problem, the Lefschetz-thimble path-integral method and the complex Langevin method are promising and extensively discussed. In these methods, real field variables are complexified and the integration manifold is determined by the flow equations or stochastically sampled. When we have singular points of the action or multiple critical points near the original integral surface, however, we have a risk to encounter the residual and global sign problems or the singular drift term problem. One of the ways to avoid the singular points is to optimize the integration path which is designed not to hit the singular points of the Boltzmann weight. By specifying the one-dimensional integration-path as z = t +if(t)(f ɛ R) and by optimizing f(t) to enhance the average phase factor, we demonstrate that we can avoid the sign problem in a one-variable toy model for which the complex Langevin method is found to fail. In this proceedings, we propose POM and discuss how we can avoid the sign problem in a toy model. We also discuss the possibility to utilize the neural network to optimize the path.

The operating room case-mix problem under uncertainty and nurses capacity constraints.

PubMed

Yahia, Zakaria; Eltawil, Amr B; Harraz, Nermine A

2016-12-01

Surgery is one of the key functions in hospitals; it generates significant revenue and admissions to hospitals. In this paper we address the decision of choosing a case-mix for a surgery department. The objective of this study is to generate an optimal case-mix plan of surgery patients with uncertain surgery operations, which includes uncertainty in surgery durations, length of stay, surgery demand and the availability of nurses. In order to obtain an optimal case-mix plan, a stochastic optimization model is proposed and the sample average approximation method is applied. The proposed model is used to determine the number of surgery cases to be weekly served, the amount of operating rooms' time dedicated to each specialty and the number of ward beds dedicated to each specialty. The optimal case-mix selection criterion is based upon a weighted score taking into account both the waiting list and the historical demand of each patient category. The score aims to maximizing the service level of the operating rooms by increasing the total number of surgery cases that could be served. A computational experiment is presented to demonstrate the performance of the proposed method. The results show that the stochastic model solution outperforms the expected value problem solution. Additional analysis is conducted to study the effect of varying the number of ORs and nurses capacity on the overall ORs' performance.

Non-linear dynamic characteristics and optimal control of giant magnetostrictive film subjected to in-plane stochastic excitation

NASA Astrophysics Data System (ADS)

Zhu, Z. W.; Zhang, W. D.; Xu, J.

2014-03-01

The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.

Wildlife Conservation Planning Using Stochastic Optimization and Importance Sampling

Treesearch

Robert G. Haight; Laurel E. Travis

1997-01-01

Formulations for determining conservation plans for sensitive wildlife species must account for economic costs of habitat protection and uncertainties about how wildlife populations will respond. This paper describes such a formulation and addresses the computational challenge of solving it. The problem is to determine the cost-efficient level of habitat protection...

Global Optimization of Interplanetary Trajectories in the Presence of Realistic Mission Contraints

NASA Technical Reports Server (NTRS)

Hinckley, David, Jr.; Englander, Jacob; Hitt, Darren

2015-01-01

Interplanetary missions are often subject to difficult constraints, like solar phase angle upon arrival at the destination, velocity at arrival, and altitudes for flybys. Preliminary design of such missions is often conducted by solving the unconstrained problem and then filtering away solutions which do not naturally satisfy the constraints. However this can bias the search into non-advantageous regions of the solution space, so it can be better to conduct preliminary design with the full set of constraints imposed. In this work two stochastic global search methods are developed which are well suited to the constrained global interplanetary trajectory optimization problem.

Intelligent Support System of Steel Technical Preparation in an Arc Furnace: Functional Scheme of Interactive Builder of the Multi Objective Optimization Problem

NASA Astrophysics Data System (ADS)

Logunova, O. S.; Sibileva, N. S.

2017-12-01

The purpose of the study is to increase the efficiency of the steelmaking process in large capacity arc furnace on the basis of implementation a new decision-making system about the composition of charge materials. The authors proposed an interactive builder for the formation of the optimization problem, taking into account the requirements of the customer, normative documents and stocks of charge materials in the warehouse. To implement the interactive builder, the sets of deterministic and stochastic model components are developed, as well as a list of preferences of criteria and constraints.

A Multi-Verse Optimizer with Levy Flights for Numerical Optimization and Its Application in Test Scheduling for Network-on-Chip.

PubMed

Hu, Cong; Li, Zhi; Zhou, Tian; Zhu, Aijun; Xu, Chuanpei

2016-01-01

We propose a new meta-heuristic algorithm named Levy flights multi-verse optimizer (LFMVO), which incorporates Levy flights into multi-verse optimizer (MVO) algorithm to solve numerical and engineering optimization problems. The Original MVO easily falls into stagnation when wormholes stochastically re-span a number of universes (solutions) around the best universe achieved over the course of iterations. Since Levy flights are superior in exploring unknown, large-scale search space, they are integrated into the previous best universe to force MVO out of stagnation. We test this method on three sets of 23 well-known benchmark test functions and an NP complete problem of test scheduling for Network-on-Chip (NoC). Experimental results prove that the proposed LFMVO is more competitive than its peers in both the quality of the resulting solutions and convergence speed.

A Multi-Verse Optimizer with Levy Flights for Numerical Optimization and Its Application in Test Scheduling for Network-on-Chip

PubMed Central

Hu, Cong; Li, Zhi; Zhou, Tian; Zhu, Aijun; Xu, Chuanpei

2016-01-01

We propose a new meta-heuristic algorithm named Levy flights multi-verse optimizer (LFMVO), which incorporates Levy flights into multi-verse optimizer (MVO) algorithm to solve numerical and engineering optimization problems. The Original MVO easily falls into stagnation when wormholes stochastically re-span a number of universes (solutions) around the best universe achieved over the course of iterations. Since Levy flights are superior in exploring unknown, large-scale search space, they are integrated into the previous best universe to force MVO out of stagnation. We test this method on three sets of 23 well-known benchmark test functions and an NP complete problem of test scheduling for Network-on-Chip (NoC). Experimental results prove that the proposed LFMVO is more competitive than its peers in both the quality of the resulting solutions and convergence speed. PMID:27926946

Network reliability maximization for stochastic-flow network subject to correlated failures using genetic algorithm and tabu\\xA0search

NASA Astrophysics Data System (ADS)

Yeh, Cheng-Ta; Lin, Yi-Kuei; Yang, Jo-Yun

2018-07-01

Network reliability is an important performance index for many real-life systems, such as electric power systems, computer systems and transportation systems. These systems can be modelled as stochastic-flow networks (SFNs) composed of arcs and nodes. Most system supervisors respect the network reliability maximization by finding the optimal multi-state resource assignment, which is one resource to each arc. However, a disaster may cause correlated failures for the assigned resources, affecting the network reliability. This article focuses on determining the optimal resource assignment with maximal network reliability for SFNs. To solve the problem, this study proposes a hybrid algorithm integrating the genetic algorithm and tabu search to determine the optimal assignment, called the hybrid GA-TS algorithm (HGTA), and integrates minimal paths, recursive sum of disjoint products and the correlated binomial distribution to calculate network reliability. Several practical numerical experiments are adopted to demonstrate that HGTA has better computational quality than several popular soft computing algorithms.

Microgrid energy dispatching for industrial zones with renewable generations and electric vehicles via stochastic optimization and learning

NASA Astrophysics Data System (ADS)

Zhang, Kai; Li, Jingzhi; He, Zhubin; Yan, Wanfeng

2018-07-01

In this paper, a stochastic optimization framework is proposed to address the microgrid energy dispatching problem with random renewable generation and vehicle activity pattern, which is closer to the practical applications. The patterns of energy generation, consumption and storage availability are all random and unknown at the beginning, and the microgrid controller design (MCD) is formulated as a Markov decision process (MDP). Hence, an online learning-based control algorithm is proposed for the microgrid, which could adapt the control policy with increasing knowledge of the system dynamics and converges to the optimal algorithm. We adopt the linear approximation idea to decompose the original value functions as the summation of each per-battery value function. As a consequence, the computational complexity is significantly reduced from exponential growth to linear growth with respect to the size of battery states. Monte Carlo simulation of different scenarios demonstrates the effectiveness and efficiency of our algorithm.

A Novel Weighted Kernel PCA-Based Method for Optimization and Uncertainty Quantification

NASA Astrophysics Data System (ADS)

Thimmisetty, C.; Talbot, C.; Chen, X.; Tong, C. H.

2016-12-01

It has been demonstrated that machine learning methods can be successfully applied to uncertainty quantification for geophysical systems through the use of the adjoint method coupled with kernel PCA-based optimization. In addition, it has been shown through weighted linear PCA how optimization with respect to both observation weights and feature space control variables can accelerate convergence of such methods. Linear machine learning methods, however, are inherently limited in their ability to represent features of non-Gaussian stochastic random fields, as they are based on only the first two statistical moments of the original data. Nonlinear spatial relationships and multipoint statistics leading to the tortuosity characteristic of channelized media, for example, are captured only to a limited extent by linear PCA. With the aim of coupling the kernel-based and weighted methods discussed, we present a novel mathematical formulation of kernel PCA, Weighted Kernel Principal Component Analysis (WKPCA), that both captures nonlinear relationships and incorporates the attribution of significance levels to different realizations of the stochastic random field of interest. We also demonstrate how new instantiations retaining defining characteristics of the random field can be generated using Bayesian methods. In particular, we present a novel WKPCA-based optimization method that minimizes a given objective function with respect to both feature space random variables and observation weights through which optimal snapshot significance levels and optimal features are learned. We showcase how WKPCA can be applied to nonlinear optimal control problems involving channelized media, and in particular demonstrate an application of the method to learning the spatial distribution of material parameter values in the context of linear elasticity, and discuss further extensions of the method to stochastic inversion.

A robust component mode synthesis method for stochastic damped vibroacoustics

NASA Astrophysics Data System (ADS)

Tran, Quang Hung; Ouisse, Morvan; Bouhaddi, Noureddine

2010-01-01

In order to reduce vibrations or sound levels in industrial vibroacoustic problems, the low-cost and efficient way consists in introducing visco- and poro-elastic materials either on the structure or on cavity walls. Depending on the frequency range of interest, several numerical approaches can be used to estimate the behavior of the coupled problem. In the context of low frequency applications related to acoustic cavities with surrounding vibrating structures, the finite elements method (FEM) is one of the most efficient techniques. Nevertheless, industrial problems lead to large FE models which are time-consuming in updating or optimization processes. A classical way to reduce calculation time is the component mode synthesis (CMS) method, whose classical formulation is not always efficient to predict dynamical behavior of structures including visco-elastic and/or poro-elastic patches. Then, to ensure an efficient prediction, the fluid and structural bases used for the model reduction need to be updated as a result of changes in a parametric optimization procedure. For complex models, this leads to prohibitive numerical costs in the optimization phase or for management and propagation of uncertainties in the stochastic vibroacoustic problem. In this paper, the formulation of an alternative CMS method is proposed and compared to classical ( u, p) CMS method: the Ritz basis is completed with static residuals associated to visco-elastic and poro-elastic behaviors. This basis is also enriched by the static response of residual forces due to structural modifications, resulting in a so-called robust basis, also adapted to Monte Carlo simulations for uncertainties propagation using reduced models.

Water resources planning and management : A stochastic dual dynamic programming approach

NASA Astrophysics Data System (ADS)

Goor, Q.; Pinte, D.; Tilmant, A.

2008-12-01

Allocating water between different users and uses, including the environment, is one of the most challenging task facing water resources managers and has always been at the heart of Integrated Water Resources Management (IWRM). As water scarcity is expected to increase over time, allocation decisions among the different uses will have to be found taking into account the complex interactions between water and the economy. Hydro-economic optimization models can capture those interactions while prescribing efficient allocation policies. Many hydro-economic models found in the literature are formulated as large-scale non linear optimization problems (NLP), seeking to maximize net benefits from the system operation while meeting operational and/or institutional constraints, and describing the main hydrological processes. However, those models rarely incorporate the uncertainty inherent to the availability of water, essentially because of the computational difficulties associated stochastic formulations. The purpose of this presentation is to present a stochastic programming model that can identify economically efficient allocation policies in large-scale multipurpose multireservoir systems. The model is based on stochastic dual dynamic programming (SDDP), an extension of traditional SDP that is not affected by the curse of dimensionality. SDDP identify efficient allocation policies while considering the hydrologic uncertainty. The objective function includes the net benefits from the hydropower and irrigation sectors, as well as penalties for not meeting operational and/or institutional constraints. To be able to implement the efficient decomposition scheme that remove the computational burden, the one-stage SDDP problem has to be a linear program. Recent developments improve the representation of the non-linear and mildly non- convex hydropower function through a convex hull approximation of the true hydropower function. This model is illustrated on a cascade of 14 reservoirs on the Nile river basin.

Simulation-optimization of large agro-hydrosystems using a decomposition approach

NASA Astrophysics Data System (ADS)

Schuetze, Niels; Grundmann, Jens

2014-05-01

In this contribution a stochastic simulation-optimization framework for decision support for optimal planning and operation of water supply of large agro-hydrosystems is presented. It is based on a decomposition solution strategy which allows for (i) the usage of numerical process models together with efficient Monte Carlo simulations for a reliable estimation of higher quantiles of the minimum agricultural water demand for full and deficit irrigation strategies at small scale (farm level), and (ii) the utilization of the optimization results at small scale for solving water resources management problems at regional scale. As a secondary result of several simulation-optimization runs at the smaller scale stochastic crop-water production functions (SCWPF) for different crops are derived which can be used as a basic tool for assessing the impact of climate variability on risk for potential yield. In addition, microeconomic impacts of climate change and the vulnerability of the agro-ecological systems are evaluated. The developed methodology is demonstrated through its application on a real-world case study for the South Al-Batinah region in the Sultanate of Oman where a coastal aquifer is affected by saltwater intrusion due to excessive groundwater withdrawal for irrigated agriculture.

Multi-objective optimization of composite structures. A review

NASA Astrophysics Data System (ADS)

Teters, G. A.; Kregers, A. F.

1996-05-01

Studies performed on the optimization of composite structures by coworkers of the Institute of Polymers Mechanics of the Latvian Academy of Sciences in recent years are reviewed. The possibility of controlling the geometry and anisotropy of laminar composite structures will make it possible to design articles that best satisfy the requirements established for them. Conflicting requirements such as maximum bearing capacity, minimum weight and/or cost, prescribed thermal conductivity and thermal expansion, etc. usually exist for optimal design. This results in the multi-objective compromise optimization of structures. Numerical methods have been developed for solution of problems of multi-objective optimization of composite structures; parameters of the structure of the reinforcement and the geometry of the design are assigned as controlling parameters. Programs designed to run on personal computers have been compiled for multi-objective optimization of the properties of composite materials, plates, and shells. Solutions are obtained for both linear and nonlinear models. The programs make it possible to establish the Pareto compromise region and special multicriterial solutions. The problem of the multi-objective optimization of the elastic moduli of a spatially reinforced fiberglass with stochastic stiffness parameters has been solved. The region of permissible solutions and the Pareto region have been found for the elastic moduli. The dimensions of the scatter ellipse have been determined for a multidimensional Gaussian probability distribution where correlation between the composite's properties being optimized are accounted for. Two types of problems involving the optimization of a laminar rectangular composite plate are considered: the plate is considered elastic and anisotropic in the first case, and viscoelastic properties are accounted for in the second. The angle of reinforcement and the relative amount of fibers in the longitudinal direction are controlling parameters. The optimized properties are the critical stresses, thermal conductivity, and thermal expansion. The properties of a plate are determined by the properties of the components in the composite, eight of which are stochastic. The region of multi-objective compromise solutions is presented, and the parameters of the scatter ellipses of the properties are given.

A Stochastic Approach to Path Planning in the Weighted-Region Problem

DTIC Science & Technology

1991-03-01

polynomial time. However, the polyhedrons in this three-dimensional obstacle-avoidance problem are all obstacles (i.e. travel is not permitted within...them). Therefore, optimal paths tend to avoid their vertices, and settle into closest approach tangents across polyhedron edges. So, in a sense...intersection update map database with new vertex for this edge 3. IF (C1 > D) and (C2 > D) THEN edge intersects ellipse at two points OR edge is

Optimal design of earth-moving machine elements with cusp catastrophe theory application

NASA Astrophysics Data System (ADS)

Pitukhin, A. V.; Skobtsov, I. G.

2017-10-01

This paper deals with the optimal design problem solution for the operator of an earth-moving machine with a roll-over protective structure (ROPS) in terms of the catastrophe theory. A brief description of the catastrophe theory is presented, the cusp catastrophe is considered, control parameters are viewed as Gaussian stochastic quantities in the first part of the paper. The statement of optimal design problem is given in the second part of the paper. It includes the choice of the objective function and independent design variables, establishment of system limits. The objective function is determined as mean total cost that includes initial cost and cost of failure according to the cusp catastrophe probability. Algorithm of random search method with an interval reduction subject to side and functional constraints is given in the last part of the paper. The way of optimal design problem solution can be applied to choose rational ROPS parameters, which will increase safety and reduce production and exploitation expenses.

Optimization in optical systems revisited: Beyond genetic algorithms

NASA Astrophysics Data System (ADS)

Gagnon, Denis; Dumont, Joey; Dubé, Louis

2013-05-01

Designing integrated photonic devices such as waveguides, beam-splitters and beam-shapers often requires optimization of a cost function over a large solution space. Metaheuristics - algorithms based on empirical rules for exploring the solution space - are specifically tailored to those problems. One of the most widely used metaheuristics is the standard genetic algorithm (SGA), based on the evolution of a population of candidate solutions. However, the stochastic nature of the SGA sometimes prevents access to the optimal solution. Our goal is to show that a parallel tabu search (PTS) algorithm is more suited to optimization problems in general, and to photonics in particular. PTS is based on several search processes using a pool of diversified initial solutions. To assess the performance of both algorithms (SGA and PTS), we consider an integrated photonics design problem, the generation of arbitrary beam profiles using a two-dimensional waveguide-based dielectric structure. The authors acknowledge financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC).

DOE Office of Scientific and Technical Information (OSTI.GOV)

Klimsiak, Tomasz, E-mail: tomas@mat.umk.pl; Rozkosz, Andrzej, E-mail: rozkosz@mat.umk.pl

In the paper we consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follow the classical multidimensional Black and Scholes model. We provide a general early exercise premium representation formula for options with payoff functions which are convex or satisfy mild regularity assumptions. Examples include index options, spread options, call on max options, put on min options, multiply strike options and power-product options. In the proof of the formula we exploit close connections between the optimal stopping problems associated with valuation of American options, obstacle problems and reflected backward stochastic differential equations.

Fusion of Hard and Soft Information in Nonparametric Density Estimation

DTIC Science & Technology

2015-06-10

and stochastic optimization models, in analysis of simulation output, and when instantiating probability models. We adopt a constrained maximum...particular, density estimation is needed for generation of input densities to simulation and stochastic optimization models, in analysis of simulation output...an essential step in simulation analysis and stochastic optimization is the generation of probability densities for input random variables; see for

Primal-dual techniques for online algorithms and mechanisms

NASA Astrophysics Data System (ADS)

Liaghat, Vahid

An offline algorithm is one that knows the entire input in advance. An online algorithm, however, processes its input in a serial fashion. In contrast to offline algorithms, an online algorithm works in a local fashion and has to make irrevocable decisions without having the entire input. Online algorithms are often not optimal since their irrevocable decisions may turn out to be inefficient after receiving the rest of the input. For a given online problem, the goal is to design algorithms which are competitive against the offline optimal solutions. In a classical offline scenario, it is often common to see a dual analysis of problems that can be formulated as a linear or convex program. Primal-dual and dual-fitting techniques have been successfully applied to many such problems. Unfortunately, the usual tricks come short in an online setting since an online algorithm should make decisions without knowing even the whole program. In this thesis, we study the competitive analysis of fundamental problems in the literature such as different variants of online matching and online Steiner connectivity, via online dual techniques. Although there are many generic tools for solving an optimization problem in the offline paradigm, in comparison, much less is known for tackling online problems. The main focus of this work is to design generic techniques for solving integral linear optimization problems where the solution space is restricted via a set of linear constraints. A general family of these problems are online packing/covering problems. Our work shows that for several seemingly unrelated problems, primal-dual techniques can be successfully applied as a unifying approach for analyzing these problems. We believe this leads to generic algorithmic frameworks for solving online problems. In the first part of the thesis, we show the effectiveness of our techniques in the stochastic settings and their applications in Bayesian mechanism design. In particular, we introduce new techniques for solving a fundamental linear optimization problem, namely, the stochastic generalized assignment problem (GAP). This packing problem generalizes various problems such as online matching, ad allocation, bin packing, etc. We furthermore show applications of such results in the mechanism design by introducing Prophet Secretary, a novel Bayesian model for online auctions. In the second part of the thesis, we focus on the covering problems. We develop the framework of "Disk Painting" for a general class of network design problems that can be characterized by proper functions. This class generalizes the node-weighted and edge-weighted variants of several well-known Steiner connectivity problems. We furthermore design a generic technique for solving the prize-collecting variants of these problems when there exists a dual analysis for the non-prize-collecting counterparts. Hence, we solve the online prize-collecting variants of several network design problems for the first time. Finally we focus on designing techniques for online problems with mixed packing/covering constraints. We initiate the study of degree-bounded graph optimization problems in the online setting by designing an online algorithm with a tight competitive ratio for the degree-bounded Steiner forest problem. We hope these techniques establishes a starting point for the analysis of the important class of online degree-bounded optimization on graphs.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baker, Kyri; Toomey, Bridget

Evolving power systems with increasing levels of stochasticity call for a need to solve optimal power flow problems with large quantities of random variables. Weather forecasts, electricity prices, and shifting load patterns introduce higher levels of uncertainty and can yield optimization problems that are difficult to solve in an efficient manner. Solution methods for single chance constraints in optimal power flow problems have been considered in the literature, ensuring single constraints are satisfied with a prescribed probability; however, joint chance constraints, ensuring multiple constraints are simultaneously satisfied, have predominantly been solved via scenario-based approaches or by utilizing Boole's inequality asmore » an upper bound. In this paper, joint chance constraints are used to solve an AC optimal power flow problem while preventing overvoltages in distribution grids under high penetrations of photovoltaic systems. A tighter version of Boole's inequality is derived and used to provide a new upper bound on the joint chance constraint, and simulation results are shown demonstrating the benefit of the proposed upper bound. The new framework allows for a less conservative and more computationally efficient solution to considering joint chance constraints, specifically regarding preventing overvoltages.« less

Non-linear dynamic characteristics and optimal control of giant magnetostrictive film subjected to in-plane stochastic excitation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Z. W., E-mail: zhuzhiwen@tju.edu.cn; Tianjin Key Laboratory of Non-linear Dynamics and Chaos Control, 300072, Tianjin; Zhang, W. D., E-mail: zhangwenditju@126.com

2014-03-15

The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposedmore » in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.« less

Pricing and location decisions in multi-objective facility location problem with M/M/m/k queuing systems

NASA Astrophysics Data System (ADS)

Tavakkoli-Moghaddam, Reza; Vazifeh-Noshafagh, Samira; Taleizadeh, Ata Allah; Hajipour, Vahid; Mahmoudi, Amin

2017-01-01

This article presents a new multi-objective model for a facility location problem with congestion and pricing policies. This model considers situations in which immobile service facilities are congested by a stochastic demand following M/M/m/k queues. The presented model belongs to the class of mixed-integer nonlinear programming models and NP-hard problems. To solve such a hard model, a new multi-objective optimization algorithm based on a vibration theory, namely multi-objective vibration damping optimization (MOVDO), is developed. In order to tune the algorithms parameters, the Taguchi approach using a response metric is implemented. The computational results are compared with those of the non-dominated ranking genetic algorithm and non-dominated sorting genetic algorithm. The outputs demonstrate the robustness of the proposed MOVDO in large-sized problems.

Distribution-Agnostic Stochastic Optimal Power Flow for Distribution Grids: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baker, Kyri; Dall'Anese, Emiliano; Summers, Tyler

2016-09-01

This paper outlines a data-driven, distributionally robust approach to solve chance-constrained AC optimal power flow problems in distribution networks. Uncertain forecasts for loads and power generated by photovoltaic (PV) systems are considered, with the goal of minimizing PV curtailment while meeting power flow and voltage regulation constraints. A data- driven approach is utilized to develop a distributionally robust conservative convex approximation of the chance-constraints; particularly, the mean and covariance matrix of the forecast errors are updated online, and leveraged to enforce voltage regulation with predetermined probability via Chebyshev-based bounds. By combining an accurate linear approximation of the AC power flowmore » equations with the distributionally robust chance constraint reformulation, the resulting optimization problem becomes convex and computationally tractable.« less

Conditioning of Model Identification Task in Immune Inspired Optimizer SILO

NASA Astrophysics Data System (ADS)

Wojdan, K.; Swirski, K.; Warchol, M.; Maciorowski, M.

2009-10-01

Methods which provide good conditioning of model identification task in immune inspired, steady-state controller SILO (Stochastic Immune Layer Optimizer) are presented in this paper. These methods are implemented in a model based optimization algorithm. The first method uses a safe model to assure that gains of the process's model can be estimated. The second method is responsible for elimination of potential linear dependences between columns of observation matrix. Moreover new results from one of SILO implementation in polish power plant are presented. They confirm high efficiency of the presented solution in solving technical problems.

Approximate dynamic programming for optimal stationary control with control-dependent noise.

PubMed

Jiang, Yu; Jiang, Zhong-Ping

2011-12-01

This brief studies the stochastic optimal control problem via reinforcement learning and approximate/adaptive dynamic programming (ADP). A policy iteration algorithm is derived in the presence of both additive and multiplicative noise using Itô calculus. The expectation of the approximated cost matrix is guaranteed to converge to the solution of some algebraic Riccati equation that gives rise to the optimal cost value. Moreover, the covariance of the approximated cost matrix can be reduced by increasing the length of time interval between two consecutive iterations. Finally, a numerical example is given to illustrate the efficiency of the proposed ADP methodology.

Optimal error functional for parameter identification in anisotropic finite strain elasto-plasticity

NASA Astrophysics Data System (ADS)

Shutov, A. V.; Kaygorodtseva, A. A.; Dranishnikov, N. S.

2017-10-01

A problem of parameter identification for a model of finite strain elasto-plasticity is discussed. The utilized phenomenological material model accounts for nonlinear isotropic and kinematic hardening; the model kinematics is described by a nested multiplicative split of the deformation gradient. A hierarchy of optimization problems is considered. First, following the standard procedure, the material parameters are identified through minimization of a certain least square error functional. Next, the focus is placed on finding optimal weighting coefficients which enter the error functional. Toward that end, a stochastic noise with systematic and non-systematic components is introduced to the available measurement results; a superordinate optimization problem seeks to minimize the sensitivity of the resulting material parameters to the introduced noise. The advantage of this approach is that no additional experiments are required; it also provides an insight into the robustness of the identification procedure. As an example, experimental data for the steel 42CrMo4 are considered and a set of weighting coefficients is found, which is optimal in a certain class.

Optimization of structures undergoing harmonic or stochastic excitation. Ph.D. Thesis; [atmospheric turbulence and white noise

NASA Technical Reports Server (NTRS)

Johnson, E. H.

1975-01-01

The optimal design was investigated of simple structures subjected to dynamic loads, with constraints on the structures' responses. Optimal designs were examined for one dimensional structures excited by harmonically oscillating loads, similar structures excited by white noise, and a wing in the presence of continuous atmospheric turbulence. The first has constraints on the maximum allowable stress while the last two place bounds on the probability of failure of the structure. Approximations were made to replace the time parameter with a frequency parameter. For the first problem, this involved the steady state response, and in the remaining cases, power spectral techniques were employed to find the root mean square values of the responses. Optimal solutions were found by using computer algorithms which combined finite elements methods with optimization techniques based on mathematical programming. It was found that the inertial loads for these dynamic problems result in optimal structures that are radically different from those obtained for structures loaded statically by forces of comparable magnitude.

Control of stochastic sensitivity in a stabilization problem for gas discharge system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bashkirtseva, Irina

2015-11-30

We consider a nonlinear dynamic stochastic system with control. A problem of stochastic sensitivity synthesis of the equilibrium is studied. A mathematical technique of the solution of this problem is discussed. This technique is applied to the problem of the stabilization of the operating mode for the stochastic gas discharge system. We construct a feedback regulator that reduces the stochastic sensitivity of the equilibrium, suppresses large-amplitude oscillations, and provides a proper operation of this engineering device.

SLFP: a stochastic linear fractional programming approach for sustainable waste management.

PubMed

Zhu, H; Huang, G H

2011-12-01

A stochastic linear fractional programming (SLFP) approach is developed for supporting sustainable municipal solid waste management under uncertainty. The SLFP method can solve ratio optimization problems associated with random information, where chance-constrained programming is integrated into a linear fractional programming framework. It has advantages in: (1) comparing objectives of two aspects, (2) reflecting system efficiency, (3) dealing with uncertainty expressed as probability distributions, and (4) providing optimal-ratio solutions under different system-reliability conditions. The method is applied to a case study of waste flow allocation within a municipal solid waste (MSW) management system. The obtained solutions are useful for identifying sustainable MSW management schemes with maximized system efficiency under various constraint-violation risks. The results indicate that SLFP can support in-depth analysis of the interrelationships among system efficiency, system cost and system-failure risk. Copyright © 2011 Elsevier Ltd. All rights reserved.

Ant Lion Optimization algorithm for kidney exchanges.

PubMed

Hamouda, Eslam; El-Metwally, Sara; Tarek, Mayada

2018-01-01

The kidney exchange programs bring new insights in the field of organ transplantation. They make the previously not allowed surgery of incompatible patient-donor pairs easier to be performed on a large scale. Mathematically, the kidney exchange is an optimization problem for the number of possible exchanges among the incompatible pairs in a given pool. Also, the optimization modeling should consider the expected quality-adjusted life of transplant candidates and the shortage of computational and operational hospital resources. In this article, we introduce a bio-inspired stochastic-based Ant Lion Optimization, ALO, algorithm to the kidney exchange space to maximize the number of feasible cycles and chains among the pool pairs. Ant Lion Optimizer-based program achieves comparable kidney exchange results to the deterministic-based approaches like integer programming. Also, ALO outperforms other stochastic-based methods such as Genetic Algorithm in terms of the efficient usage of computational resources and the quantity of resulting exchanges. Ant Lion Optimization algorithm can be adopted easily for on-line exchanges and the integration of weights for hard-to-match patients, which will improve the future decisions of kidney exchange programs. A reference implementation for ALO algorithm for kidney exchanges is written in MATLAB and is GPL licensed. It is available as free open-source software from: https://github.com/SaraEl-Metwally/ALO_algorithm_for_Kidney_Exchanges.

Review of design optimization methods for turbomachinery aerodynamics

NASA Astrophysics Data System (ADS)

Li, Zhihui; Zheng, Xinqian

2017-08-01

In today's competitive environment, new turbomachinery designs need to be not only more efficient, quieter, and ;greener; but also need to be developed at on much shorter time scales and at lower costs. A number of advanced optimization strategies have been developed to achieve these requirements. This paper reviews recent progress in turbomachinery design optimization to solve real-world aerodynamic problems, especially for compressors and turbines. This review covers the following topics that are important for optimizing turbomachinery designs. (1) optimization methods, (2) stochastic optimization combined with blade parameterization methods and the design of experiment methods, (3) gradient-based optimization methods for compressors and turbines and (4) data mining techniques for Pareto Fronts. We also present our own insights regarding the current research trends and the future optimization of turbomachinery designs.

Employing Sensitivity Derivatives for Robust Optimization under Uncertainty in CFD

NASA Technical Reports Server (NTRS)

Newman, Perry A.; Putko, Michele M.; Taylor, Arthur C., III

2004-01-01

A robust optimization is demonstrated on a two-dimensional inviscid airfoil problem in subsonic flow. Given uncertainties in statistically independent, random, normally distributed flow parameters (input variables), an approximate first-order statistical moment method is employed to represent the Computational Fluid Dynamics (CFD) code outputs as expected values with variances. These output quantities are used to form the objective function and constraints. The constraints are cast in probabilistic terms; that is, the probability that a constraint is satisfied is greater than or equal to some desired target probability. Gradient-based robust optimization of this stochastic problem is accomplished through use of both first and second-order sensitivity derivatives. For each robust optimization, the effect of increasing both input standard deviations and target probability of constraint satisfaction are demonstrated. This method provides a means for incorporating uncertainty when considering small deviations from input mean values.

On the efficacy of stochastic collocation, stochastic Galerkin, and stochastic reduced order models for solving stochastic problems

DOE PAGES

Richard V. Field, Jr.; Emery, John M.; Grigoriu, Mircea Dan

2015-05-19

The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method.more » Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.« less

Dynamic remapping of parallel computations with varying resource demands

NASA Technical Reports Server (NTRS)

Nicol, D. M.; Saltz, J. H.

1986-01-01

A large class of computational problems is characterized by frequent synchronization, and computational requirements which change as a function of time. When such a problem must be solved on a message passing multiprocessor machine, the combination of these characteristics lead to system performance which decreases in time. Performance can be improved with periodic redistribution of computational load; however, redistribution can exact a sometimes large delay cost. We study the issue of deciding when to invoke a global load remapping mechanism. Such a decision policy must effectively weigh the costs of remapping against the performance benefits. We treat this problem by constructing two analytic models which exhibit stochastically decreasing performance. One model is quite tractable; we are able to describe the optimal remapping algorithm, and the optimal decision policy governing when to invoke that algorithm. However, computational complexity prohibits the use of the optimal remapping decision policy. We then study the performance of a general remapping policy on both analytic models. This policy attempts to minimize a statistic W(n) which measures the system degradation (including the cost of remapping) per computation step over a period of n steps. We show that as a function of time, the expected value of W(n) has at most one minimum, and that when this minimum exists it defines the optimal fixed-interval remapping policy. Our decision policy appeals to this result by remapping when it estimates that W(n) is minimized. Our performance data suggests that this policy effectively finds the natural frequency of remapping. We also use the analytic models to express the relationship between performance and remapping cost, number of processors, and the computation's stochastic activity.

Clustering of financial time series with application to index and enhanced index tracking portfolio

NASA Astrophysics Data System (ADS)

Dose, Christian; Cincotti, Silvano

2005-09-01

A stochastic-optimization technique based on time series cluster analysis is described for index tracking and enhanced index tracking problems. Our methodology solves the problem in two steps, i.e., by first selecting a subset of stocks and then setting the weight of each stock as a result of an optimization process (asset allocation). Present formulation takes into account constraints on the number of stocks and on the fraction of capital invested in each of them, whilst not including transaction costs. Computational results based on clustering selection are compared to those of random techniques and show the importance of clustering in noise reduction and robust forecasting applications, in particular for enhanced index tracking.

Lie theory and control systems defined on spheres

NASA Technical Reports Server (NTRS)

Brockett, R. W.

1972-01-01

It is shown that in constructing a theory for the most elementary class of control problems defined on spheres, some results from the Lie theory play a natural role. To understand controllability, optimal control, and certain properties of stochastic equations, Lie theoretic ideas are needed. The framework considered here is the most natural departure from the usual linear system/vector space problems which have dominated control systems literature. For this reason results are compared with those previously available for the finite dimensional vector space case.

Linearly Adjustable International Portfolios

NASA Astrophysics Data System (ADS)

Fonseca, R. J.; Kuhn, D.; Rustem, B.

2010-09-01

We present an approach to multi-stage international portfolio optimization based on the imposition of a linear structure on the recourse decisions. Multiperiod decision problems are traditionally formulated as stochastic programs. Scenario tree based solutions however can become intractable as the number of stages increases. By restricting the space of decision policies to linear rules, we obtain a conservative tractable approximation to the original problem. Local asset prices and foreign exchange rates are modelled separately, which allows for a direct measure of their impact on the final portfolio value.

Optimizing Multi-Product Multi-Constraint Inventory Control Systems with Stochastic Replenishments

NASA Astrophysics Data System (ADS)

Allah Taleizadeh, Ata; Aryanezhad, Mir-Bahador; Niaki, Seyed Taghi Akhavan

Multi-periodic inventory control problems are mainly studied employing two assumptions. The first is the continuous review, where depending on the inventory level orders can happen at any time and the other is the periodic review, where orders can only happen at the beginning of each period. In this study, we relax these assumptions and assume that the periodic replenishments are stochastic in nature. Furthermore, we assume that the periods between two replenishments are independent and identically random variables. For the problem at hand, the decision variables are of integer-type and there are two kinds of space and service level constraints for each product. We develop a model of the problem in which a combination of back-order and lost-sales are considered for the shortages. Then, we show that the model is of an integer-nonlinear-programming type and in order to solve it, a search algorithm can be utilized. We employ a simulated annealing approach and provide a numerical example to demonstrate the applicability of the proposed methodology.

Stochastic Dual Algorithm for Voltage Regulation in Distribution Networks with Discrete Loads: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall-Anese, Emiliano; Zhou, Xinyang; Liu, Zhiyuan

This paper considers distribution networks with distributed energy resources and discrete-rate loads, and designs an incentive-based algorithm that allows the network operator and the customers to pursue given operational and economic objectives, while concurrently ensuring that voltages are within prescribed limits. Four major challenges include: (1) the non-convexity from discrete decision variables, (2) the non-convexity due to a Stackelberg game structure, (3) unavailable private information from customers, and (4) different update frequency from two types of devices. In this paper, we first make convex relaxation for discrete variables, then reformulate the non-convex structure into a convex optimization problem together withmore » pricing/reward signal design, and propose a distributed stochastic dual algorithm for solving the reformulated problem while restoring feasible power rates for discrete devices. By doing so, we are able to statistically achieve the solution of the reformulated problem without exposure of any private information from customers. Stability of the proposed schemes is analytically established and numerically corroborated.« less

Faster PET reconstruction with a stochastic primal-dual hybrid gradient method

NASA Astrophysics Data System (ADS)

Ehrhardt, Matthias J.; Markiewicz, Pawel; Chambolle, Antonin; Richtárik, Peter; Schott, Jonathan; Schönlieb, Carola-Bibiane

2017-08-01

Image reconstruction in positron emission tomography (PET) is computationally challenging due to Poisson noise, constraints and potentially non-smooth priors-let alone the sheer size of the problem. An algorithm that can cope well with the first three of the aforementioned challenges is the primal-dual hybrid gradient algorithm (PDHG) studied by Chambolle and Pock in 2011. However, PDHG updates all variables in parallel and is therefore computationally demanding on the large problem sizes encountered with modern PET scanners where the number of dual variables easily exceeds 100 million. In this work, we numerically study the usage of SPDHG-a stochastic extension of PDHG-but is still guaranteed to converge to a solution of the deterministic optimization problem with similar rates as PDHG. Numerical results on a clinical data set show that by introducing randomization into PDHG, similar results as the deterministic algorithm can be achieved using only around 10 % of operator evaluations. Thus, making significant progress towards the feasibility of sophisticated mathematical models in a clinical setting.

libSRES: a C library for stochastic ranking evolution strategy for parameter estimation.

PubMed

Ji, Xinglai; Xu, Ying

2006-01-01

Estimation of kinetic parameters in a biochemical pathway or network represents a common problem in systems studies of biological processes. We have implemented a C library, named libSRES, to facilitate a fast implementation of computer software for study of non-linear biochemical pathways. This library implements a (mu, lambda)-ES evolutionary optimization algorithm that uses stochastic ranking as the constraint handling technique. Considering the amount of computing time it might require to solve a parameter-estimation problem, an MPI version of libSRES is provided for parallel implementation, as well as a simple user interface. libSRES is freely available and could be used directly in any C program as a library function. We have extensively tested the performance of libSRES on various pathway parameter-estimation problems and found its performance to be satisfactory. The source code (in C) is free for academic users at http://csbl.bmb.uga.edu/~jix/science/libSRES/

The Impact of Competing Time Delays in Stochastic Coordination Problems

NASA Astrophysics Data System (ADS)

Korniss, G.; Hunt, D.; Szymanski, B. K.

2011-03-01

Coordinating, distributing, and balancing resources in coupled systems is a complex task as these operations are very sensitive to time delays. Delays are present in most real communication and information systems, including info-social and neuro-biological networks, and can be attributed to both non-zero transmission times between different units of the system and to non-zero times it takes to process the information and execute the desired action at the individual units. Here, we investigate the importance and impact of these two types of delays in a simple coordination (synchronization) problem in a noisy environment. We establish the scaling theory for the phase boundary of synchronization and for the steady-state fluctuations in the synchronizable regime. Further, we provide the asymptotic behavior near the boundary of the synchronizable regime. Our results also imply the potential for optimization and trade-offs in stochastic synchronization and coordination problems with time delays. Supported in part by DTRA, ARL, and ONR.

A fuzzy reinforcement learning approach to power control in wireless transmitters.

PubMed

Vengerov, David; Bambos, Nicholas; Berenji, Hamid R

2005-08-01

We address the issue of power-controlled shared channel access in wireless networks supporting packetized data traffic. We formulate this problem using the dynamic programming framework and present a new distributed fuzzy reinforcement learning algorithm (ACFRL-2) capable of adequately solving a class of problems to which the power control problem belongs. Our experimental results show that the algorithm converges almost deterministically to a neighborhood of optimal parameter values, as opposed to a very noisy stochastic convergence of earlier algorithms. The main tradeoff facing a transmitter is to balance its current power level with future backlog in the presence of stochastically changing interference. Simulation experiments demonstrate that the ACFRL-2 algorithm achieves significant performance gains over the standard power control approach used in CDMA2000. Such a large improvement is explained by the fact that ACFRL-2 allows transmitters to learn implicit coordination policies, which back off under stressful channel conditions as opposed to engaging in escalating "power wars."

The importance of environmental variability and management control error to optimal harvest policies

USGS Publications Warehouse

Hunter, C.M.; Runge, M.C.

2004-01-01

State-dependent strategies (SDSs) are the most general form of harvest policy because they allow the harvest rate to depend, without constraint, on the state of the system. State-dependent strategies that provide an optimal harvest rate for any system state can be calculated, and stochasticity can be appropriately accommodated in this optimization. Stochasticity poses 2 challenges to harvest policies: (1) the population will never be at the equilibrium state; and (2) stochasticity induces uncertainty about future states. We investigated the effects of 2 types of stochasticity, environmental variability and management control error, on SDS harvest policies for a white-tailed deer (Odocoileus virginianus) model, and contrasted these with a harvest policy based on maximum sustainable yield (MSY). Increasing stochasticity resulted in more conservative SDSs; that is, higher population densities were required to support the same harvest rate, but these effects were generally small. As stochastic effects increased, SDSs performed much better than MSY. Both deterministic and stochastic SDSs maintained maximum mean annual harvest yield (AHY) and optimal equilibrium population size (Neq) in a stochastic environment, whereas an MSY policy could not. We suggest 3 rules of thumb for harvest management of long-lived vertebrates in stochastic systems: (1) an SDS is advantageous over an MSY policy, (2) using an SDS rather than an MSY is more important than whether a deterministic or stochastic SDS is used, and (3) for SDSs, rankings of the variability in management outcomes (e.g., harvest yield) resulting from parameter stochasticity can be predicted by rankings of the deterministic elasticities.

Optimal Stochastic Modeling and Control of Flexible Structures

DTIC Science & Technology

1988-09-01

1.37] and McLane [1.18] considered multivariable systems and derived their optimal control characteristics. Kleinman, Gorman and Zaborsky considered...Leondes [1.72,1.73] studied various aspects of multivariable linear stochastic, discrete-time systems that are partly deterministic, and partly stochastic...June 1966. 1.8. A.V. Balaknishnan, Applied Functional Analaysis , 2nd ed., New York, N.Y.: Springer-Verlag, 1981 1.9. Peter S. Maybeck, Stochastic

Optimal portfolio selection in a Lévy market with uncontrolled cash flow and only risky assets

NASA Astrophysics Data System (ADS)

Zeng, Yan; Li, Zhongfei; Wu, Huiling

2013-03-01

This article considers an investor who has an exogenous cash flow evolving according to a Lévy process and invests in a financial market consisting of only risky assets, whose prices are governed by exponential Lévy processes. Two continuous-time portfolio selection problems are studied for the investor. One is a benchmark problem, and the other is a mean-variance problem. The first problem is solved by adopting the stochastic dynamic programming approach, and the obtained results are extended to the second problem by employing the duality theory. Closed-form solutions of these two problems are derived. Some existing results are found to be special cases of our results.

The Sharma-Parthasarathy stochastic two-body problem

NASA Astrophysics Data System (ADS)

Cresson, J.; Pierret, F.; Puig, B.

2015-03-01

We study the Sharma-Parthasarathy stochastic two-body problem introduced by Sharma and Parthasarathy in ["Dynamics of a stochastically perturbed two-body problem," Proc. R. Soc. A 463, 979-1003 (2007)]. In particular, we focus on the preservation of some fundamental features of the classical two-body problem like the Hamiltonian structure and first integrals in the stochastic case. Numerical simulations are performed which illustrate the dynamical behaviour of the osculating elements as the semi-major axis, the eccentricity, and the pericenter. We also derive a stochastic version of Gauss's equations in the planar case.

Fault Tolerant Optimal Control.

DTIC Science & Technology

1982-08-01

subsystem is modelled by deterministic or stochastic finite-dimensional vector differential or difference equations. The parameters of these equations...is no partial differential equation that must be solved. Thus we can sidestep the inability to solve the Bellman equation for control problems with x...transition models and cost functionals can be reduced to the search for solutions of nonlinear partial differential equations using ’verification

Impact of Uncertainty from Load-Based Reserves and Renewables on Dispatch Costs and Emissions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Bowen; Maroukis, Spencer D.; Lin, Yashen

2016-11-21

Aggregations of controllable loads are considered to be a fast-responding, cost-efficient, and environmental-friendly candidate for power system ancillary services. Unlike conventional service providers, the potential capacity from the aggregation is highly affected by factors like ambient conditions and load usage patterns. Previous work modeled aggregations of controllable loads (such as air conditioners) as thermal batteries, which are capable of providing reserves but with uncertain capacity. A stochastic optimal power flow problem was formulated to manage this uncertainty, as well as uncertainty in renewable generation. In this paper, we explore how the types and levels of uncertainty, generation reserve costs, andmore » controllable load capacity affect the dispatch solution, operational costs, and CO2 emissions. We also compare the results of two methods for solving the stochastic optimization problem, namely the probabilistically robust method and analytical reformulation assuming Gaussian distributions. Case studies are conducted on a modified IEEE 9-bus system with renewables, controllable loads, and congestion. We find that different types and levels of uncertainty have significant impacts on dispatch and emissions. More controllable loads and less conservative solution methodologies lead to lower costs and emissions.« less

Particle Swarm Optimization algorithms for geophysical inversion, practical hints

NASA Astrophysics Data System (ADS)

Garcia Gonzalo, E.; Fernandez Martinez, J.; Fernandez Alvarez, J.; Kuzma, H.; Menendez Perez, C.

2008-12-01

PSO is a stochastic optimization technique that has been successfully used in many different engineering fields. PSO algorithm can be physically interpreted as a stochastic damped mass-spring system (Fernandez Martinez and Garcia Gonzalo 2008). Based on this analogy we present a whole family of PSO algorithms and their respective first order and second order stability regions. Their performance is also checked using synthetic functions (Rosenbrock and Griewank) showing a degree of ill-posedness similar to that found in many geophysical inverse problems. Finally, we present the application of these algorithms to the analysis of a Vertical Electrical Sounding inverse problem associated to a seawater intrusion in a coastal aquifer in South Spain. We analyze the role of PSO parameters (inertia, local and global accelerations and discretization step), both in convergence curves and in the a posteriori sampling of the depth of an intrusion. Comparison is made with binary genetic algorithms and simulated annealing. As result of this analysis, practical hints are given to select the correct algorithm and to tune the corresponding PSO parameters. Fernandez Martinez, J.L., Garcia Gonzalo, E., 2008a. The generalized PSO: a new door to PSO evolution. Journal of Artificial Evolution and Applications. DOI:10.1155/2008/861275.

Characterization of the probabilistic traveling salesman problem.

PubMed

Bowler, Neill E; Fink, Thomas M A; Ball, Robin C

2003-09-01

We show that stochastic annealing can be successfully applied to gain new results on the probabilistic traveling salesman problem. The probabilistic "traveling salesman" must decide on an a priori order in which to visit n cities (randomly distributed over a unit square) before learning that some cities can be omitted. We find the optimized average length of the pruned tour follows E(L(pruned))=sqrt[np](0.872-0.105p)f(np), where p is the probability of a city needing to be visited, and f(np)-->1 as np--> infinity. The average length of the a priori tour (before omitting any cities) is found to follow E(L(a priori))=sqrt[n/p]beta(p), where beta(p)=1/[1.25-0.82 ln(p)] is measured for 0.05< or =p< or =0.6. Scaling arguments and indirect measurements suggest that beta(p) tends towards a constant for p<0.03. Our stochastic annealing algorithm is based on limited sampling of the pruned tour lengths, exploiting the sampling error to provide the analog of thermal fluctuations in simulated (thermal) annealing. The method has general application to the optimization of functions whose cost to evaluate rises with the precision required.

Optimizing Integrated Terminal Airspace Operations Under Uncertainty

NASA Technical Reports Server (NTRS)

Bosson, Christabelle; Xue, Min; Zelinski, Shannon

2014-01-01

In the terminal airspace, integrated departures and arrivals have the potential to increase operations efficiency. Recent research has developed geneticalgorithm- based schedulers for integrated arrival and departure operations under uncertainty. This paper presents an alternate method using a machine jobshop scheduling formulation to model the integrated airspace operations. A multistage stochastic programming approach is chosen to formulate the problem and candidate solutions are obtained by solving sample average approximation problems with finite sample size. Because approximate solutions are computed, the proposed algorithm incorporates the computation of statistical bounds to estimate the optimality of the candidate solutions. A proof-ofconcept study is conducted on a baseline implementation of a simple problem considering a fleet mix of 14 aircraft evolving in a model of the Los Angeles terminal airspace. A more thorough statistical analysis is also performed to evaluate the impact of the number of scenarios considered in the sampled problem. To handle extensive sampling computations, a multithreading technique is introduced.

Optimization in the utility maximization framework for conservation planning: a comparison of solution procedures in a study of multifunctional agriculture

PubMed Central

Stoms, David M.; Davis, Frank W.

2014-01-01

Quantitative methods of spatial conservation prioritization have traditionally been applied to issues in conservation biology and reserve design, though their use in other types of natural resource management is growing. The utility maximization problem is one form of a covering problem where multiple criteria can represent the expected social benefits of conservation action. This approach allows flexibility with a problem formulation that is more general than typical reserve design problems, though the solution methods are very similar. However, few studies have addressed optimization in utility maximization problems for conservation planning, and the effect of solution procedure is largely unquantified. Therefore, this study mapped five criteria describing elements of multifunctional agriculture to determine a hypothetical conservation resource allocation plan for agricultural land conservation in the Central Valley of CA, USA. We compared solution procedures within the utility maximization framework to determine the difference between an open source integer programming approach and a greedy heuristic, and find gains from optimization of up to 12%. We also model land availability for conservation action as a stochastic process and determine the decline in total utility compared to the globally optimal set using both solution algorithms. Our results are comparable to other studies illustrating the benefits of optimization for different conservation planning problems, and highlight the importance of maximizing the effectiveness of limited funding for conservation and natural resource management. PMID:25538868

Optimization in the utility maximization framework for conservation planning: a comparison of solution procedures in a study of multifunctional agriculture

USGS Publications Warehouse

Kreitler, Jason R.; Stoms, David M.; Davis, Frank W.

2014-01-01

Quantitative methods of spatial conservation prioritization have traditionally been applied to issues in conservation biology and reserve design, though their use in other types of natural resource management is growing. The utility maximization problem is one form of a covering problem where multiple criteria can represent the expected social benefits of conservation action. This approach allows flexibility with a problem formulation that is more general than typical reserve design problems, though the solution methods are very similar. However, few studies have addressed optimization in utility maximization problems for conservation planning, and the effect of solution procedure is largely unquantified. Therefore, this study mapped five criteria describing elements of multifunctional agriculture to determine a hypothetical conservation resource allocation plan for agricultural land conservation in the Central Valley of CA, USA. We compared solution procedures within the utility maximization framework to determine the difference between an open source integer programming approach and a greedy heuristic, and find gains from optimization of up to 12%. We also model land availability for conservation action as a stochastic process and determine the decline in total utility compared to the globally optimal set using both solution algorithms. Our results are comparable to other studies illustrating the benefits of optimization for different conservation planning problems, and highlight the importance of maximizing the effectiveness of limited funding for conservation and natural resource management.

Stochastic Leader Gravitational Search Algorithm for Enhanced Adaptive Beamforming Technique

PubMed Central

Darzi, Soodabeh; Islam, Mohammad Tariqul; Tiong, Sieh Kiong; Kibria, Salehin; Singh, Mandeep

2015-01-01

In this paper, stochastic leader gravitational search algorithm (SL-GSA) based on randomized k is proposed. Standard GSA (SGSA) utilizes the best agents without any randomization, thus it is more prone to converge at suboptimal results. Initially, the new approach randomly choses k agents from the set of all agents to improve the global search ability. Gradually, the set of agents is reduced by eliminating the agents with the poorest performances to allow rapid convergence. The performance of the SL-GSA was analyzed for six well-known benchmark functions, and the results are compared with SGSA and some of its variants. Furthermore, the SL-GSA is applied to minimum variance distortionless response (MVDR) beamforming technique to ensure compatibility with real world optimization problems. The proposed algorithm demonstrates superior convergence rate and quality of solution for both real world problems and benchmark functions compared to original algorithm and other recent variants of SGSA. PMID:26552032

A modeling framework for optimal long-term care insurance purchase decisions in retirement planning.

PubMed

Gupta, Aparna; Li, Lepeng

2004-05-01

The level of need and costs of obtaining long-term care (LTC) during retired life require that planning for it is an integral part of retirement planning. In this paper, we divide retirement planning into two phases, pre-retirement and post-retirement. On the basis of four interrelated models for health evolution, wealth evolution, LTC insurance premium and coverage, and LTC cost structure, a framework for optimal LTC insurance purchase decisions in the pre-retirement phase is developed. Optimal decisions are obtained by developing a trade-off between post-retirement LTC costs and LTC insurance premiums and coverage. Two-way branching models are used to model stochastic health events and asset returns. The resulting optimization problem is formulated as a dynamic programming problem. We compare the optimal decision under two insurance purchase scenarios: one assumes that insurance is purchased for good and other assumes it may be purchased, relinquished and re-purchased. Sensitivity analysis is performed for the retirement age.

Optimal management of a stochastically varying population when policy adjustment is costly.

PubMed

Boettiger, Carl; Bode, Michael; Sanchirico, James N; Lariviere, Jacob; Hastings, Alan; Armsworth, Paul R

2016-04-01

Ecological systems are dynamic and policies to manage them need to respond to that variation. However, policy adjustments will sometimes be costly, which means that fine-tuning a policy to track variability in the environment very tightly will only sometimes be worthwhile. We use a classic fisheries management problem, how to manage a stochastically varying population using annually varying quotas in order to maximize profit, to examine how costs of policy adjustment change optimal management recommendations. Costs of policy adjustment (changes in fishing quotas through time) could take different forms. For example, these costs may respond to the size of the change being implemented, or there could be a fixed cost any time a quota change is made. We show how different forms of policy costs have contrasting implications for optimal policies. Though it is frequently assumed that costs to adjusting policies will dampen variation in the policy, we show that certain cost structures can actually increase variation through time. We further show that failing to account for adjustment costs has a consistently worse economic impact than would assuming these costs are present when they are not.

Dynamic remapping decisions in multi-phase parallel computations

NASA Technical Reports Server (NTRS)

Nicol, D. M.; Reynolds, P. F., Jr.

1986-01-01

The effectiveness of any given mapping of workload to processors in a parallel system is dependent on the stochastic behavior of the workload. Program behavior is often characterized by a sequence of phases, with phase changes occurring unpredictably. During a phase, the behavior is fairly stable, but may become quite different during the next phase. Thus a workload assignment generated for one phase may hinder performance during the next phase. We consider the problem of deciding whether to remap a paralled computation in the face of uncertainty in remapping's utility. Fundamentally, it is necessary to balance the expected remapping performance gain against the delay cost of remapping. This paper treats this problem formally by constructing a probabilistic model of a computation with at most two phases. We use stochastic dynamic programming to show that the remapping decision policy which minimizes the expected running time of the computation has an extremely simple structure: the optimal decision at any step is followed by comparing the probability of remapping gain against a threshold. This theoretical result stresses the importance of detecting a phase change, and assessing the possibility of gain from remapping. We also empirically study the sensitivity of optimal performance to imprecise decision threshold. Under a wide range of model parameter values, we find nearly optimal performance if remapping is chosen simply when the gain probability is high. These results strongly suggest that except in extreme cases, the remapping decision problem is essentially that of dynamically determining whether gain can be achieved by remapping after a phase change; precise quantification of the decision model parameters is not necessary.

A stochastic framework for spot-scanning particle therapy.

PubMed

Robini, Marc; Yuemin Zhu; Wanyu Liu; Magnin, Isabelle

2016-08-01

In spot-scanning particle therapy, inverse treatment planning is usually limited to finding the optimal beam fluences given the beam trajectories and energies. We address the much more challenging problem of jointly optimizing the beam fluences, trajectories and energies. For this purpose, we design a simulated annealing algorithm with an exploration mechanism that balances the conflicting demands of a small mixing time at high temperatures and a reasonable acceptance rate at low temperatures. Numerical experiments substantiate the relevance of our approach and open new horizons to spot-scanning particle therapy.

Adaptive Multi-Agent Systems for Constrained Optimization

NASA Technical Reports Server (NTRS)

Macready, William; Bieniawski, Stefan; Wolpert, David H.

2004-01-01

Product Distribution (PD) theory is a new framework for analyzing and controlling distributed systems. Here we demonstrate its use for distributed stochastic optimization. First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (probability distribution of) the joint state of the agents. When the game in question is a team game with constraints, that equilibrium optimizes the expected value of the team game utility, subject to those constraints. The updating of the Lagrange parameters in the Lagrangian can be viewed as a form of automated annealing, that focuses the MAS more and more on the optimal pure strategy. This provides a simple way to map the solution of any constrained optimization problem onto the equilibrium of a Multi-Agent System (MAS). We present computer experiments involving both the Queen s problem and K-SAT validating the predictions of PD theory and its use for off-the-shelf distributed adaptive optimization.

A two-stage stochastic rule-based model to determine pre-assembly buffer content

NASA Astrophysics Data System (ADS)

Gunay, Elif Elcin; Kula, Ufuk

2018-01-01

This study considers instant decision-making needs of the automobile manufactures for resequencing vehicles before final assembly (FA). We propose a rule-based two-stage stochastic model to determine the number of spare vehicles that should be kept in the pre-assembly buffer to restore the altered sequence due to paint defects and upstream department constraints. First stage of the model decides the spare vehicle quantities, where the second stage model recovers the scrambled sequence respect to pre-defined rules. The problem is solved by sample average approximation (SAA) algorithm. We conduct a numerical study to compare the solutions of heuristic model with optimal ones and provide following insights: (i) as the mismatch between paint entrance and scheduled sequence decreases, the rule-based heuristic model recovers the scrambled sequence as good as the optimal resequencing model, (ii) the rule-based model is more sensitive to the mismatch between the paint entrance and scheduled sequences for recovering the scrambled sequence, (iii) as the defect rate increases, the difference in recovery effectiveness between rule-based heuristic and optimal solutions increases, (iv) as buffer capacity increases, the recovery effectiveness of the optimization model outperforms heuristic model, (v) as expected the rule-based model holds more inventory than the optimization model.

Planning a Target Renewable Portfolio using Atmospheric Modeling and Stochastic Optimization

NASA Astrophysics Data System (ADS)

Hart, E.; Jacobson, M. Z.

2009-12-01

A number of organizations have suggested that an 80% reduction in carbon emissions by 2050 is a necessary step to mitigate climate change and that decarbonization of the electricity sector is a crucial component of any strategy to meet this target. Integration of large renewable and intermittent generators poses many new problems in power system planning. In this study, we attempt to determine an optimal portfolio of renewable resources to meet best the fluctuating California load while also meeting an 80% carbon emissions reduction requirement. A stochastic optimization scheme is proposed that is based on a simplified model of the California electricity grid. In this single-busbar power system model, the load is met with generation from wind, solar thermal, photovoltaic, hydroelectric, geothermal, and natural gas plants. Wind speeds and insolation are calculated using GATOR-GCMOM, a global-through-urban climate-weather-air pollution model. Fields were produced for California and Nevada at 21km SN by 14 km WE spatial resolution every 15 minutes for the year 2006. Load data for 2006 were obtained from the California ISO OASIS database. Maximum installed capacities for wind and solar thermal generation were determined using a GIS analysis of potential development sites throughout the state. The stochastic optimization scheme requires that power balance be achieved in a number of meteorological and load scenarios that deviate from the forecasted (or modeled) data. By adjusting the error distributions of the forecasts, the model describes how improvements in wind speed and insolation forecasting may affect the optimal renewable portfolio. Using a simple model, we describe the diversity, size, and sensitivities of a renewable portfolio that is best suited to the resources and needs of California and that contributes significantly to reduction of the state’s carbon emissions.

Stochastic Seismic Inversion and Migration for Offshore Site Investigation in the Northern Gulf of Mexico

NASA Astrophysics Data System (ADS)

Son, J.; Medina-Cetina, Z.

2017-12-01

We discuss the comparison between deterministic and stochastic optimization approaches to the nonlinear geophysical full-waveform inverse problem, based on the seismic survey data from Mississippi Canyon in the Northern Gulf of Mexico. Since the subsea engineering and offshore construction projects actively require reliable ground models from various site investigations, the primary goal of this study is to reconstruct the accurate subsurface information of the soil and rock material profiles under the seafloor. The shallow sediment layers have naturally formed heterogeneous formations which may cause unwanted marine landslides or foundation failures of underwater infrastructure. We chose the quasi-Newton and simulated annealing as deterministic and stochastic optimization algorithms respectively. Seismic forward modeling based on finite difference method with absorbing boundary condition implements the iterative simulations in the inverse modeling. We briefly report on numerical experiments using a synthetic data as an offshore ground model which contains shallow artificial target profiles of geomaterials under the seafloor. We apply the seismic migration processing and generate Voronoi tessellation on two-dimensional space-domain to improve the computational efficiency of the imaging stratigraphical velocity model reconstruction. We then report on the detail of a field data implementation, which shows the complex geologic structures in the Northern Gulf of Mexico. Lastly, we compare the new inverted image of subsurface site profiles in the space-domain with the previously processed seismic image in the time-domain at the same location. Overall, stochastic optimization for seismic inversion with migration and Voronoi tessellation show significant promise to improve the subsurface imaging of ground models and improve the computational efficiency required for the full waveform inversion. We anticipate that by improving the inversion process of shallow layers from geophysical data will better support the offshore site investigation.

The Sharma-Parthasarathy stochastic two-body problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cresson, J.; SYRTE/Observatoire de Paris, 75014 Paris; Pierret, F.

2015-03-15

We study the Sharma-Parthasarathy stochastic two-body problem introduced by Sharma and Parthasarathy in [“Dynamics of a stochastically perturbed two-body problem,” Proc. R. Soc. A 463, 979-1003 (2007)]. In particular, we focus on the preservation of some fundamental features of the classical two-body problem like the Hamiltonian structure and first integrals in the stochastic case. Numerical simulations are performed which illustrate the dynamical behaviour of the osculating elements as the semi-major axis, the eccentricity, and the pericenter. We also derive a stochastic version of Gauss’s equations in the planar case.

A Q-Learning Approach to Flocking With UAVs in a Stochastic Environment.

PubMed

Hung, Shao-Ming; Givigi, Sidney N

2017-01-01

In the past two decades, unmanned aerial vehicles (UAVs) have demonstrated their efficacy in supporting both military and civilian applications, where tasks can be dull, dirty, dangerous, or simply too costly with conventional methods. Many of the applications contain tasks that can be executed in parallel, hence the natural progression is to deploy multiple UAVs working together as a force multiplier. However, to do so requires autonomous coordination among the UAVs, similar to swarming behaviors seen in animals and insects. This paper looks at flocking with small fixed-wing UAVs in the context of a model-free reinforcement learning problem. In particular, Peng's Q(λ) with a variable learning rate is employed by the followers to learn a control policy that facilitates flocking in a leader-follower topology. The problem is structured as a Markov decision process, where the agents are modeled as small fixed-wing UAVs that experience stochasticity due to disturbances such as winds and control noises, as well as weight and balance issues. Learned policies are compared to ones solved using stochastic optimal control (i.e., dynamic programming) by evaluating the average cost incurred during flight according to a cost function. Simulation results demonstrate the feasibility of the proposed learning approach at enabling agents to learn how to flock in a leader-follower topology, while operating in a nonstationary stochastic environment.

An energy-based perturbation and a taboo strategy for improving the searching ability of stochastic structural optimization methods

NASA Astrophysics Data System (ADS)

Cheng, Longjiu; Cai, Wensheng; Shao, Xueguang

2005-03-01

An energy-based perturbation and a new idea of taboo strategy are proposed for structural optimization and applied in a benchmark problem, i.e., the optimization of Lennard-Jones (LJ) clusters. It is proved that the energy-based perturbation is much better than the traditional random perturbation both in convergence speed and searching ability when it is combined with a simple greedy method. By tabooing the most wide-spread funnel instead of the visited solutions, the hit rate of other funnels can be significantly improved. Global minima of (LJ) clusters up to 200 atoms are found with high efficiency.

Limited variance control in statistical low thrust guidance analysis. [stochastic algorithm for SEP comet Encke flyby mission

NASA Technical Reports Server (NTRS)

Jacobson, R. A.

1975-01-01

Difficulties arise in guiding a solar electric propulsion spacecraft due to nongravitational accelerations caused by random fluctuations in the magnitude and direction of the thrust vector. These difficulties may be handled by using a low thrust guidance law based on the linear-quadratic-Gaussian problem of stochastic control theory with a minimum terminal miss performance criterion. Explicit constraints are imposed on the variances of the control parameters, and an algorithm based on the Hilbert space extension of a parameter optimization method is presented for calculation of gains in the guidance law. The terminal navigation of a 1980 flyby mission to the comet Encke is used as an example.

Final Technical Report: Sparse Grid Scenario Generation and Interior Algorithms for Stochastic Optimization in a Parallel Computing Environment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mehrotra, Sanjay

2016-09-07

The support from this grant resulted in seven published papers and a technical report. Two papers are published in SIAM J. on Optimization [87, 88]; two papers are published in IEEE Transactions on Power Systems [77, 78]; one paper is published in Smart Grid [79]; one paper is published in Computational Optimization and Applications [44] and one in INFORMS J. on Computing [67]). The works in [44, 67, 87, 88] were funded primarily by this DOE grant. The applied papers in [77, 78, 79] were also supported through a subcontract from the Argonne National Lab. We start by presenting ourmore » main research results on the scenario generation problem in Sections 1–2. We present our algorithmic results on interior point methods for convex optimization problems in Section 3. We describe a new ‘central’ cutting surface algorithm developed for solving large scale convex programming problems (as is the case with our proposed research) with semi-infinite number of constraints in Section 4. In Sections 5–6 we present our work on two application problems of interest to DOE.« less

Global optimization methods for engineering design

NASA Technical Reports Server (NTRS)

Arora, Jasbir S.

1990-01-01

The problem is to find a global minimum for the Problem P. Necessary and sufficient conditions are available for local optimality. However, global solution can be assured only under the assumption of convexity of the problem. If the constraint set S is compact and the cost function is continuous on it, existence of a global minimum is guaranteed. However, in view of the fact that no global optimality conditions are available, a global solution can be found only by an exhaustive search to satisfy Inequality. The exhaustive search can be organized in such a way that the entire design space need not be searched for the solution. This way the computational burden is reduced somewhat. It is concluded that zooming algorithm for global optimizations appears to be a good alternative to stochastic methods. More testing is needed; a general, robust, and efficient local minimizer is required. IDESIGN was used in all numerical calculations which is based on a sequential quadratic programming algorithm, and since feasible set keeps on shrinking, a good algorithm to find an initial feasible point is required. Such algorithms need to be developed and evaluated.

Reliability-based trajectory optimization using nonintrusive polynomial chaos for Mars entry mission

NASA Astrophysics Data System (ADS)

Huang, Yuechen; Li, Haiyang

2018-06-01

This paper presents the reliability-based sequential optimization (RBSO) method to settle the trajectory optimization problem with parametric uncertainties in entry dynamics for Mars entry mission. First, the deterministic entry trajectory optimization model is reviewed, and then the reliability-based optimization model is formulated. In addition, the modified sequential optimization method, in which the nonintrusive polynomial chaos expansion (PCE) method and the most probable point (MPP) searching method are employed, is proposed to solve the reliability-based optimization problem efficiently. The nonintrusive PCE method contributes to the transformation between the stochastic optimization (SO) and the deterministic optimization (DO) and to the approximation of trajectory solution efficiently. The MPP method, which is used for assessing the reliability of constraints satisfaction only up to the necessary level, is employed to further improve the computational efficiency. The cycle including SO, reliability assessment and constraints update is repeated in the RBSO until the reliability requirements of constraints satisfaction are satisfied. Finally, the RBSO is compared with the traditional DO and the traditional sequential optimization based on Monte Carlo (MC) simulation in a specific Mars entry mission to demonstrate the effectiveness and the efficiency of the proposed method.

Sparse Learning with Stochastic Composite Optimization.

PubMed

Zhang, Weizhong; Zhang, Lijun; Jin, Zhongming; Jin, Rong; Cai, Deng; Li, Xuelong; Liang, Ronghua; He, Xiaofei

2017-06-01

In this paper, we study Stochastic Composite Optimization (SCO) for sparse learning that aims to learn a sparse solution from a composite function. Most of the recent SCO algorithms have already reached the optimal expected convergence rate O(1/λT), but they often fail to deliver sparse solutions at the end either due to the limited sparsity regularization during stochastic optimization (SO) or due to the limitation in online-to-batch conversion. Even when the objective function is strongly convex, their high probability bounds can only attain O(√{log(1/δ)/T}) with δ is the failure probability, which is much worse than the expected convergence rate. To address these limitations, we propose a simple yet effective two-phase Stochastic Composite Optimization scheme by adding a novel powerful sparse online-to-batch conversion to the general Stochastic Optimization algorithms. We further develop three concrete algorithms, OptimalSL, LastSL and AverageSL, directly under our scheme to prove the effectiveness of the proposed scheme. Both the theoretical analysis and the experiment results show that our methods can really outperform the existing methods at the ability of sparse learning and at the meantime we can improve the high probability bound to approximately O(log(log(T)/δ)/λT).

A New Control Paradigm for Stochastic Differential Equations

NASA Astrophysics Data System (ADS)

Schmid, Matthias J. A.

This study presents a novel comprehensive approach to the control of dynamic systems under uncertainty governed by stochastic differential equations (SDEs). Large Deviations (LD) techniques are employed to arrive at a control law for a large class of nonlinear systems minimizing sample path deviations. Thereby, a paradigm shift is suggested from point-in-time to sample path statistics on function spaces. A suitable formal control framework which leverages embedded Freidlin-Wentzell theory is proposed and described in detail. This includes the precise definition of the control objective and comprises an accurate discussion of the adaptation of the Freidlin-Wentzell theorem to the particular situation. The new control design is enabled by the transformation of an ill-posed control objective into a well-conditioned sequential optimization problem. A direct numerical solution process is presented using quadratic programming, but the emphasis is on the development of a closed-form expression reflecting the asymptotic deviation probability of a particular nominal path. This is identified as the key factor in the success of the new paradigm. An approach employing the second variation and the differential curvature of the effective action is suggested for small deviation channels leading to the Jacobi field of the rate function and the subsequently introduced Jacobi field performance measure. This closed-form solution is utilized in combination with the supplied parametrization of the objective space. For the first time, this allows for an LD based control design applicable to a large class of nonlinear systems. Thus, Minimum Large Deviations (MLD) control is effectively established in a comprehensive structured framework. The construction of the new paradigm is completed by an optimality proof for the Jacobi field performance measure, an interpretive discussion, and a suggestion for efficient implementation. The potential of the new approach is exhibited by its extension to scalar systems subject to state-dependent noise and to systems of higher order. The suggested control paradigm is further advanced when a sequential application of MLD control is considered. This technique yields a nominal path corresponding to the minimum total deviation probability on the entire time domain. It is demonstrated that this sequential optimization concept can be unified in a single objective function which is revealed to be the Jacobi field performance index on the entire domain subject to an endpoint deviation. The emerging closed-form term replaces the previously required nested optimization and, thus, results in a highly efficient application-ready control design. This effectively substantiates Minimum Path Deviation (MPD) control. The proposed control paradigm allows the specific problem of stochastic cost control to be addressed as a special case. This new technique is employed within this study for the stochastic cost problem giving rise to Cost Constrained MPD (CCMPD) as well as to Minimum Quadratic Cost Deviation (MQCD) control. An exemplary treatment of a generic scalar nonlinear system subject to quadratic costs is performed for MQCD control to demonstrate the elementary expandability of the new control paradigm. This work concludes with a numerical evaluation of both MPD and CCMPD control for three exemplary benchmark problems. Numerical issues associated with the simulation of SDEs are briefly discussed and illustrated. The numerical examples furnish proof of the successful design. This study is complemented by a thorough review of statistical control methods, stochastic processes, Large Deviations techniques and the Freidlin-Wentzell theory, providing a comprehensive, self-contained account. The presentation of the mathematical tools and concepts is of a unique character, specifically addressing an engineering audience.

QUADRO: A SUPERVISED DIMENSION REDUCTION METHOD VIA RAYLEIGH QUOTIENT OPTIMIZATION.

PubMed

Fan, Jianqing; Ke, Zheng Tracy; Liu, Han; Xia, Lucy

We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method-named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization)-for analyzing high-dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent scientific interests. One major challenge of Rayleigh quotient optimization is that the variance of quadratic statistics involves all fourth cross-moments of predictors, which are infeasible to compute for high-dimensional applications and may accumulate too many stochastic errors. This issue is resolved by considering a family of elliptical models. Moreover, for heavy-tail distributions, robust estimates of mean vectors and covariance matrices are employed to guarantee uniform convergence in estimating non-polynomially many parameters, even though only the fourth moments are assumed. Methodologically, QUADRO is based on elliptical models which allow us to formulate the Rayleigh quotient maximization as a convex optimization problem. Computationally, we propose an efficient linearized augmented Lagrangian method to solve the constrained optimization problem. Theoretically, we provide explicit rates of convergence in terms of Rayleigh quotient under both Gaussian and general elliptical models. Thorough numerical results on both synthetic and real datasets are also provided to back up our theoretical results.

Stochastic optimization algorithms for barrier dividend strategies

NASA Astrophysics Data System (ADS)

Yin, G.; Song, Q. S.; Yang, H.

2009-01-01

This work focuses on finding optimal barrier policy for an insurance risk model when the dividends are paid to the share holders according to a barrier strategy. A new approach based on stochastic optimization methods is developed. Compared with the existing results in the literature, more general surplus processes are considered. Precise models of the surplus need not be known; only noise-corrupted observations of the dividends are used. Using barrier-type strategies, a class of stochastic optimization algorithms are developed. Convergence of the algorithm is analyzed; rate of convergence is also provided. Numerical results are reported to demonstrate the performance of the algorithm.

Gesellschaft fuer angewandte Mathematik und Mechanik, Scientific Annual Meeting, Universitaet Stuttgart, Federal Republic of Germany, Apr. 13-17, 1987, Reports

NASA Astrophysics Data System (ADS)

Recent advances in the analytical and numerical treatment of physical and engineering problems are discussed in reviews and reports. Topics addressed include fluid mechanics, numerical methods for differential equations, FEM approaches, and boundary-element methods. Consideration is given to optimization, decision theory, stochastics, actuarial mathematics, applied mathematics and mathematical physics, and numerical analysis.

A black box optimization approach to parameter estimation in a model for long/short term variations dynamics of commodity prices

NASA Astrophysics Data System (ADS)

De Santis, Alberto; Dellepiane, Umberto; Lucidi, Stefano

2012-11-01

In this paper we investigate the estimation problem for a model of the commodity prices. This model is a stochastic state space dynamical model and the problem unknowns are the state variables and the system parameters. Data are represented by the commodity spot prices, very seldom time series of Futures contracts are available for free. Both the system joint likelihood function (state variables and parameters) and the system marginal likelihood (the state variables are eliminated) function are addressed.

A two-stage stochastic optimization model for scheduling electric vehicle charging loads to relieve distribution-system constraints

DOE PAGES

Wu, Fei; Sioshansi, Ramteen

2017-05-25

Electric vehicles (EVs) hold promise to improve the energy efficiency and environmental impacts of transportation. However, widespread EV use can impose significant stress on electricity-distribution systems due to their added charging loads. This paper proposes a centralized EV charging-control model, which schedules the charging of EVs that have flexibility. This flexibility stems from EVs that are parked at the charging station for a longer duration of time than is needed to fully recharge the battery. The model is formulated as a two-stage stochastic optimization problem. The model captures the use of distributed energy resources and uncertainties around EV arrival timesmore » and charging demands upon arrival, non-EV loads on the distribution system, energy prices, and availability of energy from the distributed energy resources. We use a Monte Carlo-based sample-average approximation technique and an L-shaped method to solve the resulting optimization problem efficiently. We also apply a sequential sampling technique to dynamically determine the optimal size of the randomly sampled scenario tree to give a solution with a desired quality at minimal computational cost. Here, we demonstrate the use of our model on a Central-Ohio-based case study. We show the benefits of the model in reducing charging costs, negative impacts on the distribution system, and unserved EV-charging demand compared to simpler heuristics. Lastly, we also conduct sensitivity analyses, to show how the model performs and the resulting costs and load profiles when the design of the station or EV-usage parameters are changed.« less

Optimizing conjunctive use of surface water and groundwater resources with stochastic dynamic programming

NASA Astrophysics Data System (ADS)

Davidsen, Claus; Liu, Suxia; Mo, Xingguo; Rosbjerg, Dan; Bauer-Gottwein, Peter

2014-05-01

Optimal management of conjunctive use of surface water and groundwater has been attempted with different algorithms in the literature. In this study, a hydro-economic modelling approach to optimize conjunctive use of scarce surface water and groundwater resources under uncertainty is presented. A stochastic dynamic programming (SDP) approach is used to minimize the basin-wide total costs arising from water allocations and water curtailments. Dynamic allocation problems with inclusion of groundwater resources proved to be more complex to solve with SDP than pure surface water allocation problems due to head-dependent pumping costs. These dynamic pumping costs strongly affect the total costs and can lead to non-convexity of the future cost function. The water user groups (agriculture, industry, domestic) are characterized by inelastic demands and fixed water allocation and water supply curtailment costs. As in traditional SDP approaches, one step-ahead sub-problems are solved to find the optimal management at any time knowing the inflow scenario and reservoir/aquifer storage levels. These non-linear sub-problems are solved using a genetic algorithm (GA) that minimizes the sum of the immediate and future costs for given surface water reservoir and groundwater aquifer end storages. The immediate cost is found by solving a simple linear allocation sub-problem, and the future costs are assessed by interpolation in the total cost matrix from the following time step. Total costs for all stages, reservoir states, and inflow scenarios are used as future costs to drive a forward moving simulation under uncertain water availability. The use of a GA to solve the sub-problems is computationally more costly than a traditional SDP approach with linearly interpolated future costs. However, in a two-reservoir system the future cost function would have to be represented by a set of planes, and strict convexity in both the surface water and groundwater dimension cannot be maintained. The optimization framework based on the GA is still computationally feasible and represents a clean and customizable method. The method has been applied to the Ziya River basin, China. The basin is located on the North China Plain and is subject to severe water scarcity, which includes surface water droughts and groundwater over-pumping. The head-dependent groundwater pumping costs will enable assessment of the long-term effects of increased electricity prices on the groundwater pumping. The coupled optimization framework is used to assess realistic alternative development scenarios for the basin. In particular the potential for using electricity pricing policies to reach sustainable groundwater pumping is investigated.

Diagnostic Assessment of the Difficulty Using Direct Policy Search in Many-Objective Reservoir Control

NASA Astrophysics Data System (ADS)

Zatarain-Salazar, J.; Reed, P. M.; Herman, J. D.; Giuliani, M.; Castelletti, A.

2014-12-01

Globally reservoir operations provide fundamental services to water supply, energy generation, recreation, and ecosystems. The pressures of expanding populations, climate change, and increased energy demands are motivating a significant investment in re-operationalizing existing reservoirs or defining operations for new reservoirs. Recent work has highlighted the potential benefits of exploiting recent advances in many-objective optimization and direct policy search (DPS) to aid in addressing these systems' multi-sector demand tradeoffs. This study contributes to a comprehensive diagnostic assessment of multi-objective evolutionary optimization algorithms (MOEAs) efficiency, effectiveness, reliability, and controllability when supporting DPS for the Conowingo dam in the Lower Susquehanna River Basin. The Lower Susquehanna River is an interstate water body that has been subject to intensive water management efforts due to the system's competing demands from urban water supply, atomic power plant cooling, hydropower production, and federally regulated environmental flows. Seven benchmark and state-of-the-art MOEAs are tested on deterministic and stochastic instances of the Susquehanna test case. In the deterministic formulation, the operating objectives are evaluated over the historical realization of the hydroclimatic variables (i.e., inflows and evaporation rates). In the stochastic formulation, the same objectives are instead evaluated over an ensemble of stochastic inflows and evaporation rates realizations. The algorithms are evaluated in their ability to support DPS in discovering reservoir operations that compose the tradeoffs for six multi-sector performance objectives with thirty-two decision variables. Our diagnostic results highlight that many-objective DPS is very challenging for modern MOEAs and that epsilon dominance is critical for attaining high levels of performance. Epsilon dominance algorithms epsilon-MOEA, epsilon-NSGAII and the auto adaptive Borg MOEA, are statistically superior for the six-objective Susquehanna instance of this important class of problems. Additionally, shifting from deterministic history-based DPS to stochastic DPS significantly increases the difficulty of the problem.

Multi-period project portfolio selection under risk considerations and stochastic income

NASA Astrophysics Data System (ADS)

Tofighian, Ali Asghar; Moezzi, Hamid; Khakzar Barfuei, Morteza; Shafiee, Mahmood

2018-02-01

This paper deals with multi-period project portfolio selection problem. In this problem, the available budget is invested on the best portfolio of projects in each period such that the net profit is maximized. We also consider more realistic assumptions to cover wider range of applications than those reported in previous studies. A novel mathematical model is presented to solve the problem, considering risks, stochastic incomes, and possibility of investing extra budget in each time period. Due to the complexity of the problem, an effective meta-heuristic method hybridized with a local search procedure is presented to solve the problem. The algorithm is based on genetic algorithm (GA), which is a prominent method to solve this type of problems. The GA is enhanced by a new solution representation and well selected operators. It also is hybridized with a local search mechanism to gain better solution in shorter time. The performance of the proposed algorithm is then compared with well-known algorithms, like basic genetic algorithm (GA), particle swarm optimization (PSO), and electromagnetism-like algorithm (EM-like) by means of some prominent indicators. The computation results show the superiority of the proposed algorithm in terms of accuracy, robustness and computation time. At last, the proposed algorithm is wisely combined with PSO to improve the computing time considerably.

Quadruped Robot Locomotion using a Global Optimization Stochastic Algorithm

NASA Astrophysics Data System (ADS)

Oliveira, Miguel; Santos, Cristina; Costa, Lino; Ferreira, Manuel

2011-09-01

The problem of tuning nonlinear dynamical systems parameters, such that the attained results are considered good ones, is a relevant one. This article describes the development of a gait optimization system that allows a fast but stable robot quadruped crawl gait. We combine bio-inspired Central Patterns Generators (CPGs) and Genetic Algorithms (GA). CPGs are modelled as autonomous differential equations, that generate the necessar y limb movement to perform the required walking gait. The GA finds parameterizations of the CPGs parameters which attain good gaits in terms of speed, vibration and stability. Moreover, two constraint handling techniques based on tournament selection and repairing mechanism are embedded in the GA to solve the proposed constrained optimization problem and make the search more efficient. The experimental results, performed on a simulated Aibo robot, demonstrate that our approach allows low vibration with a high velocity and wide stability margin for a quadruped slow crawl gait.

The quasi-optimality criterion in the linear functional strategy

NASA Astrophysics Data System (ADS)

Kindermann, Stefan; Pereverzyev, Sergiy, Jr.; Pilipenko, Andrey

2018-07-01

The linear functional strategy for the regularization of inverse problems is considered. For selecting the regularization parameter therein, we propose the heuristic quasi-optimality principle and some modifications including the smoothness of the linear functionals. We prove convergence rates for the linear functional strategy with these heuristic rules taking into account the smoothness of the solution and the functionals and imposing a structural condition on the noise. Furthermore, we study these noise conditions in both a deterministic and stochastic setup and verify that for mildly-ill-posed problems and Gaussian noise, these conditions are satisfied almost surely, where on the contrary, in the severely-ill-posed case and in a similar setup, the corresponding noise condition fails to hold. Moreover, we propose an aggregation method for adaptively optimizing the parameter choice rule by making use of improved rates for linear functionals. Numerical results indicate that this method yields better results than the standard heuristic rule.

A Multiobjective Optimization Framework for Online Stochastic Optimal Control in Hybrid Electric Vehicles

DOE PAGES

Malikopoulos, Andreas

2015-01-01

The increasing urgency to extract additional efficiency from hybrid propulsion systems has led to the development of advanced power management control algorithms. In this paper we address the problem of online optimization of the supervisory power management control in parallel hybrid electric vehicles (HEVs). We model HEV operation as a controlled Markov chain and we show that the control policy yielding the Pareto optimal solution minimizes online the long-run expected average cost per unit time criterion. The effectiveness of the proposed solution is validated through simulation and compared to the solution derived with dynamic programming using the average cost criterion.more » Both solutions achieved the same cumulative fuel consumption demonstrating that the online Pareto control policy is an optimal control policy.« less

Post Pareto optimization-A case

NASA Astrophysics Data System (ADS)

Popov, Stoyan; Baeva, Silvia; Marinova, Daniela

2017-12-01

Simulation performance may be evaluated according to multiple quality measures that are in competition and their simultaneous consideration poses a conflict. In the current study we propose a practical framework for investigating such simulation performance criteria, exploring the inherent conflicts amongst them and identifying the best available tradeoffs, based upon multi-objective Pareto optimization. This approach necessitates the rigorous derivation of performance criteria to serve as objective functions and undergo vector optimization. We demonstrate the effectiveness of our proposed approach by applying it with multiple stochastic quality measures. We formulate performance criteria of this use-case, pose an optimization problem, and solve it by means of a simulation-based Pareto approach. Upon attainment of the underlying Pareto Frontier, we analyze it and prescribe preference-dependent configurations for the optimal simulation training.

Improved hybrid optimization algorithm for 3D protein structure prediction.

PubMed

Zhou, Changjun; Hou, Caixia; Wei, Xiaopeng; Zhang, Qiang

2014-07-01

A new improved hybrid optimization algorithm - PGATS algorithm, which is based on toy off-lattice model, is presented for dealing with three-dimensional protein structure prediction problems. The algorithm combines the particle swarm optimization (PSO), genetic algorithm (GA), and tabu search (TS) algorithms. Otherwise, we also take some different improved strategies. The factor of stochastic disturbance is joined in the particle swarm optimization to improve the search ability; the operations of crossover and mutation that are in the genetic algorithm are changed to a kind of random liner method; at last tabu search algorithm is improved by appending a mutation operator. Through the combination of a variety of strategies and algorithms, the protein structure prediction (PSP) in a 3D off-lattice model is achieved. The PSP problem is an NP-hard problem, but the problem can be attributed to a global optimization problem of multi-extremum and multi-parameters. This is the theoretical principle of the hybrid optimization algorithm that is proposed in this paper. The algorithm combines local search and global search, which overcomes the shortcoming of a single algorithm, giving full play to the advantage of each algorithm. In the current universal standard sequences, Fibonacci sequences and real protein sequences are certified. Experiments show that the proposed new method outperforms single algorithms on the accuracy of calculating the protein sequence energy value, which is proved to be an effective way to predict the structure of proteins.

Comparison of SVAT models for simulating and optimizing deficit irrigation systems in arid and semi-arid countries under climate variability

NASA Astrophysics Data System (ADS)

Kloss, Sebastian; Schuetze, Niels; Schmitz, Gerd H.

2010-05-01

The strong competition for fresh water in order to fulfill the increased demand for food worldwide has led to a renewed interest in techniques to improve water use efficiency (WUE) such as controlled deficit irrigation. Furthermore, as the implementation of crop models into complex decision support systems becomes more and more common, it is imperative to reliably predict the WUE as ratio of water consumption and yield. The objective of this paper is the assessment of the problems the crop models - such as FAO-33, DAISY, and APSIM in this study - face when maximizing the WUE. We applied these crop models for calculating the risk in yield reduction in view of different sources of uncertainty (e.g. climate) employing a stochastic framework for decision support for the planning of water supply in irrigation. The stochastic framework consists of: (i) a weather generator for simulating regional impacts of climate change; (ii) a new tailor-made evolutionary optimization algorithm for optimal irrigation scheduling with limited water supply; and (iii) the above mentioned models for simulating water transport and crop growth in a sound manner. The results present stochastic crop water production functions (SCWPF) for different crops which can be used as basic tools for assessing the impact of climate variability on the risk for the potential yield. Case studies from India, Oman, Malawi, and France are presented to assess the differences in modeling water stress and yield response for the different crop models.

Robust Adaptive Modified Newton Algorithm for Generalized Eigendecomposition and Its Application

NASA Astrophysics Data System (ADS)

Yang, Jian; Yang, Feng; Xi, Hong-Sheng; Guo, Wei; Sheng, Yanmin

2007-12-01

We propose a robust adaptive algorithm for generalized eigendecomposition problems that arise in modern signal processing applications. To that extent, the generalized eigendecomposition problem is reinterpreted as an unconstrained nonlinear optimization problem. Starting from the proposed cost function and making use of an approximation of the Hessian matrix, a robust modified Newton algorithm is derived. A rigorous analysis of its convergence properties is presented by using stochastic approximation theory. We also apply this theory to solve the signal reception problem of multicarrier DS-CDMA to illustrate its practical application. The simulation results show that the proposed algorithm has fast convergence and excellent tracking capability, which are important in a practical time-varying communication environment.

Efficient boundary hunting via vector quantization

NASA Astrophysics Data System (ADS)

Diamantini, Claudia; Panti, Maurizio

2001-03-01

A great amount of information about a classification problem is contained in those instances falling near the decision boundary. This intuition dates back to the earliest studies in pattern recognition, and in the more recent adaptive approaches to the so called boundary hunting, such as the work of Aha et alii on Instance Based Learning and the work of Vapnik et alii on Support Vector Machines. The last work is of particular interest, since theoretical and experimental results ensure the accuracy of boundary reconstruction. However, its optimization approach has heavy computational and memory requirements, which limits its application on huge amounts of data. In the paper we describe an alternative approach to boundary hunting based on adaptive labeled quantization architectures. The adaptation is performed by a stochastic gradient algorithm for the minimization of the error probability. Error probability minimization guarantees the accurate approximation of the optimal decision boundary, while the use of a stochastic gradient algorithm defines an efficient method to reach such approximation. In the paper comparisons to Support Vector Machines are considered.

Application of stochastic particle swarm optimization algorithm to determine the graded refractive index distribution in participating media

NASA Astrophysics Data System (ADS)

Wei, Lin-Yang; Qi, Hong; Ren, Ya-Tao; Ruan, Li-Ming

2016-11-01

Inverse estimation of the refractive index distribution in one-dimensional participating media with graded refractive index (GRI) is investigated. The forward radiative transfer problem is solved by the Chebyshev collocation spectral method. The stochastic particle swarm optimization (SPSO) algorithm is employed to retrieve three kinds of GRI distribution, i.e. the linear, sinusoidal and quadratic GRI distribution. The retrieval accuracy of GRI distribution with different wall emissivity, optical thickness, absorption coefficients and scattering coefficients are discussed thoroughly. To improve the retrieval accuracy of quadratic GRI distribution, a double-layer model is proposed to supply more measurement information. The influence of measurement errors upon the precision of estimated results is also investigated. Considering the GRI distribution is unknown beforehand in practice, a quadratic function is employed to retrieve the linear GRI by SPSO algorithm. All the results show that the SPSO algorithm is applicable to retrieve different GRI distributions in participating media accurately even with noisy data.

Stochastic user equilibrium model with a tradable credit scheme and application in maximizing network reserve capacity

NASA Astrophysics Data System (ADS)

Han, Fei; Cheng, Lin

2017-04-01

The tradable credit scheme (TCS) outperforms congestion pricing in terms of social equity and revenue neutrality, apart from the same perfect performance on congestion mitigation. This article investigates the effectiveness and efficiency of TCS on enhancing transportation network capacity in a stochastic user equilibrium (SUE) modelling framework. First, the SUE and credit market equilibrium conditions are presented; then an equivalent general SUE model with TCS is established by virtue of two constructed functions, which can be further simplified under a specific probability distribution. To enhance the network capacity by utilizing TCS, a bi-level mathematical programming model is established for the optimal TCS design problem, with the upper level optimization objective maximizing network reserve capacity and lower level being the proposed SUE model. The heuristic sensitivity analysis-based algorithm is developed to solve the bi-level model. Three numerical examples are provided to illustrate the improvement effect of TCS on the network in different scenarios.

A robust multi-objective global supplier selection model under currency fluctuation and price discount

NASA Astrophysics Data System (ADS)

Zarindast, Atousa; Seyed Hosseini, Seyed Mohamad; Pishvaee, Mir Saman

2017-06-01

Robust supplier selection problem, in a scenario-based approach has been proposed, when the demand and exchange rates are subject to uncertainties. First, a deterministic multi-objective mixed integer linear programming is developed; then, the robust counterpart of the proposed mixed integer linear programming is presented using the recent extension in robust optimization theory. We discuss decision variables, respectively, by a two-stage stochastic planning model, a robust stochastic optimization planning model which integrates worst case scenario in modeling approach and finally by equivalent deterministic planning model. The experimental study is carried out to compare the performances of the three models. Robust model resulted in remarkable cost saving and it illustrated that to cope with such uncertainties, we should consider them in advance in our planning. In our case study different supplier were selected due to this uncertainties and since supplier selection is a strategic decision, it is crucial to consider these uncertainties in planning approach.

An integrated production-inventory model for the singlevendor two-buyer problem with partial backorder, stochastic demand, and service level constraints

NASA Astrophysics Data System (ADS)

Arfawi Kurdhi, Nughthoh; Adi Diwiryo, Toray; Sutanto

2016-02-01

This paper presents an integrated single-vendor two-buyer production-inventory model with stochastic demand and service level constraints. Shortage is permitted in the model, and partial backordered partial lost sale. The lead time demand is assumed follows a normal distribution and the lead time can be reduced by adding crashing cost. The lead time and ordering cost reductions are interdependent with logaritmic function relationship. A service level constraint policy corresponding to each buyer is considered in the model in order to limit the level of inventory shortages. The purpose of this research is to minimize joint total cost inventory model by finding the optimal order quantity, safety stock, lead time, and the number of lots delivered in one production run. The optimal production-inventory policy gained by the Lagrange method is shaped to account for the service level restrictions. Finally, a numerical example and effects of the key parameters are performed to illustrate the results of the proposed model.

Metaheuristic simulation optimisation for the stochastic multi-retailer supply chain

NASA Astrophysics Data System (ADS)

Omar, Marina; Mustaffa, Noorfa Haszlinna H.; Othman, Siti Norsyahida

2013-04-01

Supply Chain Management (SCM) is an important activity in all producing facilities and in many organizations to enable vendors, manufacturers and suppliers to interact gainfully and plan optimally their flow of goods and services. A simulation optimization approach has been widely used in research nowadays on finding the best solution for decision-making process in Supply Chain Management (SCM) that generally faced a complexity with large sources of uncertainty and various decision factors. Metahueristic method is the most popular simulation optimization approach. However, very few researches have applied this approach in optimizing the simulation model for supply chains. Thus, this paper interested in evaluating the performance of metahueristic method for stochastic supply chains in determining the best flexible inventory replenishment parameters that minimize the total operating cost. The simulation optimization model is proposed based on the Bees algorithm (BA) which has been widely applied in engineering application such as training neural networks for pattern recognition. BA is a new member of meta-heuristics. BA tries to model natural behavior of honey bees in food foraging. Honey bees use several mechanisms like waggle dance to optimally locate food sources and to search new ones. This makes them a good candidate for developing new algorithms for solving optimization problems. This model considers an outbound centralised distribution system consisting of one supplier and 3 identical retailers and is assumed to be independent and identically distributed with unlimited supply capacity at supplier.

Mean-Variance Hedging on Uncertain Time Horizon in a Market with a Jump

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kharroubi, Idris, E-mail: kharroubi@ceremade.dauphine.fr; Lim, Thomas, E-mail: lim@ensiie.fr; Ngoupeyou, Armand, E-mail: armand.ngoupeyou@univ-paris-diderot.fr

2013-12-15

In this work, we study the problem of mean-variance hedging with a random horizon T∧τ, where T is a deterministic constant and τ is a jump time of the underlying asset price process. We first formulate this problem as a stochastic control problem and relate it to a system of BSDEs with a jump. We then provide a verification theorem which gives the optimal strategy for the mean-variance hedging using the solution of the previous system of BSDEs. Finally, we prove that this system of BSDEs admits a solution via a decomposition approach coming from filtration enlargement theory.

General Results in Optimal Control of Discrete-Time Nonlinear Stochastic Systems

DTIC Science & Technology

1988-01-01

P. J. McLane, "Optimal Stochastic Control of Linear System. with State- and Control-Dependent Distur- bances," ZEEE Trans. 4uto. Contr., Vol. 16, No...Vol. 45, No. 1, pp. 359-362, 1987 (9] R. R. Mohler and W. J. Kolodziej, "An Overview of Stochastic Bilinear Control Processes," ZEEE Trans. Syst...34 J. of Math. anal. App.:, Vol. 47, pp. 156-161, 1974 [14) E. Yaz, "A Control Scheme for a Class of Discrete Nonlinear Stochastic Systems," ZEEE Trans

Optimal Estimation of Clock Values and Trends from Finite Data

NASA Technical Reports Server (NTRS)

Greenhall, Charles

2005-01-01

We show how to solve two problems of optimal linear estimation from a finite set of phase data. Clock noise is modeled as a stochastic process with stationary dth increments. The covariance properties of such a process are contained in the generalized autocovariance function (GACV). We set up two principles for optimal estimation: with the help of the GACV, these principles lead to a set of linear equations for the regression coefficients and some auxiliary parameters. The mean square errors of the estimators are easily calculated. The method can be used to check the results of other methods and to find good suboptimal estimators based on a small subset of the available data.

A theoretical comparison of evolutionary algorithms and simulated annealing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hart, W.E.

1995-08-28

This paper theoretically compares the performance of simulated annealing and evolutionary algorithms. Our main result is that under mild conditions a wide variety of evolutionary algorithms can be shown to have greater performance than simulated annealing after a sufficiently large number of function evaluations. This class of EAs includes variants of evolutionary strategie and evolutionary programming, the canonical genetic algorithm, as well as a variety of genetic algorithms that have been applied to combinatorial optimization problems. The proof of this result is based on a performance analysis of a very general class of stochastic optimization algorithms, which has implications formore » the performance of a variety of other optimization algorithm.« less

New control concepts for uncertain water resources systems: 1. Theory

NASA Astrophysics Data System (ADS)

Georgakakos, Aris P.; Yao, Huaming

1993-06-01

A major complicating factor in water resources systems management is handling unknown inputs. Stochastic optimization provides a sound mathematical framework but requires that enough data exist to develop statistical input representations. In cases where data records are insufficient (e.g., extreme events) or atypical of future input realizations, stochastic methods are inadequate. This article presents a control approach where input variables are only expected to belong in certain sets. The objective is to determine sets of admissible control actions guaranteeing that the system will remain within desirable bounds. The solution is based on dynamic programming and derived for the case where all sets are convex polyhedra. A companion paper (Yao and Georgakakos, this issue) addresses specific applications and problems in relation to reservoir system management.

Utility indifference pricing of insurance catastrophe derivatives.

PubMed

Eichler, Andreas; Leobacher, Gunther; Szölgyenyi, Michaela

2017-01-01

We propose a model for an insurance loss index and the claims process of a single insurance company holding a fraction of the total number of contracts that captures both ordinary losses and losses due to catastrophes. In this model we price a catastrophe derivative by the method of utility indifference pricing. The associated stochastic optimization problem is treated by techniques for piecewise deterministic Markov processes. A numerical study illustrates our results.

Decentralized Network Interdiction Games

DTIC Science & Technology

2015-12-31

approach is termed as the sample average approximation ( SAA ) method, and theories on the asymptotic convergence to the original problem’s optimal...used in the SAA method’s convergence. While we provided detailed proof of such convergence in [P3], a side benefit of the proof is that it weakens the...conditions required when applying the general SAA approach to the block-structured stochastic programming problem 17. As the conditions known in the

Airport security inspection process model and optimization based on GSPN

NASA Astrophysics Data System (ADS)

Mao, Shuainan

2018-04-01

Aiming at the efficiency of airport security inspection process, Generalized Stochastic Petri Net is used to establish the security inspection process model. The model is used to analyze the bottleneck problem of airport security inspection process. The solution to the bottleneck is given, which can significantly improve the efficiency and reduce the waiting time by adding the place for people to remove their clothes and the X-ray detector.

Stochastic gradient ascent outperforms gamers in the Quantum Moves game

NASA Astrophysics Data System (ADS)

Sels, Dries

2018-04-01

In a recent work on quantum state preparation, Sørensen and co-workers [Nature (London) 532, 210 (2016), 10.1038/nature17620] explore the possibility of using video games to help design quantum control protocols. The authors present a game called "Quantum Moves" (https://www.scienceathome.org/games/quantum-moves/) in which gamers have to move an atom from A to B by means of optical tweezers. They report that, "players succeed where purely numerical optimization fails." Moreover, by harnessing the player strategies, they can "outperform the most prominent established numerical methods." The aim of this Rapid Communication is to analyze the problem in detail and show that those claims are untenable. In fact, without any prior knowledge and starting from a random initial seed, a simple stochastic local optimization method finds near-optimal solutions which outperform all players. Counterdiabatic driving can even be used to generate protocols without resorting to numeric optimization. The analysis results in an accurate analytic estimate of the quantum speed limit which, apart from zero-point motion, is shown to be entirely classical in nature. The latter might explain why gamers are reasonably good at the game. A simple modification of the BringHomeWater challenge is proposed to test this hypothesis.

An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heydari, M.H., E-mail: heydari@stu.yazd.ac.ir; The Laboratory of Quantum Information Processing, Yazd University, Yazd; Hooshmandasl, M.R., E-mail: hooshmandasl@yazd.ac.ir

Because of the nonlinearity, closed-form solutions of many important stochastic functional equations are virtually impossible to obtain. Thus, numerical solutions are a viable alternative. In this paper, a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of Itô-integration is proposed for solving nonlinear stochastic Itô integral equations in large intervals. In the proposed method, a new technique for computing nonlinear terms in such problems is presented. The main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved. Errormore » analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As two useful applications, the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem.« less

Problems of Mathematical Finance by Stochastic Control Methods

NASA Astrophysics Data System (ADS)

Stettner, Łukasz

The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.

A Stochastic Employment Problem

ERIC Educational Resources Information Center

Wu, Teng

2013-01-01

The Stochastic Employment Problem(SEP) is a variation of the Stochastic Assignment Problem which analyzes the scenario that one assigns balls into boxes. Balls arrive sequentially with each one having a binary vector X = (X[subscript 1], X[subscript 2],...,X[subscript n]) attached, with the interpretation being that if X[subscript i] = 1 the ball…

A System-Oriented Approach for the Optimal Control of Process Chains under Stochastic Influences

NASA Astrophysics Data System (ADS)

Senn, Melanie; Schäfer, Julian; Pollak, Jürgen; Link, Norbert

2011-09-01

Process chains in manufacturing consist of multiple connected processes in terms of dynamic systems. The properties of a product passing through such a process chain are influenced by the transformation of each single process. There exist various methods for the control of individual processes, such as classical state controllers from cybernetics or function mapping approaches realized by statistical learning. These controllers ensure that a desired state is obtained at process end despite of variations in the input and disturbances. The interactions between the single processes are thereby neglected, but play an important role in the optimization of the entire process chain. We divide the overall optimization into two phases: (1) the solution of the optimization problem by Dynamic Programming to find the optimal control variable values for each process for any encountered end state of its predecessor and (2) the application of the optimal control variables at runtime for the detected initial process state. The optimization problem is solved by selecting adequate control variables for each process in the chain backwards based on predefined quality requirements for the final product. For the demonstration of the proposed concept, we have chosen a process chain from sheet metal manufacturing with simplified transformation functions.

Performance evaluation of different types of particle representation procedures of Particle Swarm Optimization in Job-shop Scheduling Problems

NASA Astrophysics Data System (ADS)

Izah Anuar, Nurul; Saptari, Adi

2016-02-01

This paper addresses the types of particle representation (encoding) procedures in a population-based stochastic optimization technique in solving scheduling problems known in the job-shop manufacturing environment. It intends to evaluate and compare the performance of different particle representation procedures in Particle Swarm Optimization (PSO) in the case of solving Job-shop Scheduling Problems (JSP). Particle representation procedures refer to the mapping between the particle position in PSO and the scheduling solution in JSP. It is an important step to be carried out so that each particle in PSO can represent a schedule in JSP. Three procedures such as Operation and Particle Position Sequence (OPPS), random keys representation and random-key encoding scheme are used in this study. These procedures have been tested on FT06 and FT10 benchmark problems available in the OR-Library, where the objective function is to minimize the makespan by the use of MATLAB software. Based on the experimental results, it is discovered that OPPS gives the best performance in solving both benchmark problems. The contribution of this paper is the fact that it demonstrates to the practitioners involved in complex scheduling problems that different particle representation procedures can have significant effects on the performance of PSO in solving JSP.

High performance GPU processing for inversion using uniform grid searches

NASA Astrophysics Data System (ADS)

Venetis, Ioannis E.; Saltogianni, Vasso; Stiros, Stathis; Gallopoulos, Efstratios

2017-04-01

Many geophysical problems are described by systems of redundant, highly non-linear systems of ordinary equations with constant terms deriving from measurements and hence representing stochastic variables. Solution (inversion) of such problems is based on numerical, optimization methods, based on Monte Carlo sampling or on exhaustive searches in cases of two or even three "free" unknown variables. Recently the TOPological INVersion (TOPINV) algorithm, a grid search-based technique in the Rn space, has been proposed. TOPINV is not based on the minimization of a certain cost function and involves only forward computations, hence avoiding computational errors. The basic concept is to transform observation equations into inequalities on the basis of an optimization parameter k and of their standard errors, and through repeated "scans" of n-dimensional search grids for decreasing values of k to identify the optimal clusters of gridpoints which satisfy observation inequalities and by definition contain the "true" solution. Stochastic optimal solutions and their variance-covariance matrices are then computed as first and second statistical moments. Such exhaustive uniform searches produce an excessive computational load and are extremely time consuming for common computers based on a CPU. An alternative is to use a computing platform based on a GPU, which nowadays is affordable to the research community, which provides a much higher computing performance. Using the CUDA programming language to implement TOPINV allows the investigation of the attained speedup in execution time on such a high performance platform. Based on synthetic data we compared the execution time required for two typical geophysical problems, modeling magma sources and seismic faults, described with up to 18 unknown variables, on both CPU/FORTRAN and GPU/CUDA platforms. The same problems for several different sizes of search grids (up to 1012 gridpoints) and numbers of unknown variables were solved on both platforms, and execution time as a function of the grid dimension for each problem was recorded. Results indicate an average speedup in calculations by a factor of 100 on the GPU platform; for example problems with 1012 grid-points require less than two hours instead of several days on conventional desktop computers. Such a speedup encourages the application of TOPINV on high performance platforms, as a GPU, in cases where nearly real time decisions are necessary, for example finite fault modeling to identify possible tsunami sources.

Competitive Facility Location with Fuzzy Random Demands

NASA Astrophysics Data System (ADS)

Uno, Takeshi; Katagiri, Hideki; Kato, Kosuke

2010-10-01

This paper proposes a new location problem of competitive facilities, e.g. shops, with uncertainty and vagueness including demands for the facilities in a plane. By representing the demands for facilities as fuzzy random variables, the location problem can be formulated as a fuzzy random programming problem. For solving the fuzzy random programming problem, first the α-level sets for fuzzy numbers are used for transforming it to a stochastic programming problem, and secondly, by using their expectations and variances, it can be reformulated to a deterministic programming problem. After showing that one of their optimal solutions can be found by solving 0-1 programming problems, their solution method is proposed by improving the tabu search algorithm with strategic oscillation. The efficiency of the proposed method is shown by applying it to numerical examples of the facility location problems.

QUADRO: A SUPERVISED DIMENSION REDUCTION METHOD VIA RAYLEIGH QUOTIENT OPTIMIZATION

PubMed Central

Fan, Jianqing; Ke, Zheng Tracy; Liu, Han; Xia, Lucy

2016-01-01

We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method—named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization)—for analyzing high-dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent scientific interests. One major challenge of Rayleigh quotient optimization is that the variance of quadratic statistics involves all fourth cross-moments of predictors, which are infeasible to compute for high-dimensional applications and may accumulate too many stochastic errors. This issue is resolved by considering a family of elliptical models. Moreover, for heavy-tail distributions, robust estimates of mean vectors and covariance matrices are employed to guarantee uniform convergence in estimating non-polynomially many parameters, even though only the fourth moments are assumed. Methodologically, QUADRO is based on elliptical models which allow us to formulate the Rayleigh quotient maximization as a convex optimization problem. Computationally, we propose an efficient linearized augmented Lagrangian method to solve the constrained optimization problem. Theoretically, we provide explicit rates of convergence in terms of Rayleigh quotient under both Gaussian and general elliptical models. Thorough numerical results on both synthetic and real datasets are also provided to back up our theoretical results. PMID:26778864

Calibration of a stochastic health evolution model using NHIS data

NASA Astrophysics Data System (ADS)

Gupta, Aparna; Li, Zhisheng

2011-10-01

This paper presents and calibrates an individual's stochastic health evolution model. In this health evolution model, the uncertainty of health incidents is described by a stochastic process with a finite number of possible outcomes. We construct a comprehensive health status index (HSI) to describe an individual's health status, as well as a health risk factor system (RFS) to classify individuals into different risk groups. Based on the maximum likelihood estimation (MLE) method and the method of nonlinear least squares fitting, model calibration is formulated in terms of two mixed-integer nonlinear optimization problems. Using the National Health Interview Survey (NHIS) data, the model is calibrated for specific risk groups. Longitudinal data from the Health and Retirement Study (HRS) is used to validate the calibrated model, which displays good validation properties. The end goal of this paper is to provide a model and methodology, whose output can serve as a crucial component of decision support for strategic planning of health related financing and risk management.

Computational modeling of the nonlinear stochastic dynamics of horizontal drillstrings

NASA Astrophysics Data System (ADS)

Cunha, Americo; Soize, Christian; Sampaio, Rubens

2015-11-01

This work intends to analyze the nonlinear stochastic dynamics of drillstrings in horizontal configuration. For this purpose, it considers a beam theory, with effects of rotatory inertia and shear deformation, which is capable of reproducing the large displacements that the beam undergoes. The friction and shock effects, due to beam/borehole wall transversal impacts, as well as the force and torque induced by bit-rock interaction, are also considered in the model. Uncertainties of bit-rock interaction model are taken into account using a parametric probabilistic approach. Numerical simulations have shown that the mechanical system of interest has a very rich nonlinear stochastic dynamics, which generate phenomena such as bit-bounce, stick-slip, and transverse impacts. A study aiming to maximize the drilling process efficiency, varying drillstring velocities of translation and rotation is presented. Also, the work presents the definition and solution of two optimizations problems, one deterministic and one robust, where the objective is to maximize drillstring rate of penetration into the soil respecting its structural limits.

New bounding and decomposition approaches for MILP investment problems: Multi-area transmission and generation planning under policy constraints

DOE PAGES

Munoz, F. D.; Hobbs, B. F.; Watson, J. -P.

2016-02-01

A novel two-phase bounding and decomposition approach to compute optimal and near-optimal solutions to large-scale mixed-integer investment planning problems is proposed and it considers a large number of operating subproblems, each of which is a convex optimization. Our motivating application is the planning of power transmission and generation in which policy constraints are designed to incentivize high amounts of intermittent generation in electric power systems. The bounding phase exploits Jensen’s inequality to define a lower bound, which we extend to stochastic programs that use expected-value constraints to enforce policy objectives. The decomposition phase, in which the bounds are tightened, improvesmore » upon the standard Benders’ algorithm by accelerating the convergence of the bounds. The lower bound is tightened by using a Jensen’s inequality-based approach to introduce an auxiliary lower bound into the Benders master problem. Upper bounds for both phases are computed using a sub-sampling approach executed on a parallel computer system. Numerical results show that only the bounding phase is necessary if loose optimality gaps are acceptable. But, the decomposition phase is required to attain optimality gaps. Moreover, use of both phases performs better, in terms of convergence speed, than attempting to solve the problem using just the bounding phase or regular Benders decomposition separately.« less

New bounding and decomposition approaches for MILP investment problems: Multi-area transmission and generation planning under policy constraints

DOE Office of Scientific and Technical Information (OSTI.GOV)

Munoz, F. D.; Hobbs, B. F.; Watson, J. -P.

A novel two-phase bounding and decomposition approach to compute optimal and near-optimal solutions to large-scale mixed-integer investment planning problems is proposed and it considers a large number of operating subproblems, each of which is a convex optimization. Our motivating application is the planning of power transmission and generation in which policy constraints are designed to incentivize high amounts of intermittent generation in electric power systems. The bounding phase exploits Jensen’s inequality to define a lower bound, which we extend to stochastic programs that use expected-value constraints to enforce policy objectives. The decomposition phase, in which the bounds are tightened, improvesmore » upon the standard Benders’ algorithm by accelerating the convergence of the bounds. The lower bound is tightened by using a Jensen’s inequality-based approach to introduce an auxiliary lower bound into the Benders master problem. Upper bounds for both phases are computed using a sub-sampling approach executed on a parallel computer system. Numerical results show that only the bounding phase is necessary if loose optimality gaps are acceptable. But, the decomposition phase is required to attain optimality gaps. Moreover, use of both phases performs better, in terms of convergence speed, than attempting to solve the problem using just the bounding phase or regular Benders decomposition separately.« less

Linear theory for filtering nonlinear multiscale systems with model error

PubMed Central

Berry, Tyrus; Harlim, John

2014-01-01

In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online, as part of a filtering procedure, simultaneously produce accurate filtering and equilibrium statistical prediction. In contrast, an offline estimation technique based on a linear regression, which fits the parameters to a training dataset without using the filter, yields filter estimates which are worse than the observations or even divergent when the slow variables are not fully observed. This finding does not imply that all offline methods are inherently inferior to the online method for nonlinear estimation problems, it only suggests that an ideal estimation technique should estimate all parameters simultaneously whether it is online or offline. PMID:25002829

pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations

DOE PAGES

Nicholson, Bethany; Siirola, John D.; Watson, Jean-Paul; ...

2017-12-20

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differentialmore » equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers.« less

pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nicholson, Bethany; Siirola, John D.; Watson, Jean-Paul

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differentialmore » equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers.« less

A framework for quantifying and optimizing the value of seismic monitoring of infrastructure

NASA Astrophysics Data System (ADS)

Omenzetter, Piotr

2017-04-01

This paper outlines a framework for quantifying and optimizing the value of information from structural health monitoring (SHM) technology deployed on large infrastructure, which may sustain damage in a series of earthquakes (the main and the aftershocks). The evolution of the damage state of the infrastructure without or with SHM is presented as a time-dependent, stochastic, discrete-state, observable and controllable nonlinear dynamical system. The pre-posterior Bayesian analysis and the decision tree are used for quantifying and optimizing the value of SHM information. An optimality problem is then formulated how to decide on the adoption of SHM and how to manage optimally the usage and operations of the possibly damaged infrastructure and its repair schedule using the information from SHM. The objective function to minimize is the expected total cost or risk.

A stochastic multi-agent optimization model for energy infrastructure planning under uncertainty and competition.

DOT National Transportation Integrated Search

2017-07-04

This paper presents a stochastic multi-agent optimization model that supports energy infrastruc- : ture planning under uncertainty. The interdependence between dierent decision entities in the : system is captured in an energy supply chain network, w...

Dual-mode nested search method for categorical uncertain multi-objective optimization

NASA Astrophysics Data System (ADS)

Tang, Long; Wang, Hu

2016-10-01

Categorical multi-objective optimization is an important issue involved in many matching design problems. Non-numerical variables and their uncertainty are the major challenges of such optimizations. Therefore, this article proposes a dual-mode nested search (DMNS) method. In the outer layer, kriging metamodels are established using standard regular simplex mapping (SRSM) from categorical candidates to numerical values. Assisted by the metamodels, a k-cluster-based intelligent sampling strategy is developed to search Pareto frontier points. The inner layer uses an interval number method to model the uncertainty of categorical candidates. To improve the efficiency, a multi-feature convergent optimization via most-promising-area stochastic search (MFCOMPASS) is proposed to determine the bounds of objectives. Finally, typical numerical examples are employed to demonstrate the effectiveness of the proposed DMNS method.

The Deterministic Information Bottleneck

NASA Astrophysics Data System (ADS)

Strouse, D. J.; Schwab, David

2015-03-01

A fundamental and ubiquitous task that all organisms face is prediction of the future based on past sensory experience. Since an individual's memory resources are limited and costly, however, there is a tradeoff between memory cost and predictive payoff. The information bottleneck (IB) method (Tishby, Pereira, & Bialek 2000) formulates this tradeoff as a mathematical optimization problem using an information theoretic cost function. IB encourages storing as few bits of past sensory input as possible while selectively preserving the bits that are most predictive of the future. Here we introduce an alternative formulation of the IB method, which we call the deterministic information bottleneck (DIB). First, we argue for an alternative cost function, which better represents the biologically-motivated goal of minimizing required memory resources. Then, we show that this seemingly minor change has the dramatic effect of converting the optimal memory encoder from stochastic to deterministic. Next, we propose an iterative algorithm for solving the DIB problem. Additionally, we compare the IB and DIB methods on a variety of synthetic datasets, and examine the performance of retinal ganglion cell populations relative to the optimal encoding strategy for each problem.

Portable parallel stochastic optimization for the design of aeropropulsion components

NASA Technical Reports Server (NTRS)

Sues, Robert H.; Rhodes, G. S.

1994-01-01

This report presents the results of Phase 1 research to develop a methodology for performing large-scale Multi-disciplinary Stochastic Optimization (MSO) for the design of aerospace systems ranging from aeropropulsion components to complete aircraft configurations. The current research recognizes that such design optimization problems are computationally expensive, and require the use of either massively parallel or multiple-processor computers. The methodology also recognizes that many operational and performance parameters are uncertain, and that uncertainty must be considered explicitly to achieve optimum performance and cost. The objective of this Phase 1 research was to initialize the development of an MSO methodology that is portable to a wide variety of hardware platforms, while achieving efficient, large-scale parallelism when multiple processors are available. The first effort in the project was a literature review of available computer hardware, as well as review of portable, parallel programming environments. The first effort was to implement the MSO methodology for a problem using the portable parallel programming language, Parallel Virtual Machine (PVM). The third and final effort was to demonstrate the example on a variety of computers, including a distributed-memory multiprocessor, a distributed-memory network of workstations, and a single-processor workstation. Results indicate the MSO methodology can be well-applied towards large-scale aerospace design problems. Nearly perfect linear speedup was demonstrated for computation of optimization sensitivity coefficients on both a 128-node distributed-memory multiprocessor (the Intel iPSC/860) and a network of workstations (speedups of almost 19 times achieved for 20 workstations). Very high parallel efficiencies (75 percent for 31 processors and 60 percent for 50 processors) were also achieved for computation of aerodynamic influence coefficients on the Intel. Finally, the multi-level parallelization strategy that will be needed for large-scale MSO problems was demonstrated to be highly efficient. The same parallel code instructions were used on both platforms, demonstrating portability. There are many applications for which MSO can be applied, including NASA's High-Speed-Civil Transport, and advanced propulsion systems. The use of MSO will reduce design and development time and testing costs dramatically.

Optimal generalized multistep integration formulae for real-time digital simulation

NASA Technical Reports Server (NTRS)

Moerder, D. D.; Halyo, N.

1985-01-01

The problem of discretizing a dynamical system for real-time digital simulation is considered. Treating the system and its simulation as stochastic processes leads to a statistical characterization of simulator fidelity. A plant discretization procedure based on an efficient matrix generalization of explicit linear multistep discrete integration formulae is introduced, which minimizes a weighted sum of the mean squared steady-state and transient error between the system and simulator outputs.

Auditing: Perspectives from Multiperson Decision Theory.

DTIC Science & Technology

1982-10-01

Transmission" by W.P. Rogerson 378. "Unemployment Equilibrium with Stochastic Rationing of Supplies" by Ho-mo i WU. 379. " Optimal Price and Income... rational with enormous powers of calculation. At first this may seem utterly inappropriate for the study of problems in accounting. Nevertheless, there...that at any price the investor offers he will tend to get acceptance only from an owner with assets having a lesser value. Similarly, if the owner

Optimizing signal recycling for detecting a stochastic gravitational-wave background

NASA Astrophysics Data System (ADS)

Tao, Duo; Christensen, Nelson

2018-06-01

Signal recycling is applied in laser interferometers such as the Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO) to increase their sensitivity to gravitational waves. In this study, signal recycling configurations for detecting a stochastic gravitational wave background are optimized based on aLIGO parameters. Optimal transmission of the signal recycling mirror (SRM) and detuning phase of the signal recycling cavity under a fixed laser power and low-frequency cutoff are calculated. Based on the optimal configurations, the compatibility with a binary neutron star (BNS) search is discussed. Then, different laser powers and low-frequency cutoffs are considered. Two models for the dimensionless energy density of gravitational waves , the flat model and the model, are studied. For a stochastic background search, it is found that an interferometer using signal recycling has a better sensitivity than an interferometer not using it. The optimal stochastic search configurations are typically found when both the SRM transmission and the signal recycling detuning phase are low. In this region, the BNS range mostly lies between 160 and 180 Mpc. When a lower laser power is used the optimal signal recycling detuning phase increases, the optimal SRM transmission increases and the optimal sensitivity improves. A reduced low-frequency cutoff gives a better sensitivity limit. For both models of , a typical optimal sensitivity limit on the order of 10‑10 is achieved at a reference frequency of Hz.

Towards Stochastic Optimization-Based Electric Vehicle Penetration in a Novel Archipelago Microgrid.

PubMed

Yang, Qingyu; An, Dou; Yu, Wei; Tan, Zhengan; Yang, Xinyu

2016-06-17

Due to the advantage of avoiding upstream disturbance and voltage fluctuation from a power transmission system, Islanded Micro-Grids (IMG) have attracted much attention. In this paper, we first propose a novel self-sufficient Cyber-Physical System (CPS) supported by Internet of Things (IoT) techniques, namely "archipelago micro-grid (MG)", which integrates the power grid and sensor networks to make the grid operation effective and is comprised of multiple MGs while disconnected with the utility grid. The Electric Vehicles (EVs) are used to replace a portion of Conventional Vehicles (CVs) to reduce CO 2 emission and operation cost. Nonetheless, the intermittent nature and uncertainty of Renewable Energy Sources (RESs) remain a challenging issue in managing energy resources in the system. To address these issues, we formalize the optimal EV penetration problem as a two-stage Stochastic Optimal Penetration (SOP) model, which aims to minimize the emission and operation cost in the system. Uncertainties coming from RESs (e.g., wind, solar, and load demand) are considered in the stochastic model and random parameters to represent those uncertainties are captured by the Monte Carlo-based method. To enable the reasonable deployment of EVs in each MGs, we develop two scheduling schemes, namely Unlimited Coordinated Scheme (UCS) and Limited Coordinated Scheme (LCS), respectively. An extensive simulation study based on a modified 9 bus system with three MGs has been carried out to show the effectiveness of our proposed schemes. The evaluation data indicates that our proposed strategy can reduce both the environmental pollution created by CO 2 emissions and operation costs in UCS and LCS.

Towards Stochastic Optimization-Based Electric Vehicle Penetration in a Novel Archipelago Microgrid

PubMed Central

Yang, Qingyu; An, Dou; Yu, Wei; Tan, Zhengan; Yang, Xinyu

2016-01-01

Due to the advantage of avoiding upstream disturbance and voltage fluctuation from a power transmission system, Islanded Micro-Grids (IMG) have attracted much attention. In this paper, we first propose a novel self-sufficient Cyber-Physical System (CPS) supported by Internet of Things (IoT) techniques, namely “archipelago micro-grid (MG)”, which integrates the power grid and sensor networks to make the grid operation effective and is comprised of multiple MGs while disconnected with the utility grid. The Electric Vehicles (EVs) are used to replace a portion of Conventional Vehicles (CVs) to reduce CO2 emission and operation cost. Nonetheless, the intermittent nature and uncertainty of Renewable Energy Sources (RESs) remain a challenging issue in managing energy resources in the system. To address these issues, we formalize the optimal EV penetration problem as a two-stage Stochastic Optimal Penetration (SOP) model, which aims to minimize the emission and operation cost in the system. Uncertainties coming from RESs (e.g., wind, solar, and load demand) are considered in the stochastic model and random parameters to represent those uncertainties are captured by the Monte Carlo-based method. To enable the reasonable deployment of EVs in each MGs, we develop two scheduling schemes, namely Unlimited Coordinated Scheme (UCS) and Limited Coordinated Scheme (LCS), respectively. An extensive simulation study based on a modified 9 bus system with three MGs has been carried out to show the effectiveness of our proposed schemes. The evaluation data indicates that our proposed strategy can reduce both the environmental pollution created by CO2 emissions and operation costs in UCS and LCS. PMID:27322281

Risk-Constrained Dynamic Programming for Optimal Mars Entry, Descent, and Landing

NASA Technical Reports Server (NTRS)

Ono, Masahiro; Kuwata, Yoshiaki

2013-01-01

A chance-constrained dynamic programming algorithm was developed that is capable of making optimal sequential decisions within a user-specified risk bound. This work handles stochastic uncertainties over multiple stages in the CEMAT (Combined EDL-Mobility Analyses Tool) framework. It was demonstrated by a simulation of Mars entry, descent, and landing (EDL) using real landscape data obtained from the Mars Reconnaissance Orbiter. Although standard dynamic programming (DP) provides a general framework for optimal sequential decisionmaking under uncertainty, it typically achieves risk aversion by imposing an arbitrary penalty on failure states. Such a penalty-based approach cannot explicitly bound the probability of mission failure. A key idea behind the new approach is called risk allocation, which decomposes a joint chance constraint into a set of individual chance constraints and distributes risk over them. The joint chance constraint was reformulated into a constraint on an expectation over a sum of an indicator function, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the chance-constraint optimization problem can be turned into an unconstrained optimization over a Lagrangian, which can be solved efficiently using a standard DP approach.

Operation of Power Grids with High Penetration of Wind Power

NASA Astrophysics Data System (ADS)

Al-Awami, Ali Taleb

The integration of wind power into the power grid poses many challenges due to its highly uncertain nature. This dissertation involves two main components related to the operation of power grids with high penetration of wind energy: wind-thermal stochastic dispatch and wind-thermal coordinated bidding in short-term electricity markets. In the first part, a stochastic dispatch (SD) algorithm is proposed that takes into account the stochastic nature of the wind power output. The uncertainty associated with wind power output given the forecast is characterized using conditional probability density functions (CPDF). Several functions are examined to characterize wind uncertainty including Beta, Weibull, Extreme Value, Generalized Extreme Value, and Mixed Gaussian distributions. The unique characteristics of the Mixed Gaussian distribution are then utilized to facilitate the speed of convergence of the SD algorithm. A case study is carried out to evaluate the effectiveness of the proposed algorithm. Then, the SD algorithm is extended to simultaneously optimize the system operating costs and emissions. A modified multi-objective particle swarm optimization algorithm is suggested to identify the Pareto-optimal solutions defined by the two conflicting objectives. A sensitivity analysis is carried out to study the effect of changing load level and imbalance cost factors on the Pareto front. In the second part of this dissertation, coordinated trading of wind and thermal energy is proposed to mitigate risks due to those uncertainties. The problem of wind-thermal coordinated trading is formulated as a mixed-integer stochastic linear program. The objective is to obtain the optimal tradeoff bidding strategy that maximizes the total expected profits while controlling trading risks. For risk control, a weighted term of the conditional value at risk (CVaR) is included in the objective function. The CVaR aims to maximize the expected profits of the least profitable scenarios, thus improving trading risk control. A case study comparing coordinated with uncoordinated bidding strategies depending on the trader's risk attitude is included. Simulation results show that coordinated bidding can improve the expected profits while significantly improving the CVaR.

Uncertainty Propagation for Turbulent, Compressible Flow in a Quasi-1D Nozzle Using Stochastic Methods

NASA Technical Reports Server (NTRS)

Zang, Thomas A.; Mathelin, Lionel; Hussaini, M. Yousuff; Bataille, Francoise

2003-01-01

This paper describes a fully spectral, Polynomial Chaos method for the propagation of uncertainty in numerical simulations of compressible, turbulent flow, as well as a novel stochastic collocation algorithm for the same application. The stochastic collocation method is key to the efficient use of stochastic methods on problems with complex nonlinearities, such as those associated with the turbulence model equations in compressible flow and for CFD schemes requiring solution of a Riemann problem. Both methods are applied to compressible flow in a quasi-one-dimensional nozzle. The stochastic collocation method is roughly an order of magnitude faster than the fully Galerkin Polynomial Chaos method on the inviscid problem.

A variable-gain output feedback control design methodology

NASA Technical Reports Server (NTRS)

Halyo, Nesim; Moerder, Daniel D.; Broussard, John R.; Taylor, Deborah B.

1989-01-01

A digital control system design technique is developed in which the control system gain matrix varies with the plant operating point parameters. The design technique is obtained by formulating the problem as an optimal stochastic output feedback control law with variable gains. This approach provides a control theory framework within which the operating range of a control law can be significantly extended. Furthermore, the approach avoids the major shortcomings of the conventional gain-scheduling techniques. The optimal variable gain output feedback control problem is solved by embedding the Multi-Configuration Control (MCC) problem, previously solved at ICS. An algorithm to compute the optimal variable gain output feedback control gain matrices is developed. The algorithm is a modified version of the MCC algorithm improved so as to handle the large dimensionality which arises particularly in variable-gain control problems. The design methodology developed is applied to a reconfigurable aircraft control problem. A variable-gain output feedback control problem was formulated to design a flight control law for an AFTI F-16 aircraft which can automatically reconfigure its control strategy to accommodate failures in the horizontal tail control surface. Simulations of the closed-loop reconfigurable system show that the approach produces a control design which can accommodate such failures with relative ease. The technique can be applied to many other problems including sensor failure accommodation, mode switching control laws and super agility.

Best Longitudinal Adjustment of Satellite Trajectories for the Observation of Forest Fires (Blastoff): A Stochastic Programming Approach to Satellite System Design

NASA Astrophysics Data System (ADS)

Hoskins, Aaron B.

Forest fires cause a significant amount of damage and destruction each year. Optimally dispatching resources reduces the amount of damage a forest fire can cause. Models predict the fire spread to provide the data required to optimally dispatch resources. However, the models are only as accurate as the data used to build them. Satellites are one valuable tool in the collection of data for the forest fire models. Satellites provide data on the types of vegetation, the wind speed and direction, the soil moisture content, etc. The current operating paradigm is to passively collect data when possible. However, images from directly overhead provide better resolution and are easier to process. Maneuvering a constellation of satellites to fly directly over the forest fire provides higher quality data than is achieved with the current operating paradigm. Before launch, the location of the forest fire is unknown. Therefore, it is impossible to optimize the initial orbits for the satellites. Instead, the expected cost of maneuvering to observe the forest fire determines the optimal initial orbits. A two-stage stochastic programming approach is well suited for this class of problem where initial decisions are made with an uncertain future and then subsequent decisions are made once a scenario is realized. A repeat ground track orbit provides a non-maneuvering, natural solution providing a daily flyover of the forest fire. However, additional maneuvers provide a second daily flyover of the forest fire. The additional maneuvering comes at a significant cost in terms of additional fuel, but provides more data collection opportunities. After data are collected, ground stations receive the data for processing. Optimally selecting the ground station locations reduce the number of built ground stations and reduces the data fusion issues. However, the location of the forest fire alters the optimal ground station sites. A two-stage stochastic programming approach optimizes the selection of ground stations to maximize the expected amount of data downloaded from a satellite. The approaches of selecting initial orbits and ground station locations including uncertainty will provide a robust system to reduce the amount of damage caused by forest fires.

Application of IFT and SPSA to servo system control.

PubMed

Rădac, Mircea-Bogdan; Precup, Radu-Emil; Petriu, Emil M; Preitl, Stefan

2011-12-01

This paper treats the application of two data-based model-free gradient-based stochastic optimization techniques, i.e., iterative feedback tuning (IFT) and simultaneous perturbation stochastic approximation (SPSA), to servo system control. The representative case of controlled processes modeled by second-order systems with an integral component is discussed. New IFT and SPSA algorithms are suggested to tune the parameters of the state feedback controllers with an integrator in the linear-quadratic-Gaussian (LQG) problem formulation. An implementation case study concerning the LQG-based design of an angular position controller for a direct current servo system laboratory equipment is included to highlight the pros and cons of IFT and SPSA from an application's point of view. The comparison of IFT and SPSA algorithms is focused on an insight into their implementation.

Structural Properties and Estimation of Delay Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kwong, R. H. S.

1975-01-01

Two areas in the theory of delay systems were studied: structural properties and their applications to feedback control, and optimal linear and nonlinear estimation. The concepts of controllability, stabilizability, observability, and detectability were investigated. The property of pointwise degeneracy of linear time-invariant delay systems is considered. Necessary and sufficient conditions for three dimensional linear systems to be made pointwise degenerate by delay feedback were obtained, while sufficient conditions for this to be possible are given for higher dimensional linear systems. These results were applied to obtain solvability conditions for the minimum time output zeroing control problem by delay feedback. A representation theorem is given for conditional moment functionals of general nonlinear stochastic delay systems, and stochastic differential equations are derived for conditional moment functionals satisfying certain smoothness properties.

Identification of dynamic systems, theory and formulation

NASA Technical Reports Server (NTRS)

Maine, R. E.; Iliff, K. W.

1985-01-01

The problem of estimating parameters of dynamic systems is addressed in order to present the theoretical basis of system identification and parameter estimation in a manner that is complete and rigorous, yet understandable with minimal prerequisites. Maximum likelihood and related estimators are highlighted. The approach used requires familiarity with calculus, linear algebra, and probability, but does not require knowledge of stochastic processes or functional analysis. The treatment emphasizes unification of the various areas in estimation in dynamic systems is treated as a direct outgrowth of the static system theory. Topics covered include basic concepts and definitions; numerical optimization methods; probability; statistical estimators; estimation in static systems; stochastic processes; state estimation in dynamic systems; output error, filter error, and equation error methods of parameter estimation in dynamic systems, and the accuracy of the estimates.

Economic policy optimization based on both one stochastic model and the parametric control theory

NASA Astrophysics Data System (ADS)

Ashimov, Abdykappar; Borovskiy, Yuriy; Onalbekov, Mukhit

2016-06-01

A nonlinear dynamic stochastic general equilibrium model with financial frictions is developed to describe two interacting national economies in the environment of the rest of the world. Parameters of nonlinear model are estimated based on its log-linearization by the Bayesian approach. The nonlinear model is verified by retroprognosis, estimation of stability indicators of mappings specified by the model, and estimation the degree of coincidence for results of internal and external shocks' effects on macroeconomic indicators on the basis of the estimated nonlinear model and its log-linearization. On the base of the nonlinear model, the parametric control problems of economic growth and volatility of macroeconomic indicators of Kazakhstan are formulated and solved for two exchange rate regimes (free floating and managed floating exchange rates)

The influence of the free space environment on the superlight-weight thermal protection system: conception, methods, and risk analysis

NASA Astrophysics Data System (ADS)

Yatsenko, Vitaliy; Falchenko, Iurii; Fedorchuk, Viktor; Petrushynets, Lidiia

2016-07-01

This report focuses on the results of the EU project "Superlight-weight thermal protection system for space application (LIGHT-TPS)". The bottom line is an analysis of influence of the free space environment on the superlight-weight thermal protection system (TPS). This report focuses on new methods that based on the following models: synergetic, physical, and computational. This report concentrates on four approaches. The first concerns the synergetic approach. The synergetic approach to the solution of problems of self-controlled synthesis of structures and creation of self-organizing technologies is considered in connection with the super-problem of creation of materials with new functional properties. Synergetics methods and mathematical design are considered according to actual problems of material science. The second approach describes how the optimization methods can be used to determine material microstructures with optimized or targeted properties. This technique enables one to find unexpected microstructures with exotic behavior (e.g., negative thermal expansion coefficients). The third approach concerns the dynamic probabilistic risk analysis of TPS l elements with complex characterizations for damages using a physical model of TPS system and a predictable level of ionizing radiation and space weather. Focusing is given mainly on the TPS model, mathematical models for dynamic probabilistic risk assessment and software for the modeling and prediction of the influence of the free space environment. The probabilistic risk assessment method for TPS is presented considering some deterministic and stochastic factors. The last approach concerns results of experimental research of the temperature distribution on the surface of the honeycomb sandwich panel size 150 x 150 x 20 mm at the diffusion welding in vacuum are considered. An equipment, which provides alignment of temperature fields in a product for the formation of equal strength of welded joints is considered. Many tasks in computational materials science can be posed as optimization problems. This technique enables one to find unexpected microstructures with exotic behavior (e.g., negative thermal expansion coefficients). The last approach is concerned with the generation of realizations of materials with specified but limited microstructural information: an intriguing inverse problem of both fundamental and practical importance. Computational models based upon the theories of molecular dynamics or quantum mechanics would enable the prediction and modification of fundamental materials properties. This problem is solved using deterministic and stochastic optimization techniques. The main optimization approaches in the frame of the EU project "Superlight-weight thermal protection system for space application" are discussed. Optimization approach to the alloys for obtaining materials with required properties using modeling techniques and experimental data will be also considered. This report is supported by the EU project "Superlight-weight thermal protection system for space application (LIGHT-TPS)"

Reactive power planning under high penetration of wind energy using Benders decomposition

DOE PAGES

Xu, Yan; Wei, Yanli; Fang, Xin; ...

2015-11-05

This study addresses the optimal allocation of reactive power volt-ampere reactive (VAR) sources under the paradigm of high penetration of wind energy. Reactive power planning (RPP) in this particular condition involves a high level of uncertainty because of wind power characteristic. To properly model wind generation uncertainty, a multi-scenario framework optimal power flow that considers the voltage stability constraint under the worst wind scenario and transmission N 1 contingency is developed. The objective of RPP in this study is to minimise the total cost including the VAR investment cost and the expected generation cost. Therefore RPP under this condition ismore » modelled as a two-stage stochastic programming problem to optimise the VAR location and size in one stage, then to minimise the fuel cost in the other stage, and eventually, to find the global optimal RPP results iteratively. Benders decomposition is used to solve this model with an upper level problem (master problem) for VAR allocation optimisation and a lower problem (sub-problem) for generation cost minimisation. Impact of the potential reactive power support from doubly-fed induction generator (DFIG) is also analysed. Lastly, case studies on the IEEE 14-bus and 118-bus systems are provided to verify the proposed method.« less

Optimal exploitation strategies for an animal population in a Markovian environment: A theory and an example

USGS Publications Warehouse

Anderson, D.R.

1975-01-01

Optimal exploitation strategies were studied for an animal population in a Markovian (stochastic, serially correlated) environment. This is a general case and encompasses a number of important special cases as simplifications. Extensive empirical data on the Mallard (Anas platyrhynchos) were used as an example of general theory. The number of small ponds on the central breeding grounds was used as an index to the state of the environment. A general mathematical model was formulated to provide a synthesis of the existing literature, estimates of parameters developed from an analysis of data, and hypotheses regarding the specific effect of exploitation on total survival. The literature and analysis of data were inconclusive concerning the effect of exploitation on survival. Therefore, two hypotheses were explored: (1) exploitation mortality represents a largely additive form of mortality, and (2) exploitation mortality is compensatory with other forms of mortality, at least to some threshold level. Models incorporating these two hypotheses were formulated as stochastic dynamic programming models and optimal exploitation strategies were derived numerically on a digital computer. Optimal exploitation strategies were found to exist under the rather general conditions. Direct feedback control was an integral component in the optimal decision-making process. Optimal exploitation was found to be substantially different depending upon the hypothesis regarding the effect of exploitation on the population. If we assume that exploitation is largely an additive force of mortality in Mallards, then optimal exploitation decisions are a convex function of the size of the breeding population and a linear or slight concave function of the environmental conditions. Under the hypothesis of compensatory mortality forces, optimal exploitation decisions are approximately linearly related to the size of the Mallard breeding population. Dynamic programming is suggested as a very general formulation for realistic solutions to the general optimal exploitation problem. The concepts of state vectors and stage transformations are completely general. Populations can be modeled stochastically and the objective function can include extra-biological factors. The optimal level of exploitation in year t must be based on the observed size of the population and the state of the environment in year t unless the dynamics of the population, the state of the environment, and the result of the exploitation decisions are completely deterministic. Exploitation based on an average harvest, or harvest rate, or designed to maintain a constant breeding population size is inefficient.

Optimal control strategy for an impulsive stochastic competition system with time delays and jumps

NASA Astrophysics Data System (ADS)

Liu, Lidan; Meng, Xinzhu; Zhang, Tonghua

2017-07-01

Driven by both white and jump noises, a stochastic delayed model with two competitive species in a polluted environment is proposed and investigated. By using the comparison theorem of stochastic differential equations and limit superior theory, sufficient conditions for persistence in mean and extinction of two species are established. In addition, we obtain that the system is asymptotically stable in distribution by using ergodic method. Furthermore, the optimal harvesting effort and the maximum of expectation of sustainable yield (ESY) are derived from Hessian matrix method and optimal harvesting theory of differential equations. Finally, some numerical simulations are provided to illustrate the theoretical results.

An application of different dioids in public key cryptography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Durcheva, Mariana I., E-mail: mdurcheva66@gmail.com

2014-11-18

Dioids provide a natural framework for analyzing a broad class of discrete event dynamical systems such as the design and analysis of bus and railway timetables, scheduling of high-throughput industrial processes, solution of combinatorial optimization problems, the analysis and improvement of flow systems in communication networks. They have appeared in several branches of mathematics such as functional analysis, optimization, stochastic systems and dynamic programming, tropical geometry, fuzzy logic. In this paper we show how to involve dioids in public key cryptography. The main goal is to create key – exchange protocols based on dioids. Additionally the digital signature scheme ismore » presented.« less

Online POMDP Algorithms for Very Large Observation Spaces

DTIC Science & Technology

2017-06-06

stochastic optimization: From sets to paths." In Advances in Neural Information Processing Systems, pp. 1585- 1593 . 2015. • Luo, Yuanfu, Haoyu Bai...and Wee Sun Lee. "Adaptive stochastic optimization: From sets to paths." In Advances in Neural Information Processing Systems, pp. 1585- 1593 . 2015

Study on probability distributions for evolution in modified extremal optimization

NASA Astrophysics Data System (ADS)

Zeng, Guo-Qiang; Lu, Yong-Zai; Mao, Wei-Jie; Chu, Jian

2010-05-01

It is widely believed that the power-law is a proper probability distribution being effectively applied for evolution in τ-EO (extremal optimization), a general-purpose stochastic local-search approach inspired by self-organized criticality, and its applications in some NP-hard problems, e.g., graph partitioning, graph coloring, spin glass, etc. In this study, we discover that the exponential distributions or hybrid ones (e.g., power-laws with exponential cutoff) being popularly used in the research of network sciences may replace the original power-laws in a modified τ-EO method called self-organized algorithm (SOA), and provide better performances than other statistical physics oriented methods, such as simulated annealing, τ-EO and SOA etc., from the experimental results on random Euclidean traveling salesman problems (TSP) and non-uniform instances. From the perspective of optimization, our results appear to demonstrate that the power-law is not the only proper probability distribution for evolution in EO-similar methods at least for TSP, the exponential and hybrid distributions may be other choices.

Chance-Constrained Day-Ahead Hourly Scheduling in Distribution System Operation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, Huaiguang; Zhang, Yingchen; Muljadi, Eduard

This paper aims to propose a two-step approach for day-ahead hourly scheduling in a distribution system operation, which contains two operation costs, the operation cost at substation level and feeder level. In the first step, the objective is to minimize the electric power purchase from the day-ahead market with the stochastic optimization. The historical data of day-ahead hourly electric power consumption is used to provide the forecast results with the forecasting error, which is presented by a chance constraint and formulated into a deterministic form by Gaussian mixture model (GMM). In the second step, the objective is to minimize themore » system loss. Considering the nonconvexity of the three-phase balanced AC optimal power flow problem in distribution systems, the second-order cone program (SOCP) is used to relax the problem. Then, a distributed optimization approach is built based on the alternating direction method of multiplier (ADMM). The results shows that the validity and effectiveness method.« less

Coherifying quantum channels

NASA Astrophysics Data System (ADS)

Korzekwa, Kamil; Czachórski, Stanisław; Puchała, Zbigniew; Życzkowski, Karol

2018-04-01

Is it always possible to explain random stochastic transitions between states of a finite-dimensional system as arising from the deterministic quantum evolution of the system? If not, then what is the minimal amount of randomness required by quantum theory to explain a given stochastic process? Here, we address this problem by studying possible coherifications of a quantum channel Φ, i.e., we look for channels {{{Φ }}}{ \\mathcal C } that induce the same classical transitions T, but are ‘more coherent’. To quantify the coherence of a channel Φ we measure the coherence of the corresponding Jamiołkowski state J Φ. We show that the classical transition matrix T can be coherified to reversible unitary dynamics if and only if T is unistochastic. Otherwise the Jamiołkowski state {J}{{Φ }}{ \\mathcal C } of the optimally coherified channel is mixed, and the dynamics must necessarily be irreversible. To assess the extent to which an optimal process {{{Φ }}}{ \\mathcal C } is indeterministic we find explicit bounds on the entropy and purity of {J}{{Φ }}{ \\mathcal C }, and relate the latter to the unitarity of {{{Φ }}}{ \\mathcal C }. We also find optimal coherifications for several classes of channels, including all one-qubit channels. Finally, we provide a non-optimal coherification procedure that works for an arbitrary channel Φ and reduces its rank (the minimal number of required Kraus operators) from {d}2 to d.

Estimation of an Optimal Stimulus Amplitude for Using Vestibular Stochastic Stimulation to Improve Balance Function

NASA Technical Reports Server (NTRS)

Goel, R.; Kofman, I.; DeDios, Y. E.; Jeevarajan, J.; Stepanyan, V.; Nair, M.; Congdon, S.; Fregia, M.; Peters, B.; Cohen, H.;

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sousedík, Bedřich, E-mail: sousedik@umbc.edu; Elman, Howard C., E-mail: elman@cs.umd.edu

2016-07-01

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

DOE PAGES

Sousedík, Bedřich; Elman, Howard C.

2016-04-12

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

On two mathematical problems of canonical quantization. IV

NASA Astrophysics Data System (ADS)

Kirillov, A. I.

1992-11-01

A method for solving the problem of reconstructing a measure beginning with its logarithmic derivative is presented. The method completes that of solving the stochastic differential equation via Dirichlet forms proposed by S. Albeverio and M. Rockner. As a result one obtains the mathematical apparatus for the stochastic quantization. The apparatus is applied to prove the existence of the Feynman-Kac measure of the sine-Gordon and λφ2n/(1 + K2φ2n)-models. A synthesis of both mathematical problems of canonical quantization is obtained in the form of a second-order martingale problem for vacuum noise. It is shown that in stochastic mechanics the martingale problem is an analog of Newton's second law and enables us to find the Nelson's stochastic trajectories without determining the wave functions.

Integrating stochastic time-dependent travel speed in solution methods for the dynamic dial-a-ride problem.

PubMed

Schilde, M; Doerner, K F; Hartl, R F

2014-10-01

In urban areas, logistic transportation operations often run into problems because travel speeds change, depending on the current traffic situation. If not accounted for, time-dependent and stochastic travel speeds frequently lead to missed time windows and thus poorer service. Especially in the case of passenger transportation, it often leads to excessive passenger ride times as well. Therefore, time-dependent and stochastic influences on travel speeds are relevant for finding feasible and reliable solutions. This study considers the effect of exploiting statistical information available about historical accidents, using stochastic solution approaches for the dynamic dial-a-ride problem (dynamic DARP). The authors propose two pairs of metaheuristic solution approaches, each consisting of a deterministic method (average time-dependent travel speeds for planning) and its corresponding stochastic version (exploiting stochastic information while planning). The results, using test instances with up to 762 requests based on a real-world road network, show that in certain conditions, exploiting stochastic information about travel speeds leads to significant improvements over deterministic approaches.

Constructing probabilistic scenarios for wide-area solar power generation

DOE PAGES

Woodruff, David L.; Deride, Julio; Staid, Andrea; ...

2017-12-22

Optimizing thermal generation commitments and dispatch in the presence of high penetrations of renewable resources such as solar energy requires a characterization of their stochastic properties. In this study, we describe novel methods designed to create day-ahead, wide-area probabilistic solar power scenarios based only on historical forecasts and associated observations of solar power production. Each scenario represents a possible trajectory for solar power in next-day operations with an associated probability computed by algorithms that use historical forecast errors. Scenarios are created by segmentation of historic data, fitting non-parametric error distributions using epi-splines, and then computing specific quantiles from these distributions.more » Additionally, we address the challenge of establishing an upper bound on solar power output. Our specific application driver is for use in stochastic variants of core power systems operations optimization problems, e.g., unit commitment and economic dispatch. These problems require as input a range of possible future realizations of renewables production. However, the utility of such probabilistic scenarios extends to other contexts, e.g., operator and trader situational awareness. Finally, we compare the performance of our approach to a recently proposed method based on quantile regression, and demonstrate that our method performs comparably to this approach in terms of two widely used methods for assessing the quality of probabilistic scenarios: the Energy score and the Variogram score.« less

Optimal routing of hazardous substances in time-varying, stochastic transportation networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Woods, A.L.; Miller-Hooks, E.; Mahmassani, H.S.

This report is concerned with the selection of routes in a network along which to transport hazardous substances, taking into consideration several key factors pertaining to the cost of transport and the risk of population exposure in the event of an accident. Furthermore, the fact that travel time and the risk measures are not constant over time is explicitly recognized in the routing decisions. Existing approaches typically assume static conditions, possibly resulting in inefficient route selection and unnecessary risk exposure. The report described the application of recent advances in network analysis methodologies to the problem of routing hazardous substances. Severalmore » specific problem formulations are presented, reflecting different degrees of risk aversion on the part of the decision-maker, as well as different possible operational scenarios. All procedures explicitly consider travel times and travel costs (including risk measures) to be stochastic time-varying quantities. The procedures include both exact algorithms, which may require extensive computational effort in some situations, as well as more efficient heuristics that may not guarantee a Pareto-optimal solution. All procedures are systematically illustrated for an example application using the Texas highway network, for both normal and incident condition scenarios. The application illustrates the trade-offs between the information obtained in the solution and computational efficiency, and highlights the benefits of incorporating these procedures in a decision-support system for hazardous substance shipment routing decisions.« less

Constructing probabilistic scenarios for wide-area solar power generation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Woodruff, David L.; Deride, Julio; Staid, Andrea

Optimizing thermal generation commitments and dispatch in the presence of high penetrations of renewable resources such as solar energy requires a characterization of their stochastic properties. In this study, we describe novel methods designed to create day-ahead, wide-area probabilistic solar power scenarios based only on historical forecasts and associated observations of solar power production. Each scenario represents a possible trajectory for solar power in next-day operations with an associated probability computed by algorithms that use historical forecast errors. Scenarios are created by segmentation of historic data, fitting non-parametric error distributions using epi-splines, and then computing specific quantiles from these distributions.more » Additionally, we address the challenge of establishing an upper bound on solar power output. Our specific application driver is for use in stochastic variants of core power systems operations optimization problems, e.g., unit commitment and economic dispatch. These problems require as input a range of possible future realizations of renewables production. However, the utility of such probabilistic scenarios extends to other contexts, e.g., operator and trader situational awareness. Finally, we compare the performance of our approach to a recently proposed method based on quantile regression, and demonstrate that our method performs comparably to this approach in terms of two widely used methods for assessing the quality of probabilistic scenarios: the Energy score and the Variogram score.« less

Boosting Stochastic Problem Solvers Through Online Self-Analysis of Performance

DTIC Science & Technology

2003-07-21

Boosting Stochastic Problem Solvers Through Online Self-Analysis of Performance Vincent A. Cicirello CMU-RI-TR-03-27 Submitted in partial fulfillment...AND SUBTITLE Boosting Stochastic Problem Solvers Through Online Self-Analysis of Performance 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM...lead to the development of a search control framework, called QD-BEACON that uses online -generated statistical models of search performance to

Identification and stochastic control of helicopter dynamic modes

NASA Technical Reports Server (NTRS)

Molusis, J. A.; Bar-Shalom, Y.

1983-01-01

A general treatment of parameter identification and stochastic control for use on helicopter dynamic systems is presented. Rotor dynamic models, including specific applications to rotor blade flapping and the helicopter ground resonance problem are emphasized. Dynamic systems which are governed by periodic coefficients as well as constant coefficient models are addressed. The dynamic systems are modeled by linear state variable equations which are used in the identification and stochastic control formulation. The pure identification problem as well as the stochastic control problem which includes combined identification and control for dynamic systems is addressed. The stochastic control problem includes the effect of parameter uncertainty on the solution and the concept of learning and how this is affected by the control's duel effect. The identification formulation requires algorithms suitable for on line use and thus recursive identification algorithms are considered. The applications presented use the recursive extended kalman filter for parameter identification which has excellent convergence for systems without process noise.

Composite Particle Swarm Optimizer With Historical Memory for Function Optimization.

PubMed

Li, Jie; Zhang, JunQi; Jiang, ChangJun; Zhou, MengChu

2015-10-01

Particle swarm optimization (PSO) algorithm is a population-based stochastic optimization technique. It is characterized by the collaborative search in which each particle is attracted toward the global best position (gbest) in the swarm and its own best position (pbest). However, all of particles' historical promising pbests in PSO are lost except their current pbests. In order to solve this problem, this paper proposes a novel composite PSO algorithm, called historical memory-based PSO (HMPSO), which uses an estimation of distribution algorithm to estimate and preserve the distribution information of particles' historical promising pbests. Each particle has three candidate positions, which are generated from the historical memory, particles' current pbests, and the swarm's gbest. Then the best candidate position is adopted. Experiments on 28 CEC2013 benchmark functions demonstrate the superiority of HMPSO over other algorithms.

Adaptive optimal stochastic state feedback control of resistive wall modes in tokamaks

NASA Astrophysics Data System (ADS)

Sun, Z.; Sen, A. K.; Longman, R. W.

2006-01-01

An adaptive optimal stochastic state feedback control is developed to stabilize the resistive wall mode (RWM) instability in tokamaks. The extended least-square method with exponential forgetting factor and covariance resetting is used to identify (experimentally determine) the time-varying stochastic system model. A Kalman filter is used to estimate the system states. The estimated system states are passed on to an optimal state feedback controller to construct control inputs. The Kalman filter and the optimal state feedback controller are periodically redesigned online based on the identified system model. This adaptive controller can stabilize the time-dependent RWM in a slowly evolving tokamak discharge. This is accomplished within a time delay of roughly four times the inverse of the growth rate for the time-invariant model used.

Adaptive Optimal Stochastic State Feedback Control of Resistive Wall Modes in Tokamaks

NASA Astrophysics Data System (ADS)

Sun, Z.; Sen, A. K.; Longman, R. W.

2007-06-01

An adaptive optimal stochastic state feedback control is developed to stabilize the resistive wall mode (RWM) instability in tokamaks. The extended least square method with exponential forgetting factor and covariance resetting is used to identify the time-varying stochastic system model. A Kalman filter is used to estimate the system states. The estimated system states are passed on to an optimal state feedback controller to construct control inputs. The Kalman filter and the optimal state feedback controller are periodically redesigned online based on the identified system model. This adaptive controller can stabilize the time dependent RWM in a slowly evolving tokamak discharge. This is accomplished within a time delay of roughly four times the inverse of the growth rate for the time-invariant model used.

A Hybrid Interval-Robust Optimization Model for Water Quality Management.

PubMed

Xu, Jieyu; Li, Yongping; Huang, Guohe

2013-05-01

In water quality management problems, uncertainties may exist in many system components and pollution-related processes ( i.e. , random nature of hydrodynamic conditions, variability in physicochemical processes, dynamic interactions between pollutant loading and receiving water bodies, and indeterminacy of available water and treated wastewater). These complexities lead to difficulties in formulating and solving the resulting nonlinear optimization problems. In this study, a hybrid interval-robust optimization (HIRO) method was developed through coupling stochastic robust optimization and interval linear programming. HIRO can effectively reflect the complex system features under uncertainty, where implications of water quality/quantity restrictions for achieving regional economic development objectives are studied. By delimiting the uncertain decision space through dimensional enlargement of the original chemical oxygen demand (COD) discharge constraints, HIRO enhances the robustness of the optimization processes and resulting solutions. This method was applied to planning of industry development in association with river-water pollution concern in New Binhai District of Tianjin, China. Results demonstrated that the proposed optimization model can effectively communicate uncertainties into the optimization process and generate a spectrum of potential inexact solutions supporting local decision makers in managing benefit-effective water quality management schemes. HIRO is helpful for analysis of policy scenarios related to different levels of economic penalties, while also providing insight into the tradeoff between system benefits and environmental requirements.

Essays on the Economics of Climate Change, Biofuel and Food Prices

NASA Astrophysics Data System (ADS)

Seguin, Charles

Climate change is likely to be the most important global pollution problem that humanity has had to face so far. In this dissertation, I tackle issues directly and indirectly related to climate change, bringing my modest contribution to the body of human creativity trying to deal with climate change. First, I look at the impact of non-convex feedbacks on the optimal climate policy. Second, I try to derive the optimal biofuel policy acknowledging the potential negative impacts that biofuel production might have on food supply. Finally, I test empirically for the presence of loss aversion in food purchases, which might play a role in the consumer response to food price changes brought about by biofuel production. Non-convexities in feedback processes are increasingly found to be important in the climate system. To evaluate their impact on the optimal greenhouse gas (GHG) abate- ment policy, I introduce non-convex feedbacks in a stochastic pollution control model. I numerically calibrate the model to represent the mitigation of greenhouse gas (GHG) emissions contributing to global climate change. This approach makes two contributions to the literature. First, it develops a framework to tackle stochastic non-convex pollu- tion management problems. Second, it applies this framework to the problem of climate change. This approach is in contrast to most of the economic literature on climate change that focuses either on linear feedbacks or environmental thresholds. I find that non-convex feedbacks lead to a decision threshold in the optimal mitigation policy, and I characterize how this threshold depends on feedback parameters and stochasticity. There is great hope that biofuel can help reduce greenhouse gas emissions from fossil fuel. However, there are some concerns that biofuel would increase food prices. In an optimal control model, a co-author and I look at the optimal biofuel production when it competes for land with food production. In addition oil is not exhaustible and output is subject to climate change induced damages. We find that the competitive outcome does not necessarily yield an underproduction of biofuels, but when it does, second best policies like subsidies and mandates can improve welfare. In marketing, there has been extensive empirical research to ascertain whether there is evidence of loss aversion as predicted by several reference price preference theories. Most of that literature finds that there is indeed evidence of loss aversion for many different goods. I argue that it is possible that some of that evidence seemingly supporting loss aversion arises because price endogeneity is not properly taken into account. Using scanner data I study four product categories: bread, chicken, corn and tortilla chips, and pasta. Taking prices as exogenous, I find evidence of loss aversion for bread and corn and tortilla chips. However, when instrumenting prices, the "loss aversion evidence" disappears.

Dealing with equality and benefit for water allocation in a lake watershed: A Gini-coefficient based stochastic optimization approach

NASA Astrophysics Data System (ADS)

Dai, C.; Qin, X. S.; Chen, Y.; Guo, H. C.

2018-06-01

A Gini-coefficient based stochastic optimization (GBSO) model was developed by integrating the hydrological model, water balance model, Gini coefficient and chance-constrained programming (CCP) into a general multi-objective optimization modeling framework for supporting water resources allocation at a watershed scale. The framework was advantageous in reflecting the conflicting equity and benefit objectives for water allocation, maintaining the water balance of watershed, and dealing with system uncertainties. GBSO was solved by the non-dominated sorting Genetic Algorithms-II (NSGA-II), after the parameter uncertainties of the hydrological model have been quantified into the probability distribution of runoff as the inputs of CCP model, and the chance constraints were converted to the corresponding deterministic versions. The proposed model was applied to identify the Pareto optimal water allocation schemes in the Lake Dianchi watershed, China. The optimal Pareto-front results reflected the tradeoff between system benefit (αSB) and Gini coefficient (αG) under different significance levels (i.e. q) and different drought scenarios, which reveals the conflicting nature of equity and efficiency in water allocation problems. A lower q generally implies a lower risk of violating the system constraints and a worse drought intensity scenario corresponds to less available water resources, both of which would lead to a decreased system benefit and a less equitable water allocation scheme. Thus, the proposed modeling framework could help obtain the Pareto optimal schemes under complexity and ensure that the proposed water allocation solutions are effective for coping with drought conditions, with a proper tradeoff between system benefit and water allocation equity.

Optimal policies for simultaneous energy consumption and ancillary service provision for flexible loads under stochastic prices and no capacity reservation constraint

NASA Astrophysics Data System (ADS)

Kefayati, Mahdi; Baldick, Ross

2015-07-01

Flexible loads, i.e. the loads whose power trajectory is not bound to a specific one, constitute a sizable portion of current and future electric demand. This flexibility can be used to improve the performance of the grid, should the right incentives be in place. In this paper, we consider the optimal decision making problem faced by a flexible load, demanding a certain amount of energy over its availability period, subject to rate constraints. The load is also capable of providing ancillary services (AS) by decreasing or increasing its consumption in response to signals from the independent system operator (ISO). Under arbitrarily distributed and correlated Markovian energy and AS prices, we obtain the optimal policy for minimising expected total cost, which includes cost of energy and benefits from AS provision, assuming no capacity reservation requirement for AS provision. We also prove that the optimal policy has a multi-threshold form and can be computed, stored and operated efficiently. We further study the effectiveness of our proposed optimal policy and its impact on the grid. We show that, while optimal simultaneous consumption and AS provision under real-time stochastic prices are achievable with acceptable computational burden, the impact of adopting such real-time pricing schemes on the network might not be as good as suggested by the majority of the existing literature. In fact, we show that such price responsive loads are likely to induce peak-to-average ratios much more than what is observed in the current distribution networks and adversely affect the grid.

On the robust optimization to the uncertain vaccination strategy problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chaerani, D., E-mail: d.chaerani@unpad.ac.id; Anggriani, N., E-mail: d.chaerani@unpad.ac.id; Firdaniza, E-mail: d.chaerani@unpad.ac.id

2014-02-21

In order to prevent an epidemic of infectious diseases, the vaccination coverage needs to be minimized and also the basic reproduction number needs to be maintained below 1. This means that as we get the vaccination coverage as minimum as possible, thus we need to prevent the epidemic to a small number of people who already get infected. In this paper, we discuss the case of vaccination strategy in term of minimizing vaccination coverage, when the basic reproduction number is assumed as an uncertain parameter that lies between 0 and 1. We refer to the linear optimization model for vaccinationmore » strategy that propose by Becker and Starrzak (see [2]). Assuming that there is parameter uncertainty involved, we can see Tanner et al (see [9]) who propose the optimal solution of the problem using stochastic programming. In this paper we discuss an alternative way of optimizing the uncertain vaccination strategy using Robust Optimization (see [3]). In this approach we assume that the parameter uncertainty lies within an ellipsoidal uncertainty set such that we can claim that the obtained result will be achieved in a polynomial time algorithm (as it is guaranteed by the RO methodology). The robust counterpart model is presented.« less

Optimizing Negotiation Conflict in the Cloud Service Negotiation Framework Using Probabilistic Decision Making Model

PubMed Central

Rajavel, Rajkumar; Thangarathinam, Mala

2015-01-01

Optimization of negotiation conflict in the cloud service negotiation framework is identified as one of the major challenging issues. This negotiation conflict occurs during the bilateral negotiation process between the participants due to the misperception, aggressive behavior, and uncertain preferences and goals about their opponents. Existing research work focuses on the prerequest context of negotiation conflict optimization by grouping similar negotiation pairs using distance, binary, context-dependent, and fuzzy similarity approaches. For some extent, these approaches can maximize the success rate and minimize the communication overhead among the participants. To further optimize the success rate and communication overhead, the proposed research work introduces a novel probabilistic decision making model for optimizing the negotiation conflict in the long-term negotiation context. This decision model formulates the problem of managing different types of negotiation conflict that occurs during negotiation process as a multistage Markov decision problem. At each stage of negotiation process, the proposed decision model generates the heuristic decision based on the past negotiation state information without causing any break-off among the participants. In addition, this heuristic decision using the stochastic decision tree scenario can maximize the revenue among the participants available in the cloud service negotiation framework. PMID:26543899

Optimizing Negotiation Conflict in the Cloud Service Negotiation Framework Using Probabilistic Decision Making Model.

PubMed

Rajavel, Rajkumar; Thangarathinam, Mala

2015-01-01

Optimization of negotiation conflict in the cloud service negotiation framework is identified as one of the major challenging issues. This negotiation conflict occurs during the bilateral negotiation process between the participants due to the misperception, aggressive behavior, and uncertain preferences and goals about their opponents. Existing research work focuses on the prerequest context of negotiation conflict optimization by grouping similar negotiation pairs using distance, binary, context-dependent, and fuzzy similarity approaches. For some extent, these approaches can maximize the success rate and minimize the communication overhead among the participants. To further optimize the success rate and communication overhead, the proposed research work introduces a novel probabilistic decision making model for optimizing the negotiation conflict in the long-term negotiation context. This decision model formulates the problem of managing different types of negotiation conflict that occurs during negotiation process as a multistage Markov decision problem. At each stage of negotiation process, the proposed decision model generates the heuristic decision based on the past negotiation state information without causing any break-off among the participants. In addition, this heuristic decision using the stochastic decision tree scenario can maximize the revenue among the participants available in the cloud service negotiation framework.

Simulation-based planning for theater air warfare

NASA Astrophysics Data System (ADS)

Popken, Douglas A.; Cox, Louis A., Jr.

2004-08-01

Planning for Theatre Air Warfare can be represented as a hierarchy of decisions. At the top level, surviving airframes must be assigned to roles (e.g., Air Defense, Counter Air, Close Air Support, and AAF Suppression) in each time period in response to changing enemy air defense capabilities, remaining targets, and roles of opposing aircraft. At the middle level, aircraft are allocated to specific targets to support their assigned roles. At the lowest level, routing and engagement decisions are made for individual missions. The decisions at each level form a set of time-sequenced Courses of Action taken by opposing forces. This paper introduces a set of simulation-based optimization heuristics operating within this planning hierarchy to optimize allocations of aircraft. The algorithms estimate distributions for stochastic outcomes of the pairs of Red/Blue decisions. Rather than using traditional stochastic dynamic programming to determine optimal strategies, we use an innovative combination of heuristics, simulation-optimization, and mathematical programming. Blue decisions are guided by a stochastic hill-climbing search algorithm while Red decisions are found by optimizing over a continuous representation of the decision space. Stochastic outcomes are then provided by fast, Lanchester-type attrition simulations. This paper summarizes preliminary results from top and middle level models.

A New Methodology for Open Pit Slope Design in Karst-Prone Ground Conditions Based on Integrated Stochastic-Limit Equilibrium Analysis

NASA Astrophysics Data System (ADS)

Zhang, Ke; Cao, Ping; Ma, Guowei; Fan, Wenchen; Meng, Jingjing; Li, Kaihui

2016-07-01

Using the Chengmenshan Copper Mine as a case study, a new methodology for open pit slope design in karst-prone ground conditions is presented based on integrated stochastic-limit equilibrium analysis. The numerical modeling and optimization design procedure contain a collection of drill core data, karst cave stochastic model generation, SLIDE simulation and bisection method optimization. Borehole investigations are performed, and the statistical result shows that the length of the karst cave fits a negative exponential distribution model, but the length of carbonatite does not exactly follow any standard distribution. The inverse transform method and acceptance-rejection method are used to reproduce the length of the karst cave and carbonatite, respectively. A code for karst cave stochastic model generation, named KCSMG, is developed. The stability of the rock slope with the karst cave stochastic model is analyzed by combining the KCSMG code and the SLIDE program. This approach is then applied to study the effect of the karst cave on the stability of the open pit slope, and a procedure to optimize the open pit slope angle is presented.

Taming the Wild: A Unified Analysis of Hogwild!-Style Algorithms.

PubMed

De Sa, Christopher; Zhang, Ce; Olukotun, Kunle; Ré, Christopher

2015-12-01

Stochastic gradient descent (SGD) is a ubiquitous algorithm for a variety of machine learning problems. Researchers and industry have developed several techniques to optimize SGD's runtime performance, including asynchronous execution and reduced precision. Our main result is a martingale-based analysis that enables us to capture the rich noise models that may arise from such techniques. Specifically, we use our new analysis in three ways: (1) we derive convergence rates for the convex case (Hogwild!) with relaxed assumptions on the sparsity of the problem; (2) we analyze asynchronous SGD algorithms for non-convex matrix problems including matrix completion; and (3) we design and analyze an asynchronous SGD algorithm, called Buckwild!, that uses lower-precision arithmetic. We show experimentally that our algorithms run efficiently for a variety of problems on modern hardware.

Static vs stochastic optimization: A case study of FTSE Bursa Malaysia sectorial indices

NASA Astrophysics Data System (ADS)

Mamat, Nur Jumaadzan Zaleha; Jaaman, Saiful Hafizah; Ahmad, Rokiah@Rozita

2014-06-01

Traditional portfolio optimization methods in the likes of Markowitz' mean-variance model and semi-variance model utilize static expected return and volatility risk from historical data to generate an optimal portfolio. The optimal portfolio may not truly be optimal in reality due to the fact that maximum and minimum values from the data may largely influence the expected return and volatility risk values. This paper considers distributions of assets' return and volatility risk to determine a more realistic optimized portfolio. For illustration purposes, the sectorial indices data in FTSE Bursa Malaysia is employed. The results show that stochastic optimization provides more stable information ratio.

Evaluating the influence of motor control on selective attention through a stochastic model: the paradigm of motor control dysfunction in cerebellar patient.

PubMed

Veneri, Giacomo; Federico, Antonio; Rufa, Alessandra

2014-01-01

Attention allows us to selectively process the vast amount of information with which we are confronted, prioritizing some aspects of information and ignoring others by focusing on a certain location or aspect of the visual scene. Selective attention is guided by two cognitive mechanisms: saliency of the image (bottom up) and endogenous mechanisms (top down). These two mechanisms interact to direct attention and plan eye movements; then, the movement profile is sent to the motor system, which must constantly update the command needed to produce the desired eye movement. A new approach is described here to study how the eye motor control could influence this selection mechanism in clinical behavior: two groups of patients (SCA2 and late onset cerebellar ataxia LOCA) with well-known problems of motor control were studied; patients performed a cognitively demanding task; the results were compared to a stochastic model based on Monte Carlo simulations and a group of healthy subjects. The analytical procedure evaluated some energy functions for understanding the process. The implemented model suggested that patients performed an optimal visual search, reducing intrinsic noise sources. Our findings theorize a strict correlation between the "optimal motor system" and the "optimal stimulus encoders."

Fast cooling for a system of stochastic oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Yongxin, E-mail: chen2468@umn.edu; Georgiou, Tryphon T., E-mail: tryphon@umn.edu; Pavon, Michele, E-mail: pavon@math.unipd.it

2015-11-15

We study feedback control of coupled nonlinear stochastic oscillators in a force field. We first consider the problem of asymptotically driving the system to a desired steady state corresponding to reduced thermal noise. Among the feedback controls achieving the desired asymptotic transfer, we find that the most efficient one from an energy point of view is characterized by time-reversibility. We also extend the theory of Schrödinger bridges to this model, thereby steering the system in finite time and with minimum effort to a target steady-state distribution. The system can then be maintained in this state through the optimal steady-state feedbackmore » control. The solution, in the finite-horizon case, involves a space-time harmonic function φ, and −logφ plays the role of an artificial, time-varying potential in which the desired evolution occurs. This framework appears extremely general and flexible and can be viewed as a considerable generalization of existing active control strategies such as macromolecular cooling. In the case of a quadratic potential, the results assume a form particularly attractive from the algorithmic viewpoint as the optimal control can be computed via deterministic matricial differential equations. An example involving inertial particles illustrates both transient and steady state optimal feedback control.« less

Variational formulation for Black-Scholes equations in stochastic volatility models

NASA Astrophysics Data System (ADS)

Gyulov, Tihomir B.; Valkov, Radoslav L.

2012-11-01

In this note we prove existence and uniqueness of weak solutions to a boundary value problem arising from stochastic volatility models in financial mathematics. Our settings are variational in weighted Sobolev spaces. Nevertheless, as it will become apparent our variational formulation agrees well with the stochastic part of the problem.

Optimization for routing vehicles of seafood product transportation

NASA Astrophysics Data System (ADS)

Soenandi, I. A.; Juan, Y.; Budi, M.

2017-12-01

Recently, increasing usage of marine products is creating new challenges for businesses of marine products in terms of transportation that used to carry the marine products like seafood to the main warehouse. This can be a problem if the carrier fleet is limited, and there are time constraints in terms of the freshness of the marine product. There are many ways to solve this problem, including the optimization of routing vehicles. In this study, this strategy is to implement in the marine product business in Indonesia with such an expected arrangement of the company to optimize routing problem in transportation with time and capacity windows. Until now, the company has not used the scientific method to manage the routing of their vehicle from warehouse to the location of marine products source. This study will solve a stochastic Vehicle Routing Problems (VRP) with time and capacity windows by using the comparison of six methods and looking the best results for the optimization, in this situation the company could choose the best method, in accordance with the existing condition. In this research, we compared the optimization with another method such as branch and bound, dynamic programming and Ant Colony Optimization (ACO). Finally, we get the best result after running ACO algorithm with existing travel time data. With ACO algorithm was able to reduce vehicle travel time by 3189.65 minutes, which is about 23% less than existing and based on consideration of the constraints of time within 2 days (including rest time for the driver) using 28 tons capacity of truck and the companies need two units of vehicles for transportation.

A PSO-Based Hybrid Metaheuristic for Permutation Flowshop Scheduling Problems

PubMed Central

Zhang, Le; Wu, Jinnan

2014-01-01

This paper investigates the permutation flowshop scheduling problem (PFSP) with the objectives of minimizing the makespan and the total flowtime and proposes a hybrid metaheuristic based on the particle swarm optimization (PSO). To enhance the exploration ability of the hybrid metaheuristic, a simulated annealing hybrid with a stochastic variable neighborhood search is incorporated. To improve the search diversification of the hybrid metaheuristic, a solution replacement strategy based on the pathrelinking is presented to replace the particles that have been trapped in local optimum. Computational results on benchmark instances show that the proposed PSO-based hybrid metaheuristic is competitive with other powerful metaheuristics in the literature. PMID:24672389

A PSO-based hybrid metaheuristic for permutation flowshop scheduling problems.

PubMed

Zhang, Le; Wu, Jinnan

2014-01-01

This paper investigates the permutation flowshop scheduling problem (PFSP) with the objectives of minimizing the makespan and the total flowtime and proposes a hybrid metaheuristic based on the particle swarm optimization (PSO). To enhance the exploration ability of the hybrid metaheuristic, a simulated annealing hybrid with a stochastic variable neighborhood search is incorporated. To improve the search diversification of the hybrid metaheuristic, a solution replacement strategy based on the pathrelinking is presented to replace the particles that have been trapped in local optimum. Computational results on benchmark instances show that the proposed PSO-based hybrid metaheuristic is competitive with other powerful metaheuristics in the literature.

Applying a Genetic Algorithm to Reconfigurable Hardware

NASA Technical Reports Server (NTRS)

Wells, B. Earl; Weir, John; Trevino, Luis; Patrick, Clint; Steincamp, Jim

2004-01-01

This paper investigates the feasibility of applying genetic algorithms to solve optimization problems that are implemented entirely in reconfgurable hardware. The paper highlights the pe$ormance/design space trade-offs that must be understood to effectively implement a standard genetic algorithm within a modem Field Programmable Gate Array, FPGA, reconfgurable hardware environment and presents a case-study where this stochastic search technique is applied to standard test-case problems taken from the technical literature. In this research, the targeted FPGA-based platform and high-level design environment was the Starbridge Hypercomputing platform, which incorporates multiple Xilinx Virtex II FPGAs, and the Viva TM graphical hardware description language.

Robust Transceiver Design for Multiuser MIMO Downlink with Channel Uncertainties

NASA Astrophysics Data System (ADS)

Miao, Wei; Li, Yunzhou; Chen, Xiang; Zhou, Shidong; Wang, Jing

This letter addresses the problem of robust transceiver design for the multiuser multiple-input-multiple-output (MIMO) downlink where the channel state information at the base station (BS) is imperfect. A stochastic approach which minimizes the expectation of the total mean square error (MSE) of the downlink conditioned on the channel estimates under a total transmit power constraint is adopted. The iterative algorithm reported in [2] is improved to handle the proposed robust optimization problem. Simulation results show that our proposed robust scheme effectively reduces the performance loss due to channel uncertainties and outperforms existing methods, especially when the channel errors of the users are different.

Using Ant Colony Optimization for Routing in VLSI Chips

NASA Astrophysics Data System (ADS)

Arora, Tamanna; Moses, Melanie

2009-04-01

Rapid advances in VLSI technology have increased the number of transistors that fit on a single chip to about two billion. A frequent problem in the design of such high performance and high density VLSI layouts is that of routing wires that connect such large numbers of components. Most wire-routing problems are computationally hard. The quality of any routing algorithm is judged by the extent to which it satisfies routing constraints and design objectives. Some of the broader design objectives include minimizing total routed wire length, and minimizing total capacitance induced in the chip, both of which serve to minimize power consumed by the chip. Ant Colony Optimization algorithms (ACO) provide a multi-agent framework for combinatorial optimization by combining memory, stochastic decision and strategies of collective and distributed learning by ant-like agents. This paper applies ACO to the NP-hard problem of finding optimal routes for interconnect routing on VLSI chips. The constraints on interconnect routing are used by ants as heuristics which guide their search process. We found that ACO algorithms were able to successfully incorporate multiple constraints and route interconnects on suite of benchmark chips. On an average, the algorithm routed with total wire length 5.5% less than other established routing algorithms.

Optimizing integrated airport surface and terminal airspace operations under uncertainty

NASA Astrophysics Data System (ADS)

Bosson, Christabelle S.

In airports and surrounding terminal airspaces, the integration of surface, arrival and departure scheduling and routing have the potential to improve the operations efficiency. Moreover, because both the airport surface and the terminal airspace are often altered by random perturbations, the consideration of uncertainty in flight schedules is crucial to improve the design of robust flight schedules. Previous research mainly focused on independently solving arrival scheduling problems, departure scheduling problems and surface management scheduling problems and most of the developed models are deterministic. This dissertation presents an alternate method to model the integrated operations by using a machine job-shop scheduling formulation. A multistage stochastic programming approach is chosen to formulate the problem in the presence of uncertainty and candidate solutions are obtained by solving sample average approximation problems with finite sample size. The developed mixed-integer-linear-programming algorithm-based scheduler is capable of computing optimal aircraft schedules and routings that reflect the integration of air and ground operations. The assembled methodology is applied to a Los Angeles case study. To show the benefits of integrated operations over First-Come-First-Served, a preliminary proof-of-concept is conducted for a set of fourteen aircraft evolving under deterministic conditions in a model of the Los Angeles International Airport surface and surrounding terminal areas. Using historical data, a representative 30-minute traffic schedule and aircraft mix scenario is constructed. The results of the Los Angeles application show that the integration of air and ground operations and the use of a time-based separation strategy enable both significant surface and air time savings. The solution computed by the optimization provides a more efficient routing and scheduling than the First-Come-First-Served solution. Additionally, a data driven analysis is performed for the Los Angeles environment and probabilistic distributions of pertinent uncertainty sources are obtained. A sensitivity analysis is then carried out to assess the methodology performance and find optimal sampling parameters. Finally, simulations of increasing traffic density in the presence of uncertainty are conducted first for integrated arrivals and departures, then for integrated surface and air operations. To compare the optimization results and show the benefits of integrated operations, two aircraft separation methods are implemented that offer different routing options. The simulations of integrated air operations and the simulations of integrated air and surface operations demonstrate that significant traveling time savings, both total and individual surface and air times, can be obtained when more direct routes are allowed to be traveled even in the presence of uncertainty. The resulting routings induce however extra take off delay for departing flights. As a consequence, some flights cannot meet their initial assigned runway slot which engenders runway position shifting when comparing resulting runway sequences computed under both deterministic and stochastic conditions. The optimization is able to compute an optimal runway schedule that represents an optimal balance between total schedule delays and total travel times.

Pathwise Strategies for Stochastic Differential Games with an Erratum to 'Stochastic Differential Games with Asymmetric Information'

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cardaliaguet, P., E-mail: cardaliaguet@ceremade.dauphine.fr; Rainer, C., E-mail: Catherine.Rainer@univ-brest.fr

We introduce a new notion of pathwise strategies for stochastic differential games. This allows us to give a correct meaning to some statement asserted in Cardaliaguet and Rainer (Appl. Math. Optim. 59: 1-36, 2009)

Optimal lunar soft landing trajectories using taboo evolutionary programming

NASA Astrophysics Data System (ADS)

Mutyalarao, M.; Raj, M. Xavier James

A safe lunar landing is a key factor to undertake an effective lunar exploration. Lunar lander consists of four phases such as launch phase, the earth-moon transfer phase, circumlunar phase and landing phase. The landing phase can be either hard landing or soft landing. Hard landing means the vehicle lands under the influence of gravity without any deceleration measures. However, soft landing reduces the vertical velocity of the vehicle before landing. Therefore, for the safety of the astronauts as well as the vehicle lunar soft landing with an acceptable velocity is very much essential. So it is important to design the optimal lunar soft landing trajectory with minimum fuel consumption. Optimization of Lunar Soft landing is a complex optimal control problem. In this paper, an analysis related to lunar soft landing from a parking orbit around Moon has been carried out. A two-dimensional trajectory optimization problem is attempted. The problem is complex due to the presence of system constraints. To solve the time-history of control parameters, the problem is converted into two point boundary value problem by using the maximum principle of Pontrygen. Taboo Evolutionary Programming (TEP) technique is a stochastic method developed in recent years and successfully implemented in several fields of research. It combines the features of taboo search and single-point mutation evolutionary programming. Identifying the best unknown parameters of the problem under consideration is the central idea for many space trajectory optimization problems. The TEP technique is used in the present methodology for the best estimation of initial unknown parameters by minimizing objective function interms of fuel requirements. The optimal estimation subsequently results into an optimal trajectory design of a module for soft landing on the Moon from a lunar parking orbit. Numerical simulations demonstrate that the proposed approach is highly efficient and it reduces the minimum fuel consumption. The results are compared with the available results in literature shows that the solution of present algorithm is better than some of the existing algorithms. Keywords: soft landing, trajectory optimization, evolutionary programming, control parameters, Pontrygen principle.

Adaptive, Distributed Control of Constrained Multi-Agent Systems

NASA Technical Reports Server (NTRS)

Bieniawski, Stefan; Wolpert, David H.

2004-01-01

Product Distribution (PO) theory was recently developed as a broad framework for analyzing and optimizing distributed systems. Here we demonstrate its use for adaptive distributed control of Multi-Agent Systems (MASS), i.e., for distributed stochastic optimization using MAS s. First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (Probability dist&&on on the joint state of the agents. When the game in question is a team game with constraints, that equilibrium optimizes the expected value of the team game utility, subject to those constraints. One common way to find that equilibrium is to have each agent run a Reinforcement Learning (E) algorithm. PD theory reveals this to be a particular type of search algorithm for minimizing the Lagrangian. Typically that algorithm i s quite inefficient. A more principled alternative is to use a variant of Newton's method to minimize the Lagrangian. Here we compare this alternative to RL-based search in three sets of computer experiments. These are the N Queen s problem and bin-packing problem from the optimization literature, and the Bar problem from the distributed RL literature. Our results confirm that the PD-theory-based approach outperforms the RL-based scheme in all three domains.

Use of behavioural stochastic resonance by paddle fish for feeding

NASA Astrophysics Data System (ADS)

Russell, David F.; Wilkens, Lon A.; Moss, Frank

1999-11-01

Stochastic resonance is the phenomenon whereby the addition of an optimal level of noise to a weak information-carrying input to certain nonlinear systems can enhance the information content at their outputs. Computer analysis of spike trains has been needed to reveal stochastic resonance in the responses of sensory receptors except for one study on human psychophysics. But is an animal aware of, and can it make use of, the enhanced sensory information from stochastic resonance? Here, we show that stochastic resonance enhances the normal feeding behaviour of paddlefish (Polyodon spathula), which use passive electroreceptors to detect electrical signals from planktonic prey. We demonstrate significant broadening of the spatial range for the detection of plankton when a noisy electric field of optimal amplitude is applied in the water. We also show that swarms of Daphnia plankton are a natural source of electrical noise. Our demonstration of stochastic resonance at the level of a vital animal behaviour, feeding, which has probably evolved for functional success, provides evidence that stochastic resonance in sensory nervous systems is an evolutionary adaptation.

Stochastic dynamic programming illuminates the link between environment, physiology, and evolution.

PubMed

Mangel, Marc

2015-05-01

I describe how stochastic dynamic programming (SDP), a method for stochastic optimization that evolved from the work of Hamilton and Jacobi on variational problems, allows us to connect the physiological state of organisms, the environment in which they live, and how evolution by natural selection acts on trade-offs that all organisms face. I first derive the two canonical equations of SDP. These are valuable because although they apply to no system in particular, they share commonalities with many systems (as do frictionless springs). After that, I show how we used SDP in insect behavioral ecology. I describe the puzzles that needed to be solved, the SDP equations we used to solve the puzzles, and the experiments that we used to test the predictions of the models. I then briefly describe two other applications of SDP in biology: first, understanding the developmental pathways followed by steelhead trout in California and second skipped spawning by Norwegian cod. In both cases, modeling and empirical work were closely connected. I close with lessons learned and advice for the young mathematical biologists.

A computational framework for prime implicants identification in noncoherent dynamic systems.

PubMed

Di Maio, Francesco; Baronchelli, Samuele; Zio, Enrico

2015-01-01

Dynamic reliability methods aim at complementing the capability of traditional static approaches (e.g., event trees [ETs] and fault trees [FTs]) by accounting for the system dynamic behavior and its interactions with the system state transition process. For this, the system dynamics is here described by a time-dependent model that includes the dependencies with the stochastic transition events. In this article, we present a novel computational framework for dynamic reliability analysis whose objectives are i) accounting for discrete stochastic transition events and ii) identifying the prime implicants (PIs) of the dynamic system. The framework entails adopting a multiple-valued logic (MVL) to consider stochastic transitions at discretized times. Then, PIs are originally identified by a differential evolution (DE) algorithm that looks for the optimal MVL solution of a covering problem formulated for MVL accident scenarios. For testing the feasibility of the framework, a dynamic noncoherent system composed of five components that can fail at discretized times has been analyzed, showing the applicability of the framework to practical cases. © 2014 Society for Risk Analysis.

Efficient simulation of intrinsic, extrinsic and external noise in biochemical systems

PubMed Central

Pischel, Dennis; Sundmacher, Kai; Flassig, Robert J.

2017-01-01

Abstract Motivation: Biological cells operate in a noisy regime influenced by intrinsic, extrinsic and external noise, which leads to large differences of individual cell states. Stochastic effects must be taken into account to characterize biochemical kinetics accurately. Since the exact solution of the chemical master equation, which governs the underlying stochastic process, cannot be derived for most biochemical systems, approximate methods are used to obtain a solution. Results: In this study, a method to efficiently simulate the various sources of noise simultaneously is proposed and benchmarked on several examples. The method relies on the combination of the sigma point approach to describe extrinsic and external variability and the τ-leaping algorithm to account for the stochasticity due to probabilistic reactions. The comparison of our method to extensive Monte Carlo calculations demonstrates an immense computational advantage while losing an acceptable amount of accuracy. Additionally, the application to parameter optimization problems in stochastic biochemical reaction networks is shown, which is rarely applied due to its huge computational burden. To give further insight, a MATLAB script is provided including the proposed method applied to a simple toy example of gene expression. Availability and implementation: MATLAB code is available at Bioinformatics online. Contact: flassig@mpi-magdeburg.mpg.de Supplementary information: Supplementary data are available at Bioinformatics online. PMID:28881987

Quantum Hamilton equations of motion for bound states of one-dimensional quantum systems

NASA Astrophysics Data System (ADS)

Köppe, J.; Patzold, M.; Grecksch, W.; Paul, W.

2018-06-01

On the basis of Nelson's stochastic mechanics derivation of the Schrödinger equation, a formal mathematical structure of non-relativistic quantum mechanics equivalent to the one in classical analytical mechanics has been established in the literature. We recently were able to augment this structure by deriving quantum Hamilton equations of motion by finding the Nash equilibrium of a stochastic optimal control problem, which is the generalization of Hamilton's principle of classical mechanics to quantum systems. We showed that these equations allow a description and numerical determination of the ground state of quantum problems without using the Schrödinger equation. We extend this approach here to deliver the complete discrete energy spectrum and related eigenfunctions for bound states of one-dimensional stationary quantum systems. We exemplify this analytically for the one-dimensional harmonic oscillator and numerically by analyzing a quartic double-well potential, a model of broad importance in many areas of physics. We furthermore point out a relation between the tunnel splitting of such models and mean first passage time concepts applied to Nelson's diffusion paths in the ground state.

FAST: a framework for simulation and analysis of large-scale protein-silicon biosensor circuits.

PubMed

Gu, Ming; Chakrabartty, Shantanu

2013-08-01

This paper presents a computer aided design (CAD) framework for verification and reliability analysis of protein-silicon hybrid circuits used in biosensors. It is envisioned that similar to integrated circuit (IC) CAD design tools, the proposed framework will be useful for system level optimization of biosensors and for discovery of new sensing modalities without resorting to laborious fabrication and experimental procedures. The framework referred to as FAST analyzes protein-based circuits by solving inverse problems involving stochastic functional elements that admit non-linear relationships between different circuit variables. In this regard, FAST uses a factor-graph netlist as a user interface and solving the inverse problem entails passing messages/signals between the internal nodes of the netlist. Stochastic analysis techniques like density evolution are used to understand the dynamics of the circuit and estimate the reliability of the solution. As an example, we present a complete design flow using FAST for synthesis, analysis and verification of our previously reported conductometric immunoassay that uses antibody-based circuits to implement forward error-correction (FEC).

Trends in modern system theory

NASA Technical Reports Server (NTRS)

Athans, M.

1976-01-01

The topics considered are related to linear control system design, adaptive control, failure detection, control under failure, system reliability, and large-scale systems and decentralized control. It is pointed out that the design of a linear feedback control system which regulates a process about a desirable set point or steady-state condition in the presence of disturbances is a very important problem. The linearized dynamics of the process are used for design purposes. The typical linear-quadratic design involving the solution of the optimal control problem of a linear time-invariant system with respect to a quadratic performance criterion is considered along with gain reduction theorems and the multivariable phase margin theorem. The stumbling block in many adaptive design methodologies is associated with the amount of real time computation which is necessary. Attention is also given to the desperate need to develop good theories for large-scale systems, the beginning of a microprocessor revolution, the translation of the Wiener-Hopf theory into the time domain, and advances made in dynamic team theory, dynamic stochastic games, and finite memory stochastic control.

Multi-objective robust design of energy-absorbing components using coupled process-performance simulations

NASA Astrophysics Data System (ADS)

Najafi, Ali; Acar, Erdem; Rais-Rohani, Masoud

2014-02-01

The stochastic uncertainties associated with the material, process and product are represented and propagated to process and performance responses. A finite element-based sequential coupled process-performance framework is used to simulate the forming and energy absorption responses of a thin-walled tube in a manner that both material properties and component geometry can evolve from one stage to the next for better prediction of the structural performance measures. Metamodelling techniques are used to develop surrogate models for manufacturing and performance responses. One set of metamodels relates the responses to the random variables whereas the other relates the mean and standard deviation of the responses to the selected design variables. A multi-objective robust design optimization problem is formulated and solved to illustrate the methodology and the influence of uncertainties on manufacturability and energy absorption of a metallic double-hat tube. The results are compared with those of deterministic and augmented robust optimization problems.

Proceedings of the Dundee Conference (10th) Held in Dundee, Scotland on July 1988. Ordinary and Partial Differential Equations. Volume 2

DTIC Science & Technology

1988-07-01

a priori inequalities with applications to R J Knops boundary value problems 40 Singular systems of differential equations V G Sigiilito S L...Stochastic functional differential equations S E A Mohammed 100 Optimal control of variational inequalities 125 Ennio de Giorgi Colloquium V Barbu P Kr e...location of the period-doubled bifurcation point varies slightly with Zc [ 3 ]. In addition, no significant effect is found if a smoother functional

Deterministic Methods in Stochastic Optimal Control.

DTIC Science & Technology

1992-10-01

as (0.1) by adding a correction terito Ot ,h drift . L.tt us con|sidehr the Stoclia.tic optimtal control problem (0.1),(0.2). The dynaumtic progra...with ant icipative drift ) which will be done in Secioni I .sing Ihli decomposition of solutions of SI)E’s (see Kunila [14. p. 268] and Ocone and...programllitig. In the case when nonanticipating controls appear in the drift the Wong-Zakai con•’.rgence result slates that under smoothness and boundedness

Hybrid Solution of Stochastic Optimal Control Problems Using Gauss Pseudospectral Method and Generalized Polynomial Chaos Algorithms

DTIC Science & Technology

2012-03-01

0-486-41183-4. 15. Brown , Robert G. and Patrick Y. C. Hwang . Introduction to Random Signals and Applied Kalman Filtering. Wiley, New York, 1996. ISBN...stability and perfor- mance criteria. In the 1960’s, Kalman introduced the Linear Quadratic Regulator (LQR) method using an integral performance index...feedback of the state variables and was able to apply this method to time-varying and Multi-Input Multi-Output (MIMO) systems. Kalman further showed

A hyperbolastic type-I diffusion process: Parameter estimation by means of the firefly algorithm.

PubMed

Barrera, Antonio; Román-Román, Patricia; Torres-Ruiz, Francisco

2018-01-01

A stochastic diffusion process, whose mean function is a hyperbolastic curve of type I, is presented. The main characteristics of the process are studied and the problem of maximum likelihood estimation for the parameters of the process is considered. To this end, the firefly metaheuristic optimization algorithm is applied after bounding the parametric space by a stagewise procedure. Some examples based on simulated sample paths and real data illustrate this development. Copyright © 2017 Elsevier B.V. All rights reserved.

Determination of Material Properties by Limited Scan X-Ray Tomography

DTIC Science & Technology

1981-09-01

83 4.2 Modeling Projection 88 4.3 Basic Signal-to- Noise considerations 97 4.3.1 Concept of optimal beams hardness 97 4.3.2 Selection of best...projection 100 4.3.3 The relation of Noise terms to multiscan 100 4.3.4 Uncertainty in multiscan when beams overlap...104 4.3.5 Coll imators 106 5...assumes large measurement noise - the other perfect measurements. In this latter case the stochastic nature of the problem is maintained by assuming

Real-Time Control of an Ensemble of Heterogeneous Resources

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bernstein, Andrey; Bouman, Niek J.; Le Boudec, Jean-Yves

This paper focuses on the problem of controlling an ensemble of heterogeneous resources connected to an electrical grid at the same point of common coupling (PCC). The controller receives an aggregate power setpoint for the ensemble in real time and tracks this setpoint by issuing individual optimal setpoints to the resources. The resources can have continuous or discrete nature (e.g., heating systems consisting of a finite number of heaters that each can be either switched on or off) and/or can be highly uncertain (e.g., photovoltaic (PV) systems or residential loads). A naive approach would lead to a stochastic mixed-integer optimizationmore » problem to be solved at the controller at each time step, which might be infeasible in real time. Instead, we allow the controller to solve a continuous convex optimization problem and compensate for the errors at the resource level by using a variant of the well-known error diffusion algorithm. We give conditions guaranteeing that our algorithm tracks the power setpoint at the PCC on average while issuing optimal setpoints to individual resources. We illustrate the approach numerically by controlling a collection of batteries, PV systems, and discrete loads.« less

Integrating stochastic time-dependent travel speed in solution methods for the dynamic dial-a-ride problem

PubMed Central

Schilde, M.; Doerner, K.F.; Hartl, R.F.

2014-01-01

In urban areas, logistic transportation operations often run into problems because travel speeds change, depending on the current traffic situation. If not accounted for, time-dependent and stochastic travel speeds frequently lead to missed time windows and thus poorer service. Especially in the case of passenger transportation, it often leads to excessive passenger ride times as well. Therefore, time-dependent and stochastic influences on travel speeds are relevant for finding feasible and reliable solutions. This study considers the effect of exploiting statistical information available about historical accidents, using stochastic solution approaches for the dynamic dial-a-ride problem (dynamic DARP). The authors propose two pairs of metaheuristic solution approaches, each consisting of a deterministic method (average time-dependent travel speeds for planning) and its corresponding stochastic version (exploiting stochastic information while planning). The results, using test instances with up to 762 requests based on a real-world road network, show that in certain conditions, exploiting stochastic information about travel speeds leads to significant improvements over deterministic approaches. PMID:25844013

Technologies to Increase PV Hosting Capacity in Distribution Feeders: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ding, Fei; Mather, Barry; Gotseff, Peter

This paper studies the distributed photovoltaic (PV) hosting capacity in distribution feeders by using the stochastic analysis approach. Multiple scenario simulations are conducted to analyze several factors that affect PV hosting capacity, including the existence of voltage regulator, PV location, the power factor of PV inverter and Volt/VAR control. Based on the conclusions obtained from simulation results, three approaches are then proposed to increase distributed PV hosting capacity, which can be formulated as the optimization problem to obtain the optimal solution. All technologies investigated in this paper utilize only existing assets in the feeder and therefore are implementable for amore » low cost. Additionally, the tool developed for these studies is described.« less

Technologies to Increase PV Hosting Capacity in Distribution Feeders

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ding, Fei; Mather, Barry; Gotseff, Peter

This paper studies the distributed photovoltaic (PV) hosting capacity in distribution feeders by using the stochastic analysis approach. Multiple scenario simulations are conducted to analyze several factors that affect PV hosting capacity, including the existence of voltage regulator, PV location, the power factor of PV inverter and Volt/VAR control. Based on the conclusions obtained from simulation results, three approaches are then proposed to increase distributed PV hosting capacity, which can be formulated as the optimization problem to obtain the optimal solution. All technologies investigated in this paper utilize only existing assets in the feeder and therefore are implementable for amore » low cost. Additionally, the tool developed for these studies is described.« less

On Distributed PV Hosting Capacity Estimation, Sensitivity Study, and Improvement

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ding, Fei; Mather, Barry

This paper first studies the estimated distributed PV hosting capacities of seventeen utility distribution feeders using the Monte Carlo simulation based stochastic analysis, and then analyzes the sensitivity of PV hosting capacity to both feeder and photovoltaic system characteristics. Furthermore, an active distribution network management approach is proposed to maximize PV hosting capacity by optimally switching capacitors, adjusting voltage regulator taps, managing controllable branch switches and controlling smart PV inverters. The approach is formulated as a mixed-integer nonlinear optimization problem and a genetic algorithm is developed to obtain the solution. Multiple simulation cases are studied and the effectiveness of themore » proposed approach on increasing PV hosting capacity is demonstrated.« less

Optimization of High-Dimensional Functions through Hypercube Evaluation

PubMed Central

Abiyev, Rahib H.; Tunay, Mustafa

2015-01-01

A novel learning algorithm for solving global numerical optimization problems is proposed. The proposed learning algorithm is intense stochastic search method which is based on evaluation and optimization of a hypercube and is called the hypercube optimization (HO) algorithm. The HO algorithm comprises the initialization and evaluation process, displacement-shrink process, and searching space process. The initialization and evaluation process initializes initial solution and evaluates the solutions in given hypercube. The displacement-shrink process determines displacement and evaluates objective functions using new points, and the search area process determines next hypercube using certain rules and evaluates the new solutions. The algorithms for these processes have been designed and presented in the paper. The designed HO algorithm is tested on specific benchmark functions. The simulations of HO algorithm have been performed for optimization of functions of 1000-, 5000-, or even 10000 dimensions. The comparative simulation results with other approaches demonstrate that the proposed algorithm is a potential candidate for optimization of both low and high dimensional functions. PMID:26339237

Bilevel formulation of a policy design problem considering multiple objectives and incomplete preferences

NASA Astrophysics Data System (ADS)

Hawthorne, Bryant; Panchal, Jitesh H.

2014-07-01

A bilevel optimization formulation of policy design problems considering multiple objectives and incomplete preferences of the stakeholders is presented. The formulation is presented for Feed-in-Tariff (FIT) policy design for decentralized energy infrastructure. The upper-level problem is the policy designer's problem and the lower-level problem is a Nash equilibrium problem resulting from market interactions. The policy designer has two objectives: maximizing the quantity of energy generated and minimizing policy cost. The stakeholders decide on quantities while maximizing net present value and minimizing capital investment. The Nash equilibrium problem in the presence of incomplete preferences is formulated as a stochastic linear complementarity problem and solved using expected value formulation, expected residual minimization formulation, and the Monte Carlo technique. The primary contributions in this article are the mathematical formulation of the FIT policy, the extension of computational policy design problems to multiple objectives, and the consideration of incomplete preferences of stakeholders for policy design problems.

Static vs stochastic optimization: A case study of FTSE Bursa Malaysia sectorial indices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mamat, Nur Jumaadzan Zaleha; Jaaman, Saiful Hafizah; Ahmad, Rokiah Rozita

2014-06-19

Traditional portfolio optimization methods in the likes of Markowitz' mean-variance model and semi-variance model utilize static expected return and volatility risk from historical data to generate an optimal portfolio. The optimal portfolio may not truly be optimal in reality due to the fact that maximum and minimum values from the data may largely influence the expected return and volatility risk values. This paper considers distributions of assets' return and volatility risk to determine a more realistic optimized portfolio. For illustration purposes, the sectorial indices data in FTSE Bursa Malaysia is employed. The results show that stochastic optimization provides more stablemore » information ratio.« less

Optimizing model: insemination, replacement, seasonal production, and cash flow.

PubMed

DeLorenzo, M A; Spreen, T H; Bryan, G R; Beede, D K; Van Arendonk, J A

1992-03-01

Dynamic programming to solve the Markov decision process problem of optimal insemination and replacement decisions was adapted to address large dairy herd management decision problems in the US. Expected net present values of cow states (151,200) were used to determine the optimal policy. States were specified by class of parity (n = 12), production level (n = 15), month of calving (n = 12), month of lactation (n = 16), and days open (n = 7). Methodology optimized decisions based on net present value of an individual cow and all replacements over a 20-yr decision horizon. Length of decision horizon was chosen to ensure that optimal policies were determined for an infinite planning horizon. Optimization took 286 s of central processing unit time. The final probability transition matrix was determined, in part, by the optimal policy. It was estimated iteratively to determine post-optimization steady state herd structure, milk production, replacement, feed inputs and costs, and resulting cash flow on a calendar month and annual basis if optimal policies were implemented. Implementation of the model included seasonal effects on lactation curve shapes, estrus detection rates, pregnancy rates, milk prices, replacement costs, cull prices, and genetic progress. Other inputs included calf values, values of dietary TDN and CP per kilogram, and discount rate. Stochastic elements included conception (and, thus, subsequent freshening), cow milk production level within herd, and survival. Validation of optimized solutions was by separate simulation model, which implemented policies on a simulated herd and also described herd dynamics during transition to optimized structure.

Coordination of a supply chain with consumer return under vendor-managed consignment inventory and stochastic demand

NASA Astrophysics Data System (ADS)

Wu, Zhihui; Chen, Dongyan; Yu, Hui

2016-07-01

In this paper, the problem of the coordination policy is investigated for vendor-managed consignment inventory supply chain subject to consumer return. Here, the market demand is assumed to be affected by promotional effort and consumer return policy. The optimal consignment inventory and the optimal promotional effort level are proposed under the decentralized and centralized decisions. Based on the optimal decision conditions, the markdown allowance-promotional cost-sharing contract is investigated to coordinate the supply chain. Subsequently, the comparison between the two extreme policies shows that full-refund policy dominates the no-return policy when the returning cost and the positive effect of return policy are satisfied certain conditions. Finally, a numerical example is provided to illustrate the impacts of consumer return policy on the coordination contract and optimal profit as well as the effectiveness of the proposed supply chain decision.

Particle swarm optimization and gravitational wave data analysis: Performance on a binary inspiral testbed

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang Yan; Mohanty, Soumya D.; Center for Gravitational Wave Astronomy, Department of Physics and Astronomy, University of Texas at Brownsville, 80 Fort Brown, Brownsville, Texas 78520

2010-03-15

The detection and estimation of gravitational wave signals belonging to a parameterized family of waveforms requires, in general, the numerical maximization of a data-dependent function of the signal parameters. Because of noise in the data, the function to be maximized is often highly multimodal with numerous local maxima. Searching for the global maximum then becomes computationally expensive, which in turn can limit the scientific scope of the search. Stochastic optimization is one possible approach to reducing computational costs in such applications. We report results from a first investigation of the particle swarm optimization method in this context. The method ismore » applied to a test bed motivated by the problem of detection and estimation of a binary inspiral signal. Our results show that particle swarm optimization works well in the presence of high multimodality, making it a viable candidate method for further applications in gravitational wave data analysis.« less

Complexity and approximability of quantified and stochastic constraint satisfaction problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hunt, H. B.; Stearns, R. L.; Marathe, M. V.

2001-01-01

Let D be an arbitrary (not necessarily finite) nonempty set, let C be a finite set of constant symbols denoting arbitrary elements of D, and let S be an arbitrary finite set of finite-arity relations on D. We denote the problem of determining the satisfiability of finite conjunctions of relations in S applied to variables (to variables and symbols in C) by SAT(S) (by SAT{sub c}(S)). Here, we study simultaneously the complexity of and the existence of efficient approximation algorithms for a number of variants of the problems SAT(S) and SAT{sub c}(S), and for many different D, C, and S.more » These problem variants include decision and optimization problems, for formulas, quantified formulas stochastically-quantified formulas. We denote these problems by Q-SAT(S), MAX-Q-SAT(S), S-SAT(S), MAX-S-SAT(S) MAX-NSF-Q-SAT(S) and MAX-NSF-S-SAT(S). The main contribution is the development of a unified predictive theory for characterizing the the complexity of these problems. Our unified approach is based on the following basic two basic concepts: (i) strongly-local replacements/reductions and (ii) relational/algebraic representability. Let k {ge} 2. Let S be a finite set of finite-arity relations on {Sigma}{sub k} with the following condition on S: All finite arity relations on {Sigma}{sub k} can be represented as finite existentially-quantified conjunctions of relations in S applied to variables (to variables and constant symbols in C), Then we prove the following new results: (1) The problems SAT(S) and SAT{sub c}(S) are both NQL-complete and {le}{sub logn}{sup bw}-complete for NP. (2) The problems Q-SAT(S), Q-SAT{sub c}(S), are PSPACE-complete. Letting k = 2, the problem S-SAT(S) and S-SAT{sub c}(S) are PSPACE-complete. (3) {exists} {epsilon} > 0 for which approximating the problems MAX-Q-SAT(S) within {epsilon} times optimum is PSPACE-hard. Letting k =: 2, {exists} {epsilon} > 0 for which approximating the problems MAX-S-SAT(S) within {epsilon} times optimum is PSPACE-hard. (4) {forall} {epsilon} > 0 the problems MAX-NSF-Q-SAT(S) and MAX-NSF-S-SAT(S), are PSPACE-hard to approximate within a factor of n{sup {epsilon}} times optimum. These results significantly extend the earlier results by (i) Papadimitriou [Pa851] on complexity of stochastic satisfiability, (ii) Condon, Feigenbaum, Lund and Shor [CF+93, CF+94] by identifying natural classes of PSPACE-hard optimization problems with provably PSPACE-hard {epsilon}-approximation problems. Moreover, most of our results hold not just for Boolean relations: most previous results were done only in the context of Boolean domains. The results also constitute as a significant step towards obtaining a dichotomy theorems for the problems MAX-S-SAT(S) and MAX-Q-SAT(S): a research area of recent interest [CF+93, CF+94, Cr95, KSW97, LMP99].« less

Multiobjective fuzzy stochastic linear programming problems with inexact probability distribution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hamadameen, Abdulqader Othman; Zainuddin, Zaitul Marlizawati

This study deals with multiobjective fuzzy stochastic linear programming problems with uncertainty probability distribution which are defined as fuzzy assertions by ambiguous experts. The problem formulation has been presented and the two solutions strategies are; the fuzzy transformation via ranking function and the stochastic transformation when α{sup –}. cut technique and linguistic hedges are used in the uncertainty probability distribution. The development of Sen’s method is employed to find a compromise solution, supported by illustrative numerical example.

Efficient Robust Optimization of Metal Forming Processes using a Sequential Metamodel Based Strategy

NASA Astrophysics Data System (ADS)

Wiebenga, J. H.; Klaseboer, G.; van den Boogaard, A. H.

2011-08-01

The coupling of Finite Element (FE) simulations to mathematical optimization techniques has contributed significantly to product improvements and cost reductions in the metal forming industries. The next challenge is to bridge the gap between deterministic optimization techniques and the industrial need for robustness. This paper introduces a new and generally applicable structured methodology for modeling and solving robust optimization problems. Stochastic design variables or noise variables are taken into account explicitly in the optimization procedure. The metamodel-based strategy is combined with a sequential improvement algorithm to efficiently increase the accuracy of the objective function prediction. This is only done at regions of interest containing the optimal robust design. Application of the methodology to an industrial V-bending process resulted in valuable process insights and an improved robust process design. Moreover, a significant improvement of the robustness (>2σ) was obtained by minimizing the deteriorating effects of several noise variables. The robust optimization results demonstrate the general applicability of the robust optimization strategy and underline the importance of including uncertainty and robustness explicitly in the numerical optimization procedure.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Z.; Liu, C.; Botterud, A.

Renewable energy resources have been rapidly integrated into power systems in many parts of the world, contributing to a cleaner and more sustainable supply of electricity. Wind and solar resources also introduce new challenges for system operations and planning in terms of economics and reliability because of their variability and uncertainty. Operational strategies based on stochastic optimization have been developed recently to address these challenges. In general terms, these stochastic strategies either embed uncertainties into the scheduling formulations (e.g., the unit commitment [UC] problem) in probabilistic forms or develop more appropriate operating reserve strategies to take advantage of advanced forecastingmore » techniques. Other approaches to address uncertainty are also proposed, where operational feasibility is ensured within an uncertainty set of forecasting intervals. In this report, a comprehensive review is conducted to present the state of the art through Spring 2015 in the area of stochastic methods applied to power system operations with high penetration of renewable energy. Chapters 1 and 2 give a brief introduction and overview of power system and electricity market operations, as well as the impact of renewable energy and how this impact is typically considered in modeling tools. Chapter 3 reviews relevant literature on operating reserves and specifically probabilistic methods to estimate the need for system reserve requirements. Chapter 4 looks at stochastic programming formulations of the UC and economic dispatch (ED) problems, highlighting benefits reported in the literature as well as recent industry developments. Chapter 5 briefly introduces alternative formulations of UC under uncertainty, such as robust, chance-constrained, and interval programming. Finally, in Chapter 6, we conclude with the main observations from our review and important directions for future work.« less

Stochastic optimization of intensity modulated radiotherapy to account for uncertainties in patient sensitivity

NASA Astrophysics Data System (ADS)

Kåver, Gereon; Lind, Bengt K.; Löf, Johan; Liander, Anders; Brahme, Anders

1999-12-01

The aim of the present work is to better account for the known uncertainties in radiobiological response parameters when optimizing radiation therapy. The radiation sensitivity of a specific patient is usually unknown beyond the expectation value and possibly the standard deviation that may be derived from studies on groups of patients. Instead of trying to find the treatment with the highest possible probability of a desirable outcome for a patient of average sensitivity, it is more desirable to maximize the expectation value of the probability for the desirable outcome over the possible range of variation of the radiation sensitivity of the patient. Such a stochastic optimization will also have to consider the distribution function of the radiation sensitivity and the larger steepness of the response for the individual patient. The results of stochastic optimization are also compared with simpler methods such as using biological response `margins' to account for the range of sensitivity variation. By using stochastic optimization, the absolute gain will typically be of the order of a few per cent and the relative improvement compared with non-stochastic optimization is generally less than about 10 per cent. The extent of this gain varies with the level of interpatient variability as well as with the difficulty and complexity of the case studied. Although the dose changes are rather small (<5 Gy) there is a strong desire to make treatment plans more robust, and tolerant of the likely range of variation of the radiation sensitivity of each individual patient. When more accurate predictive assays of the radiation sensitivity for each patient become available, the need to consider the range of variations can be reduced considerably.

A Projection free method for Generalized Eigenvalue Problem with a nonsmooth Regularizer.

PubMed

Hwang, Seong Jae; Collins, Maxwell D; Ravi, Sathya N; Ithapu, Vamsi K; Adluru, Nagesh; Johnson, Sterling C; Singh, Vikas

2015-12-01

Eigenvalue problems are ubiquitous in computer vision, covering a very broad spectrum of applications ranging from estimation problems in multi-view geometry to image segmentation. Few other linear algebra problems have a more mature set of numerical routines available and many computer vision libraries leverage such tools extensively. However, the ability to call the underlying solver only as a "black box" can often become restrictive. Many 'human in the loop' settings in vision frequently exploit supervision from an expert, to the extent that the user can be considered a subroutine in the overall system. In other cases, there is additional domain knowledge, side or even partial information that one may want to incorporate within the formulation. In general, regularizing a (generalized) eigenvalue problem with such side information remains difficult. Motivated by these needs, this paper presents an optimization scheme to solve generalized eigenvalue problems (GEP) involving a (nonsmooth) regularizer. We start from an alternative formulation of GEP where the feasibility set of the model involves the Stiefel manifold. The core of this paper presents an end to end stochastic optimization scheme for the resultant problem. We show how this general algorithm enables improved statistical analysis of brain imaging data where the regularizer is derived from other 'views' of the disease pathology, involving clinical measurements and other image-derived representations.

Partial ASL extensions for stochastic programming.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gay, David

2010-03-31

partially completed extensions for stochastic programming to the AMPL/solver interface library (ASL).modeling and experimenting with stochastic recourse problems. This software is not primarily for military applications

Parallel Computation of Flow in Heterogeneous Media Modelled by Mixed Finite Elements

NASA Astrophysics Data System (ADS)

Cliffe, K. A.; Graham, I. G.; Scheichl, R.; Stals, L.

2000-11-01

In this paper we describe a fast parallel method for solving highly ill-conditioned saddle-point systems arising from mixed finite element simulations of stochastic partial differential equations (PDEs) modelling flow in heterogeneous media. Each realisation of these stochastic PDEs requires the solution of the linear first-order velocity-pressure system comprising Darcy's law coupled with an incompressibility constraint. The chief difficulty is that the permeability may be highly variable, especially when the statistical model has a large variance and a small correlation length. For reasonable accuracy, the discretisation has to be extremely fine. We solve these problems by first reducing the saddle-point formulation to a symmetric positive definite (SPD) problem using a suitable basis for the space of divergence-free velocities. The reduced problem is solved using parallel conjugate gradients preconditioned with an algebraically determined additive Schwarz domain decomposition preconditioner. The result is a solver which exhibits a good degree of robustness with respect to the mesh size as well as to the variance and to physically relevant values of the correlation length of the underlying permeability field. Numerical experiments exhibit almost optimal levels of parallel efficiency. The domain decomposition solver (DOUG, http://www.maths.bath.ac.uk/~parsoft) used here not only is applicable to this problem but can be used to solve general unstructured finite element systems on a wide range of parallel architectures.

Training-based descreening.

PubMed

Siddiqui, Hasib; Bouman, Charles A

2007-03-01

Conventional halftoning methods employed in electrophotographic printers tend to produce Moiré artifacts when used for printing images scanned from printed material, such as books and magazines. We present a novel approach for descreening color scanned documents aimed at providing an efficient solution to the Moiré problem in practical imaging devices, including copiers and multifunction printers. The algorithm works by combining two nonlinear image-processing techniques, resolution synthesis-based denoising (RSD), and modified smallest univalue segment assimilating nucleus (SUSAN) filtering. The RSD predictor is based on a stochastic image model whose parameters are optimized beforehand in a separate training procedure. Using the optimized parameters, RSD classifies the local window around the current pixel in the scanned image and applies filters optimized for the selected classes. The output of the RSD predictor is treated as a first-order estimate to the descreened image. The modified SUSAN filter uses the output of RSD for performing an edge-preserving smoothing on the raw scanned data and produces the final output of the descreening algorithm. Our method does not require any knowledge of the screening method, such as the screen frequency or dither matrix coefficients, that produced the printed original. The proposed scheme not only suppresses the Moiré artifacts, but, in addition, can be trained with intrinsic sharpening for deblurring scanned documents. Finally, once optimized for a periodic clustered-dot halftoning method, the same algorithm can be used to inverse halftone scanned images containing stochastic error diffusion halftone noise.

Output Feedback Stabilization for a Class of Multi-Variable Bilinear Stochastic Systems with Stochastic Coupling Attenuation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Qichun; Zhou, Jinglin; Wang, Hong

In this paper, stochastic coupling attenuation is investigated for a class of multi-variable bilinear stochastic systems and a novel output feedback m-block backstepping controller with linear estimator is designed, where gradient descent optimization is used to tune the design parameters of the controller. It has been shown that the trajectories of the closed-loop stochastic systems are bounded in probability sense and the stochastic coupling of the system outputs can be effectively attenuated by the proposed control algorithm. Moreover, the stability of the stochastic systems is analyzed and the effectiveness of the proposed method has been demonstrated using a simulated example.

Feedback control for unsteady flow and its application to the stochastic Burgers equation

NASA Technical Reports Server (NTRS)

Choi, Haecheon; Temam, Roger; Moin, Parviz; Kim, John

1993-01-01

The study applies mathematical methods of control theory to the problem of control of fluid flow with the long-range objective of developing effective methods for the control of turbulent flows. Model problems are employed through the formalism and language of control theory to present the procedure of how to cast the problem of controlling turbulence into a problem in optimal control theory. Methods of calculus of variations through the adjoint state and gradient algorithms are used to present a suboptimal control and feedback procedure for stationary and time-dependent problems. Two types of controls are investigated: distributed and boundary controls. Several cases of both controls are numerically simulated to investigate the performances of the control algorithm. Most cases considered show significant reductions of the costs to be minimized. The dependence of the control algorithm on the time-descretization method is discussed.

Solution of the finite Milne problem in stochastic media with RVT Technique

NASA Astrophysics Data System (ADS)

Slama, Howida; El-Bedwhey, Nabila A.; El-Depsy, Alia; Selim, Mustafa M.

2017-12-01

This paper presents the solution to the Milne problem in the steady state with isotropic scattering phase function. The properties of the medium are considered as stochastic ones with Gaussian or exponential distributions and hence the problem treated as a stochastic integro-differential equation. To get an explicit form for the radiant energy density, the linear extrapolation distance, reflectivity and transmissivity in the deterministic case the problem is solved using the Pomraning-Eddington method. The obtained solution is found to be dependent on the optical space variable and thickness of the medium which are considered as random variables. The random variable transformation (RVT) technique is used to find the first probability density function (1-PDF) of the solution process. Then the stochastic linear extrapolation distance, reflectivity and transmissivity are calculated. For illustration, numerical results with conclusions are provided.

An Approximation Solution to Refinery Crude Oil Scheduling Problem with Demand Uncertainty Using Joint Constrained Programming

PubMed Central

Duan, Qianqian; Yang, Genke; Xu, Guanglin; Pan, Changchun

2014-01-01

This paper is devoted to develop an approximation method for scheduling refinery crude oil operations by taking into consideration the demand uncertainty. In the stochastic model the demand uncertainty is modeled as random variables which follow a joint multivariate distribution with a specific correlation structure. Compared to deterministic models in existing works, the stochastic model can be more practical for optimizing crude oil operations. Using joint chance constraints, the demand uncertainty is treated by specifying proximity level on the satisfaction of product demands. However, the joint chance constraints usually hold strong nonlinearity and consequently, it is still hard to handle it directly. In this paper, an approximation method combines a relax-and-tight technique to approximately transform the joint chance constraints to a serial of parameterized linear constraints so that the complicated problem can be attacked iteratively. The basic idea behind this approach is to approximate, as much as possible, nonlinear constraints by a lot of easily handled linear constraints which will lead to a well balance between the problem complexity and tractability. Case studies are conducted to demonstrate the proposed methods. Results show that the operation cost can be reduced effectively compared with the case without considering the demand correlation. PMID:24757433

An approximation solution to refinery crude oil scheduling problem with demand uncertainty using joint constrained programming.

PubMed

Duan, Qianqian; Yang, Genke; Xu, Guanglin; Pan, Changchun

2014-01-01

This paper is devoted to develop an approximation method for scheduling refinery crude oil operations by taking into consideration the demand uncertainty. In the stochastic model the demand uncertainty is modeled as random variables which follow a joint multivariate distribution with a specific correlation structure. Compared to deterministic models in existing works, the stochastic model can be more practical for optimizing crude oil operations. Using joint chance constraints, the demand uncertainty is treated by specifying proximity level on the satisfaction of product demands. However, the joint chance constraints usually hold strong nonlinearity and consequently, it is still hard to handle it directly. In this paper, an approximation method combines a relax-and-tight technique to approximately transform the joint chance constraints to a serial of parameterized linear constraints so that the complicated problem can be attacked iteratively. The basic idea behind this approach is to approximate, as much as possible, nonlinear constraints by a lot of easily handled linear constraints which will lead to a well balance between the problem complexity and tractability. Case studies are conducted to demonstrate the proposed methods. Results show that the operation cost can be reduced effectively compared with the case without considering the demand correlation.

Comparison of stochastic optimization methods for all-atom folding of the Trp-Cage protein.

PubMed

Schug, Alexander; Herges, Thomas; Verma, Abhinav; Lee, Kyu Hwan; Wenzel, Wolfgang

2005-12-09

The performances of three different stochastic optimization methods for all-atom protein structure prediction are investigated and compared. We use the recently developed all-atom free-energy force field (PFF01), which was demonstrated to correctly predict the native conformation of several proteins as the global optimum of the free energy surface. The trp-cage protein (PDB-code 1L2Y) is folded with the stochastic tunneling method, a modified parallel tempering method, and the basin-hopping technique. All the methods correctly identify the native conformation, and their relative efficiency is discussed.

Optimization of vibratory energy harvesters with stochastic parametric uncertainty: a new perspective

NASA Astrophysics Data System (ADS)

Haji Hosseinloo, Ashkan; Turitsyn, Konstantin

2016-04-01

Vibration energy harvesting has been shown as a promising power source for many small-scale applications mainly because of the considerable reduction in the energy consumption of the electronics and scalability issues of the conventional batteries. However, energy harvesters may not be as robust as the conventional batteries and their performance could drastically deteriorate in the presence of uncertainty in their parameters. Hence, study of uncertainty propagation and optimization under uncertainty is essential for proper and robust performance of harvesters in practice. While all studies have focused on expectation optimization, we propose a new and more practical optimization perspective; optimization for the worst-case (minimum) power. We formulate the problem in a generic fashion and as a simple example apply it to a linear piezoelectric energy harvester. We study the effect of parametric uncertainty in its natural frequency, load resistance, and electromechanical coupling coefficient on its worst-case power and then optimize for it under different confidence levels. The results show that there is a significant improvement in the worst-case power of thus designed harvester compared to that of a naively-optimized (deterministically-optimized) harvester.

Optimal land use management for soil erosion control by using an interval-parameter fuzzy two-stage stochastic programming approach.

PubMed

Han, Jing-Cheng; Huang, Guo-He; Zhang, Hua; Li, Zhong

2013-09-01

Soil erosion is one of the most serious environmental and public health problems, and such land degradation can be effectively mitigated through performing land use transitions across a watershed. Optimal land use management can thus provide a way to reduce soil erosion while achieving the maximum net benefit. However, optimized land use allocation schemes are not always successful since uncertainties pertaining to soil erosion control are not well presented. This study applied an interval-parameter fuzzy two-stage stochastic programming approach to generate optimal land use planning strategies for soil erosion control based on an inexact optimization framework, in which various uncertainties were reflected. The modeling approach can incorporate predefined soil erosion control policies, and address inherent system uncertainties expressed as discrete intervals, fuzzy sets, and probability distributions. The developed model was demonstrated through a case study in the Xiangxi River watershed, China's Three Gorges Reservoir region. Land use transformations were employed as decision variables, and based on these, the land use change dynamics were yielded for a 15-year planning horizon. Finally, the maximum net economic benefit with an interval value of [1.197, 6.311] × 10(9) $ was obtained as well as corresponding land use allocations in the three planning periods. Also, the resulting soil erosion amount was found to be decreased and controlled at a tolerable level over the watershed. Thus, results confirm that the developed model is a useful tool for implementing land use management as not only does it allow local decision makers to optimize land use allocation, but can also help to answer how to accomplish land use changes.

Optimal Land Use Management for Soil Erosion Control by Using an Interval-Parameter Fuzzy Two-Stage Stochastic Programming Approach

NASA Astrophysics Data System (ADS)

Han, Jing-Cheng; Huang, Guo-He; Zhang, Hua; Li, Zhong

2013-09-01

Soil erosion is one of the most serious environmental and public health problems, and such land degradation can be effectively mitigated through performing land use transitions across a watershed. Optimal land use management can thus provide a way to reduce soil erosion while achieving the maximum net benefit. However, optimized land use allocation schemes are not always successful since uncertainties pertaining to soil erosion control are not well presented. This study applied an interval-parameter fuzzy two-stage stochastic programming approach to generate optimal land use planning strategies for soil erosion control based on an inexact optimization framework, in which various uncertainties were reflected. The modeling approach can incorporate predefined soil erosion control policies, and address inherent system uncertainties expressed as discrete intervals, fuzzy sets, and probability distributions. The developed model was demonstrated through a case study in the Xiangxi River watershed, China's Three Gorges Reservoir region. Land use transformations were employed as decision variables, and based on these, the land use change dynamics were yielded for a 15-year planning horizon. Finally, the maximum net economic benefit with an interval value of [1.197, 6.311] × 109 was obtained as well as corresponding land use allocations in the three planning periods. Also, the resulting soil erosion amount was found to be decreased and controlled at a tolerable level over the watershed. Thus, results confirm that the developed model is a useful tool for implementing land use management as not only does it allow local decision makers to optimize land use allocation, but can also help to answer how to accomplish land use changes.

Path optimization with limited sensing ability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kang, Sung Ha, E-mail: kang@math.gatech.edu; Kim, Seong Jun, E-mail: skim396@math.gatech.edu; Zhou, Haomin, E-mail: hmzhou@math.gatech.edu

2015-10-15

We propose a computational strategy to find the optimal path for a mobile sensor with limited coverage to traverse a cluttered region. The goal is to find one of the shortest feasible paths to achieve the complete scan of the environment. We pose the problem in the level set framework, and first consider a related question of placing multiple stationary sensors to obtain the full surveillance of the environment. By connecting the stationary locations using the nearest neighbor strategy, we form the initial guess for the path planning problem of the mobile sensor. Then the path is optimized by reducingmore » its length, via solving a system of ordinary differential equations (ODEs), while maintaining the complete scan of the environment. Furthermore, we use intermittent diffusion, which converts the ODEs into stochastic differential equations (SDEs), to find an optimal path whose length is globally minimal. To improve the computation efficiency, we introduce two techniques, one to remove redundant connecting points to reduce the dimension of the system, and the other to deal with the entangled path so the solution can escape the local traps. Numerical examples are shown to illustrate the effectiveness of the proposed method.« less

Joint optimization of regional water-power systems

NASA Astrophysics Data System (ADS)

Pereira-Cardenal, Silvio J.; Mo, Birger; Gjelsvik, Anders; Riegels, Niels D.; Arnbjerg-Nielsen, Karsten; Bauer-Gottwein, Peter

2016-06-01

Energy and water resources systems are tightly coupled; energy is needed to deliver water and water is needed to extract or produce energy. Growing pressure on these resources has raised concerns about their long-term management and highlights the need to develop integrated solutions. A method for joint optimization of water and electric power systems was developed in order to identify methodologies to assess the broader interactions between water and energy systems. The proposed method is to include water users and power producers into an economic optimization problem that minimizes the cost of power production and maximizes the benefits of water allocation, subject to constraints from the power and hydrological systems. The method was tested on the Iberian Peninsula using simplified models of the seven major river basins and the power market. The optimization problem was successfully solved using stochastic dual dynamic programming. The results showed that current water allocation to hydropower producers in basins with high irrigation productivity, and to irrigation users in basins with high hydropower productivity was sub-optimal. Optimal allocation was achieved by managing reservoirs in very distinct ways, according to the local inflow, storage capacity, hydropower productivity, and irrigation demand and productivity. This highlights the importance of appropriately representing the water users' spatial distribution and marginal benefits and costs when allocating water resources optimally. The method can handle further spatial disaggregation and can be extended to include other aspects of the water-energy nexus.

A Hybrid Interval–Robust Optimization Model for Water Quality Management

PubMed Central

Xu, Jieyu; Li, Yongping; Huang, Guohe

2013-01-01

Abstract In water quality management problems, uncertainties may exist in many system components and pollution-related processes (i.e., random nature of hydrodynamic conditions, variability in physicochemical processes, dynamic interactions between pollutant loading and receiving water bodies, and indeterminacy of available water and treated wastewater). These complexities lead to difficulties in formulating and solving the resulting nonlinear optimization problems. In this study, a hybrid interval–robust optimization (HIRO) method was developed through coupling stochastic robust optimization and interval linear programming. HIRO can effectively reflect the complex system features under uncertainty, where implications of water quality/quantity restrictions for achieving regional economic development objectives are studied. By delimiting the uncertain decision space through dimensional enlargement of the original chemical oxygen demand (COD) discharge constraints, HIRO enhances the robustness of the optimization processes and resulting solutions. This method was applied to planning of industry development in association with river-water pollution concern in New Binhai District of Tianjin, China. Results demonstrated that the proposed optimization model can effectively communicate uncertainties into the optimization process and generate a spectrum of potential inexact solutions supporting local decision makers in managing benefit-effective water quality management schemes. HIRO is helpful for analysis of policy scenarios related to different levels of economic penalties, while also providing insight into the tradeoff between system benefits and environmental requirements. PMID:23922495

Methods for High-Order Multi-Scale and Stochastic Problems Analysis, Algorithms, and Applications

DTIC Science & Technology

2016-10-17

finite volume schemes, discontinuous Galerkin finite element method, and related methods, for solving computational fluid dynamics (CFD) problems and...approximation for finite element methods. (3) The development of methods of simulation and analysis for the study of large scale stochastic systems of...laws, finite element method, Bernstein-Bezier finite elements , weakly interacting particle systems, accelerated Monte Carlo, stochastic networks 16