Sample records for hard optimization problem

  1. Parameter meta-optimization of metaheuristics of solving specific NP-hard facility location problem

    NASA Astrophysics Data System (ADS)

    Skakov, E. S.; Malysh, V. N.

    2018-03-01

    The aim of the work is to create an evolutionary method for optimizing the values of the control parameters of metaheuristics of solving the NP-hard facility location problem. A system analysis of the tuning process of optimization algorithms parameters is carried out. The problem of finding the parameters of a metaheuristic algorithm is formulated as a meta-optimization problem. Evolutionary metaheuristic has been chosen to perform the task of meta-optimization. Thus, the approach proposed in this work can be called “meta-metaheuristic”. Computational experiment proving the effectiveness of the procedure of tuning the control parameters of metaheuristics has been performed.

  2. Quantum algorithm for energy matching in hard optimization problems

    NASA Astrophysics Data System (ADS)

    Baldwin, C. L.; Laumann, C. R.

    2018-06-01

    We consider the ability of local quantum dynamics to solve the "energy-matching" problem: given an instance of a classical optimization problem and a low-energy state, find another macroscopically distinct low-energy state. Energy matching is difficult in rugged optimization landscapes, as the given state provides little information about the distant topography. Here, we show that the introduction of quantum dynamics can provide a speedup over classical algorithms in a large class of hard optimization problems. Tunneling allows the system to explore the optimization landscape while approximately conserving the classical energy, even in the presence of large barriers. Specifically, we study energy matching in the random p -spin model of spin-glass theory. Using perturbation theory and exact diagonalization, we show that introducing a transverse field leads to three sharp dynamical phases, only one of which solves the matching problem: (1) a small-field "trapped" phase, in which tunneling is too weak for the system to escape the vicinity of the initial state; (2) a large-field "excited" phase, in which the field excites the system into high-energy states, effectively forgetting the initial energy; and (3) the intermediate "tunneling" phase, in which the system succeeds at energy matching. The rate at which distant states are found in the tunneling phase, although exponentially slow in system size, is exponentially faster than classical search algorithms.

  3. Human Performance on Hard Non-Euclidean Graph Problems: Vertex Cover

    ERIC Educational Resources Information Center

    Carruthers, Sarah; Masson, Michael E. J.; Stege, Ulrike

    2012-01-01

    Recent studies on a computationally hard visual optimization problem, the Traveling Salesperson Problem (TSP), indicate that humans are capable of finding close to optimal solutions in near-linear time. The current study is a preliminary step in investigating human performance on another hard problem, the Minimum Vertex Cover Problem, in which…

  4. Solving NP-Hard Problems with Physarum-Based Ant Colony System.

    PubMed

    Liu, Yuxin; Gao, Chao; Zhang, Zili; Lu, Yuxiao; Chen, Shi; Liang, Mingxin; Tao, Li

    2017-01-01

    NP-hard problems exist in many real world applications. Ant colony optimization (ACO) algorithms can provide approximate solutions for those NP-hard problems, but the performance of ACO algorithms is significantly reduced due to premature convergence and weak robustness, etc. With these observations in mind, this paper proposes a Physarum-based pheromone matrix optimization strategy in ant colony system (ACS) for solving NP-hard problems such as traveling salesman problem (TSP) and 0/1 knapsack problem (0/1 KP). In the Physarum-inspired mathematical model, one of the unique characteristics is that critical tubes can be reserved in the process of network evolution. The optimized updating strategy employs the unique feature and accelerates the positive feedback process in ACS, which contributes to the quick convergence of the optimal solution. Some experiments were conducted using both benchmark and real datasets. The experimental results show that the optimized ACS outperforms other meta-heuristic algorithms in accuracy and robustness for solving TSPs. Meanwhile, the convergence rate and robustness for solving 0/1 KPs are better than those of classical ACS.

  5. Global Optimal Trajectory in Chaos and NP-Hardness

    NASA Astrophysics Data System (ADS)

    Latorre, Vittorio; Gao, David Yang

    This paper presents an unconventional theory and method for solving general nonlinear dynamical systems. Instead of the direct iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. A newly developed canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by linear iterative methods are mainly due to the intrinsic numerical error accumulations. Otherwise, the global optimization problem could be NP-hard and the nonlinear system can be really chaotic. A conjecture is proposed, which reveals the connection between chaos in nonlinear dynamics and NP-hardness in computer science. The methodology and the conjecture are verified by applications to the well-known logistic equation, a forced memristive circuit and the Lorenz system. Computational results show that the canonical duality theory can be used to identify chaotic systems and to obtain realistic global optimal solutions in nonlinear dynamical systems. The method and results presented in this paper should bring some new insights into nonlinear dynamical systems and NP-hardness in computational complexity theory.

  6. Parameterized Algorithmics for Finding Exact Solutions of NP-Hard Biological Problems.

    PubMed

    Hüffner, Falk; Komusiewicz, Christian; Niedermeier, Rolf; Wernicke, Sebastian

    2017-01-01

    Fixed-parameter algorithms are designed to efficiently find optimal solutions to some computationally hard (NP-hard) problems by identifying and exploiting "small" problem-specific parameters. We survey practical techniques to develop such algorithms. Each technique is introduced and supported by case studies of applications to biological problems, with additional pointers to experimental results.

  7. The Role of the Goal in Solving Hard Computational Problems: Do People Really Optimize?

    ERIC Educational Resources Information Center

    Carruthers, Sarah; Stege, Ulrike; Masson, Michael E. J.

    2018-01-01

    The role that the mental, or internal, representation plays when people are solving hard computational problems has largely been overlooked to date, despite the reality that this internal representation drives problem solving. In this work we investigate how performance on versions of two hard computational problems differs based on what internal…

  8. Must "Hard Problems" Be Hard?

    ERIC Educational Resources Information Center

    Kolata, Gina

    1985-01-01

    To determine how hard it is for computers to solve problems, researchers have classified groups of problems (polynomial hierarchy) according to how much time they seem to require for their solutions. A difficult and complex proof is offered which shows that a combinatorial approach (using Boolean circuits) may resolve the problem. (JN)

  9. Hard Constraints in Optimization Under Uncertainty

    NASA Technical Reports Server (NTRS)

    Crespo, Luis G.; Giesy, Daniel P.; Kenny, Sean P.

    2008-01-01

    This paper proposes a methodology for the analysis and design of systems subject to parametric uncertainty where design requirements are specified via hard inequality constraints. Hard constraints are those that must be satisfied for all parameter realizations within a given uncertainty model. Uncertainty models given by norm-bounded perturbations from a nominal parameter value, i.e., hyper-spheres, and by sets of independently bounded uncertain variables, i.e., hyper-rectangles, are the focus of this paper. These models, which are also quite practical, allow for a rigorous mathematical treatment within the proposed framework. Hard constraint feasibility is determined by sizing the largest uncertainty set for which the design requirements are satisfied. Analytically verifiable assessments of robustness are attained by comparing this set with the actual uncertainty model. Strategies that enable the comparison of the robustness characteristics of competing design alternatives, the description and approximation of the robust design space, and the systematic search for designs with improved robustness are also proposed. Since the problem formulation is generic and the tools derived only require standard optimization algorithms for their implementation, this methodology is applicable to a broad range of engineering problems.

  10. Statistical physics of hard combinatorial optimization: Vertex cover problem

    NASA Astrophysics Data System (ADS)

    Zhao, Jin-Hua; Zhou, Hai-Jun

    2014-07-01

    Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years, the replica-symmetry-breaking mean field theory of spin glasses and the associated message-passing algorithms have greatly deepened our understanding of typical-case computation complexity. In this paper, we use the vertex cover problem, a basic nondeterministic-polynomial (NP)-complete combinatorial optimization problem of wide application, as an example to introduce the statistical physical methods and algorithms. We do not go into the technical details but emphasize mainly the intuitive physical meanings of the message-passing equations. A nonfamiliar reader shall be able to understand to a large extent the physics behind the mean field approaches and to adjust the mean field methods in solving other optimization problems.

  11. Optimal recombination in genetic algorithms for flowshop scheduling problems

    NASA Astrophysics Data System (ADS)

    Kovalenko, Julia

    2016-10-01

    The optimal recombination problem consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. We prove NP-hardness of the optimal recombination for various variants of the flowshop scheduling problem with makespan criterion and criterion of maximum lateness. An algorithm for solving the optimal recombination problem for permutation flowshop problems is built, using enumeration of prefect matchings in a special bipartite graph. The algorithm is adopted for the classical flowshop scheduling problem and for the no-wait flowshop problem. It is shown that the optimal recombination problem for the permutation flowshop scheduling problem is solvable in polynomial time for almost all pairs of parent solutions as the number of jobs tends to infinity.

  12. Directed Bee Colony Optimization Algorithm to Solve the Nurse Rostering Problem.

    PubMed

    Rajeswari, M; Amudhavel, J; Pothula, Sujatha; Dhavachelvan, P

    2017-01-01

    The Nurse Rostering Problem is an NP-hard combinatorial optimization, scheduling problem for assigning a set of nurses to shifts per day by considering both hard and soft constraints. A novel metaheuristic technique is required for solving Nurse Rostering Problem (NRP). This work proposes a metaheuristic technique called Directed Bee Colony Optimization Algorithm using the Modified Nelder-Mead Method for solving the NRP. To solve the NRP, the authors used a multiobjective mathematical programming model and proposed a methodology for the adaptation of a Multiobjective Directed Bee Colony Optimization (MODBCO). MODBCO is used successfully for solving the multiobjective problem of optimizing the scheduling problems. This MODBCO is an integration of deterministic local search, multiagent particle system environment, and honey bee decision-making process. The performance of the algorithm is assessed using the standard dataset INRC2010, and it reflects many real-world cases which vary in size and complexity. The experimental analysis uses statistical tools to show the uniqueness of the algorithm on assessment criteria.

  13. Directed Bee Colony Optimization Algorithm to Solve the Nurse Rostering Problem

    PubMed Central

    Amudhavel, J.; Pothula, Sujatha; Dhavachelvan, P.

    2017-01-01

    The Nurse Rostering Problem is an NP-hard combinatorial optimization, scheduling problem for assigning a set of nurses to shifts per day by considering both hard and soft constraints. A novel metaheuristic technique is required for solving Nurse Rostering Problem (NRP). This work proposes a metaheuristic technique called Directed Bee Colony Optimization Algorithm using the Modified Nelder-Mead Method for solving the NRP. To solve the NRP, the authors used a multiobjective mathematical programming model and proposed a methodology for the adaptation of a Multiobjective Directed Bee Colony Optimization (MODBCO). MODBCO is used successfully for solving the multiobjective problem of optimizing the scheduling problems. This MODBCO is an integration of deterministic local search, multiagent particle system environment, and honey bee decision-making process. The performance of the algorithm is assessed using the standard dataset INRC2010, and it reflects many real-world cases which vary in size and complexity. The experimental analysis uses statistical tools to show the uniqueness of the algorithm on assessment criteria. PMID:28473849

  14. The coral reefs optimization algorithm: a novel metaheuristic for efficiently solving optimization problems.

    PubMed

    Salcedo-Sanz, S; Del Ser, J; Landa-Torres, I; Gil-López, S; Portilla-Figueras, J A

    2014-01-01

    This paper presents a novel bioinspired algorithm to tackle complex optimization problems: the coral reefs optimization (CRO) algorithm. The CRO algorithm artificially simulates a coral reef, where different corals (namely, solutions to the optimization problem considered) grow and reproduce in coral colonies, fighting by choking out other corals for space in the reef. This fight for space, along with the specific characteristics of the corals' reproduction, produces a robust metaheuristic algorithm shown to be powerful for solving hard optimization problems. In this research the CRO algorithm is tested in several continuous and discrete benchmark problems, as well as in practical application scenarios (i.e., optimum mobile network deployment and off-shore wind farm design). The obtained results confirm the excellent performance of the proposed algorithm and open line of research for further application of the algorithm to real-world problems.

  15. The Coral Reefs Optimization Algorithm: A Novel Metaheuristic for Efficiently Solving Optimization Problems

    PubMed Central

    Salcedo-Sanz, S.; Del Ser, J.; Landa-Torres, I.; Gil-López, S.; Portilla-Figueras, J. A.

    2014-01-01

    This paper presents a novel bioinspired algorithm to tackle complex optimization problems: the coral reefs optimization (CRO) algorithm. The CRO algorithm artificially simulates a coral reef, where different corals (namely, solutions to the optimization problem considered) grow and reproduce in coral colonies, fighting by choking out other corals for space in the reef. This fight for space, along with the specific characteristics of the corals' reproduction, produces a robust metaheuristic algorithm shown to be powerful for solving hard optimization problems. In this research the CRO algorithm is tested in several continuous and discrete benchmark problems, as well as in practical application scenarios (i.e., optimum mobile network deployment and off-shore wind farm design). The obtained results confirm the excellent performance of the proposed algorithm and open line of research for further application of the algorithm to real-world problems. PMID:25147860

  16. Optimal Water-Power Flow Problem: Formulation and Distributed Optimal Solution

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

    Dall-Anese, Emiliano; Zhao, Changhong; Zamzam, Admed S.

    This paper formalizes an optimal water-power flow (OWPF) problem to optimize the use of controllable assets across power and water systems while accounting for the couplings between the two infrastructures. Tanks and pumps are optimally managed to satisfy water demand while improving power grid operations; {for the power network, an AC optimal power flow formulation is augmented to accommodate the controllability of water pumps.} Unfortunately, the physics governing the operation of the two infrastructures and coupling constraints lead to a nonconvex (and, in fact, NP-hard) problem; however, after reformulating OWPF as a nonconvex, quadratically-constrained quadratic problem, a feasible point pursuit-successivemore » convex approximation approach is used to identify feasible and optimal solutions. In addition, a distributed solver based on the alternating direction method of multipliers enables water and power operators to pursue individual objectives while respecting the couplings between the two networks. The merits of the proposed approach are demonstrated for the case of a distribution feeder coupled with a municipal water distribution network.« less

  17. Optimization of lattice surgery is NP-hard

    NASA Astrophysics Data System (ADS)

    Herr, Daniel; Nori, Franco; Devitt, Simon J.

    2017-09-01

    The traditional method for computation in either the surface code or in the Raussendorf model is the creation of holes or "defects" within the encoded lattice of qubits that are manipulated via topological braiding to enact logic gates. However, this is not the only way to achieve universal, fault-tolerant computation. In this work, we focus on the lattice surgery representation, which realizes transversal logic operations without destroying the intrinsic 2D nearest-neighbor properties of the braid-based surface code and achieves universality without defects and braid-based logic. For both techniques there are open questions regarding the compilation and resource optimization of quantum circuits. Optimization in braid-based logic is proving to be difficult and the classical complexity associated with this problem has yet to be determined. In the context of lattice-surgery-based logic, we can introduce an optimality condition, which corresponds to a circuit with the lowest resource requirements in terms of physical qubits and computational time, and prove that the complexity of optimizing a quantum circuit in the lattice surgery model is NP-hard.

  18. Optimization of Error-Bounded Lossy Compression for Hard-to-Compress HPC Data

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

    Di, Sheng; Cappello, Franck

    Since today’s scientific applications are producing vast amounts of data, compressing them before storage/transmission is critical. Results of existing compressors show two types of HPC data sets: highly compressible and hard to compress. In this work, we carefully design and optimize the error-bounded lossy compression for hard-tocompress scientific data. We propose an optimized algorithm that can adaptively partition the HPC data into best-fit consecutive segments each having mutually close data values, such that the compression condition can be optimized. Another significant contribution is the optimization of shifting offset such that the XOR-leading-zero length between two consecutive unpredictable data points canmore » be maximized. We finally devise an adaptive method to select the best-fit compressor at runtime for maximizing the compression factor. We evaluate our solution using 13 benchmarks based on real-world scientific problems, and we compare it with 9 other state-of-the-art compressors. Experiments show that our compressor can always guarantee the compression errors within the user-specified error bounds. Most importantly, our optimization can improve the compression factor effectively, by up to 49% for hard-tocompress data sets with similar compression/decompression time cost.« less

  19. On the complexity and approximability of some Euclidean optimal summing problems

    NASA Astrophysics Data System (ADS)

    Eremeev, A. V.; Kel'manov, A. V.; Pyatkin, A. V.

    2016-10-01

    The complexity status of several well-known discrete optimization problems with the direction of optimization switching from maximum to minimum is analyzed. The task is to find a subset of a finite set of Euclidean points (vectors). In these problems, the objective functions depend either only on the norm of the sum of the elements from the subset or on this norm and the cardinality of the subset. It is proved that, if the dimension of the space is a part of the input, then all these problems are strongly NP-hard. Additionally, it is shown that, if the space dimension is fixed, then all the problems are NP-hard even for dimension 2 (on a plane) and there are no approximation algorithms with a guaranteed accuracy bound for them unless P = NP. It is shown that, if the coordinates of the input points are integer, then all the problems can be solved in pseudopolynomial time in the case of a fixed space dimension.

  20. Solving the Container Stowage Problem (CSP) using Particle Swarm Optimization (PSO)

    NASA Astrophysics Data System (ADS)

    Matsaini; Santosa, Budi

    2018-04-01

    Container Stowage Problem (CSP) is a problem of containers arrangement into ships by considering rules such as: total weight, weight of one stack, destination, equilibrium, and placement of containers on vessel. Container stowage problem is combinatorial problem and hard to solve with enumeration technique. It is an NP-Hard Problem. Therefore, to find a solution, metaheuristics is preferred. The objective of solving the problem is to minimize the amount of shifting such that the unloading time is minimized. Particle Swarm Optimization (PSO) is proposed to solve the problem. The implementation of PSO is combined with some steps which are stack position change rules, stack changes based on destination, and stack changes based on the weight type of the stacks (light, medium, and heavy). The proposed method was applied on five different cases. The results were compared to Bee Swarm Optimization (BSO) and heuristics method. PSO provided mean of 0.87% gap and time gap of 60 second. While BSO provided mean of 2,98% gap and 459,6 second to the heuristcs.

  1. Phase Transitions in Planning Problems: Design and Analysis of Parameterized Families of Hard Planning Problems

    NASA Technical Reports Server (NTRS)

    Hen, Itay; Rieffel, Eleanor G.; Do, Minh; Venturelli, Davide

    2014-01-01

    There are two common ways to evaluate algorithms: performance on benchmark problems derived from real applications and analysis of performance on parametrized families of problems. The two approaches complement each other, each having its advantages and disadvantages. The planning community has concentrated on the first approach, with few ways of generating parametrized families of hard problems known prior to this work. Our group's main interest is in comparing approaches to solving planning problems using a novel type of computational device - a quantum annealer - to existing state-of-the-art planning algorithms. Because only small-scale quantum annealers are available, we must compare on small problem sizes. Small problems are primarily useful for comparison only if they are instances of parametrized families of problems for which scaling analysis can be done. In this technical report, we discuss our approach to the generation of hard planning problems from classes of well-studied NP-complete problems that map naturally to planning problems or to aspects of planning problems that many practical planning problems share. These problem classes exhibit a phase transition between easy-to-solve and easy-to-show-unsolvable planning problems. The parametrized families of hard planning problems lie at the phase transition. The exponential scaling of hardness with problem size is apparent in these families even at very small problem sizes, thus enabling us to characterize even very small problems as hard. The families we developed will prove generally useful to the planning community in analyzing the performance of planning algorithms, providing a complementary approach to existing evaluation methods. We illustrate the hardness of these problems and their scaling with results on four state-of-the-art planners, observing significant differences between these planners on these problem families. Finally, we describe two general, and quite different, mappings of planning

  2. Solving optimization problems by the public goods game

    NASA Astrophysics Data System (ADS)

    Javarone, Marco Alberto

    2017-09-01

    We introduce a method based on the Public Goods Game for solving optimization tasks. In particular, we focus on the Traveling Salesman Problem, i.e. a NP-hard problem whose search space exponentially grows increasing the number of cities. The proposed method considers a population whose agents are provided with a random solution to the given problem. In doing so, agents interact by playing the Public Goods Game using the fitness of their solution as currency of the game. Notably, agents with better solutions provide higher contributions, while those with lower ones tend to imitate the solution of richer agents for increasing their fitness. Numerical simulations show that the proposed method allows to compute exact solutions, and suboptimal ones, in the considered search spaces. As result, beyond to propose a new heuristic for combinatorial optimization problems, our work aims to highlight the potentiality of evolutionary game theory beyond its current horizons.

  3. A case study in programming a quantum annealer for hard operational planning problems

    NASA Astrophysics Data System (ADS)

    Rieffel, Eleanor G.; Venturelli, Davide; O'Gorman, Bryan; Do, Minh B.; Prystay, Elicia M.; Smelyanskiy, Vadim N.

    2015-01-01

    We report on a case study in programming an early quantum annealer to attack optimization problems related to operational planning. While a number of studies have looked at the performance of quantum annealers on problems native to their architecture, and others have examined performance of select problems stemming from an application area, ours is one of the first studies of a quantum annealer's performance on parametrized families of hard problems from a practical domain. We explore two different general mappings of planning problems to quadratic unconstrained binary optimization (QUBO) problems, and apply them to two parametrized families of planning problems, navigation-type and scheduling-type. We also examine two more compact, but problem-type specific, mappings to QUBO, one for the navigation-type planning problems and one for the scheduling-type planning problems. We study embedding properties and parameter setting and examine their effect on the efficiency with which the quantum annealer solves these problems. From these results, we derive insights useful for the programming and design of future quantum annealers: problem choice, the mapping used, the properties of the embedding, and the annealing profile all matter, each significantly affecting the performance.

  4. Comparing genetic algorithm and particle swarm optimization for solving capacitated vehicle routing problem

    NASA Astrophysics Data System (ADS)

    Iswari, T.; Asih, A. M. S.

    2018-04-01

    In the logistics system, transportation plays an important role to connect every element in the supply chain, but it can produces the greatest cost. Therefore, it is important to make the transportation costs as minimum as possible. Reducing the transportation cost can be done in several ways. One of the ways to minimizing the transportation cost is by optimizing the routing of its vehicles. It refers to Vehicle Routing Problem (VRP). The most common type of VRP is Capacitated Vehicle Routing Problem (CVRP). In CVRP, the vehicles have their own capacity and the total demands from the customer should not exceed the capacity of the vehicle. CVRP belongs to the class of NP-hard problems. These NP-hard problems make it more complex to solve such that exact algorithms become highly time-consuming with the increases in problem sizes. Thus, for large-scale problem instances, as typically found in industrial applications, finding an optimal solution is not practicable. Therefore, this paper uses two kinds of metaheuristics approach to solving CVRP. Those are Genetic Algorithm and Particle Swarm Optimization. This paper compares the results of both algorithms and see the performance of each algorithm. The results show that both algorithms perform well in solving CVRP but still needs to be improved. From algorithm testing and numerical example, Genetic Algorithm yields a better solution than Particle Swarm Optimization in total distance travelled.

  5. The Hard Problem of Cooperation

    PubMed Central

    Eriksson, Kimmo; Strimling, Pontus

    2012-01-01

    Based on individual variation in cooperative inclinations, we define the “hard problem of cooperation” as that of achieving high levels of cooperation in a group of non-cooperative types. Can the hard problem be solved by institutions with monitoring and sanctions? In a laboratory experiment we find that the answer is affirmative if the institution is imposed on the group but negative if development of the institution is left to the group to vote on. In the experiment, participants were divided into groups of either cooperative types or non-cooperative types depending on their behavior in a public goods game. In these homogeneous groups they repeatedly played a public goods game regulated by an institution that incorporated several of the key properties identified by Ostrom: operational rules, monitoring, rewards, punishments, and (in one condition) change of rules. When change of rules was not possible and punishments were set to be high, groups of both types generally abided by operational rules demanding high contributions to the common good, and thereby achieved high levels of payoffs. Under less severe rules, both types of groups did worse but non-cooperative types did worst. Thus, non-cooperative groups profited the most from being governed by an institution demanding high contributions and employing high punishments. Nevertheless, in a condition where change of rules through voting was made possible, development of the institution in this direction was more often voted down in groups of non-cooperative types. We discuss the relevance of the hard problem and fit our results into a bigger picture of institutional and individual determinants of cooperative behavior. PMID:22792282

  6. Optimization of topological quantum algorithms using Lattice Surgery is hard

    NASA Astrophysics Data System (ADS)

    Herr, Daniel; Nori, Franco; Devitt, Simon

    The traditional method for computation in the surface code or the Raussendorf model is the creation of holes or ''defects'' within the encoded lattice of qubits which are manipulated via topological braiding to enact logic gates. However, this is not the only way to achieve universal, fault-tolerant computation. In this work we turn attention to the Lattice Surgery representation, which realizes encoded logic operations without destroying the intrinsic 2D nearest-neighbor interactions sufficient for braided based logic and achieves universality without using defects for encoding information. In both braided and lattice surgery logic there are open questions regarding the compilation and resource optimization of quantum circuits. Optimization in braid-based logic is proving to be difficult to define and the classical complexity associated with this problem has yet to be determined. In the context of lattice surgery based logic, we can introduce an optimality condition, which corresponds to a circuit with lowest amount of physical qubit requirements, and prove that the complexity of optimizing the geometric (lattice surgery) representation of a quantum circuit is NP-hard.

  7. Bicriteria Network Optimization Problem using Priority-based Genetic Algorithm

    NASA Astrophysics Data System (ADS)

    Gen, Mitsuo; Lin, Lin; Cheng, Runwei

    Network optimization is being an increasingly important and fundamental issue in the fields such as engineering, computer science, operations research, transportation, telecommunication, decision support systems, manufacturing, and airline scheduling. In many applications, however, there are several criteria associated with traversing each edge of a network. For example, cost and flow measures are both important in the networks. As a result, there has been recent interest in solving Bicriteria Network Optimization Problem. The Bicriteria Network Optimization Problem is known a NP-hard. The efficient set of paths may be very large, possibly exponential in size. Thus the computational effort required to solve it can increase exponentially with the problem size in the worst case. In this paper, we propose a genetic algorithm (GA) approach used a priority-based chromosome for solving the bicriteria network optimization problem including maximum flow (MXF) model and minimum cost flow (MCF) model. The objective is to find the set of Pareto optimal solutions that give possible maximum flow with minimum cost. This paper also combines Adaptive Weight Approach (AWA) that utilizes some useful information from the current population to readjust weights for obtaining a search pressure toward a positive ideal point. Computer simulations show the several numerical experiments by using some difficult-to-solve network design problems, and show the effectiveness of the proposed method.

  8. Solving Hard Computational Problems Efficiently: Asymptotic Parametric Complexity 3-Coloring Algorithm

    PubMed Central

    Martín H., José Antonio

    2013-01-01

    Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular biology, e.g., genome sequencing; global alignment of multiple genomes; identifying siblings or discovery of dysregulated pathways. In almost all of these problems, there is the need for proving a hypothesis about certain property of an object that can be present if and only if it adopts some particular admissible structure (an NP-certificate) or be absent (no admissible structure), however, none of the standard approaches can discard the hypothesis when no solution can be found, since none can provide a proof that there is no admissible structure. This article presents an algorithm that introduces a novel type of solution method to “efficiently” solve the graph 3-coloring problem; an NP-complete problem. The proposed method provides certificates (proofs) in both cases: present or absent, so it is possible to accept or reject the hypothesis on the basis of a rigorous proof. It provides exact solutions and is polynomial-time (i.e., efficient) however parametric. The only requirement is sufficient computational power, which is controlled by the parameter . Nevertheless, here it is proved that the probability of requiring a value of to obtain a solution for a random graph decreases exponentially: , making tractable almost all problem instances. Thorough experimental analyses were performed. The algorithm was tested on random graphs, planar graphs and 4-regular planar graphs. The obtained experimental results are in accordance with the theoretical expected results. PMID:23349711

  9. Harmony search algorithm: application to the redundancy optimization problem

    NASA Astrophysics Data System (ADS)

    Nahas, Nabil; Thien-My, Dao

    2010-09-01

    The redundancy optimization problem is a well known NP-hard problem which involves the selection of elements and redundancy levels to maximize system performance, given different system-level constraints. This article presents an efficient algorithm based on the harmony search algorithm (HSA) to solve this optimization problem. The HSA is a new nature-inspired algorithm which mimics the improvization process of music players. Two kinds of problems are considered in testing the proposed algorithm, with the first limited to the binary series-parallel system, where the problem consists of a selection of elements and redundancy levels used to maximize the system reliability given various system-level constraints; the second problem for its part concerns the multi-state series-parallel systems with performance levels ranging from perfect operation to complete failure, and in which identical redundant elements are included in order to achieve a desirable level of availability. Numerical results for test problems from previous research are reported and compared. The results of HSA showed that this algorithm could provide very good solutions when compared to those obtained through other approaches.

  10. On unified modeling, theory, and method for solving multi-scale global optimization problems

    NASA Astrophysics Data System (ADS)

    Gao, David Yang

    2016-10-01

    A unified model is proposed for general optimization problems in multi-scale complex systems. Based on this model and necessary assumptions in physics, the canonical duality theory is presented in a precise way to include traditional duality theories and popular methods as special applications. Two conjectures on NP-hardness are proposed, which should play important roles for correctly understanding and efficiently solving challenging real-world problems. Applications are illustrated for both nonconvex continuous optimization and mixed integer nonlinear programming.

  11. Heterogeneous quantum computing for satellite constellation optimization: solving the weighted k-clique problem

    NASA Astrophysics Data System (ADS)

    Bass, Gideon; Tomlin, Casey; Kumar, Vaibhaw; Rihaczek, Pete; Dulny, Joseph, III

    2018-04-01

    NP-hard optimization problems scale very rapidly with problem size, becoming unsolvable with brute force methods, even with supercomputing resources. Typically, such problems have been approximated with heuristics. However, these methods still take a long time and are not guaranteed to find an optimal solution. Quantum computing offers the possibility of producing significant speed-up and improved solution quality. Current quantum annealing (QA) devices are designed to solve difficult optimization problems, but they are limited by hardware size and qubit connectivity restrictions. We present a novel heterogeneous computing stack that combines QA and classical machine learning, allowing the use of QA on problems larger than the hardware limits of the quantum device. These results represent experiments on a real-world problem represented by the weighted k-clique problem. Through this experiment, we provide insight into the state of quantum machine learning.

  12. Ant colony optimization for solving university facility layout problem

    NASA Astrophysics Data System (ADS)

    Mohd Jani, Nurul Hafiza; Mohd Radzi, Nor Haizan; Ngadiman, Mohd Salihin

    2013-04-01

    Quadratic Assignment Problems (QAP) is classified as the NP hard problem. It has been used to model a lot of problem in several areas such as operational research, combinatorial data analysis and also parallel and distributed computing, optimization problem such as graph portioning and Travel Salesman Problem (TSP). In the literature, researcher use exact algorithm, heuristics algorithm and metaheuristic approaches to solve QAP problem. QAP is largely applied in facility layout problem (FLP). In this paper we used QAP to model university facility layout problem. There are 8 facilities that need to be assigned to 8 locations. Hence we have modeled a QAP problem with n ≤ 10 and developed an Ant Colony Optimization (ACO) algorithm to solve the university facility layout problem. The objective is to assign n facilities to n locations such that the minimum product of flows and distances is obtained. Flow is the movement from one to another facility, whereas distance is the distance between one locations of a facility to other facilities locations. The objective of the QAP is to obtain minimum total walking (flow) of lecturers from one destination to another (distance).

  13. Hard decoding algorithm for optimizing thresholds under general Markovian noise

    NASA Astrophysics Data System (ADS)

    Chamberland, Christopher; Wallman, Joel; Beale, Stefanie; Laflamme, Raymond

    2017-04-01

    Quantum error correction is instrumental in protecting quantum systems from noise in quantum computing and communication settings. Pauli channels can be efficiently simulated and threshold values for Pauli error rates under a variety of error-correcting codes have been obtained. However, realistic quantum systems can undergo noise processes that differ significantly from Pauli noise. In this paper, we present an efficient hard decoding algorithm for optimizing thresholds and lowering failure rates of an error-correcting code under general completely positive and trace-preserving (i.e., Markovian) noise. We use our hard decoding algorithm to study the performance of several error-correcting codes under various non-Pauli noise models by computing threshold values and failure rates for these codes. We compare the performance of our hard decoding algorithm to decoders optimized for depolarizing noise and show improvements in thresholds and reductions in failure rates by several orders of magnitude. Our hard decoding algorithm can also be adapted to take advantage of a code's non-Pauli transversal gates to further suppress noise. For example, we show that using the transversal gates of the 5-qubit code allows arbitrary rotations around certain axes to be perfectly corrected. Furthermore, we show that Pauli twirling can increase or decrease the threshold depending upon the code properties. Lastly, we show that even if the physical noise model differs slightly from the hypothesized noise model used to determine an optimized decoder, failure rates can still be reduced by applying our hard decoding algorithm.

  14. Hard and Soft Constraints in Reliability-Based Design Optimization

    NASA Technical Reports Server (NTRS)

    Crespo, L.uis G.; Giesy, Daniel P.; Kenny, Sean P.

    2006-01-01

    This paper proposes a framework for the analysis and design optimization of models subject to parametric uncertainty where design requirements in the form of inequality constraints are present. Emphasis is given to uncertainty models prescribed by norm bounded perturbations from a nominal parameter value and by sets of componentwise bounded uncertain variables. These models, which often arise in engineering problems, allow for a sharp mathematical manipulation. Constraints can be implemented in the hard sense, i.e., constraints must be satisfied for all parameter realizations in the uncertainty model, and in the soft sense, i.e., constraints can be violated by some realizations of the uncertain parameter. In regard to hard constraints, this methodology allows (i) to determine if a hard constraint can be satisfied for a given uncertainty model and constraint structure, (ii) to generate conclusive, formally verifiable reliability assessments that allow for unprejudiced comparisons of competing design alternatives and (iii) to identify the critical combination of uncertain parameters leading to constraint violations. In regard to soft constraints, the methodology allows the designer (i) to use probabilistic uncertainty models, (ii) to calculate upper bounds to the probability of constraint violation, and (iii) to efficiently estimate failure probabilities via a hybrid method. This method integrates the upper bounds, for which closed form expressions are derived, along with conditional sampling. In addition, an l(sub infinity) formulation for the efficient manipulation of hyper-rectangular sets is also proposed.

  15. Methodological problems with gamma-ray burst hardness/intensity correlations

    NASA Technical Reports Server (NTRS)

    Schaefer, Bradley E.

    1993-01-01

    The hardness and intensity are easily measured quantities for all gamma-ray bursts (GRBs), and so, many past and current studies have sought correlations between them. This Letter presents many serious methodological problems with the practical definitions for both hardness and intensity. These difficulties are such that significant correlations can be easily introduced as artifacts of the reduction procedure. In particular, cosmological models of GRBs cannot be tested with hardness/intensity correlations with current instrumentation and the time evolution of the hardness in a given burst may be correlated with intensity for reasons that are unrelated to intrinsic change in the spectral shape.

  16. HSTLBO: A hybrid algorithm based on Harmony Search and Teaching-Learning-Based Optimization for complex high-dimensional optimization problems.

    PubMed

    Tuo, Shouheng; Yong, Longquan; Deng, Fang'an; Li, Yanhai; Lin, Yong; Lu, Qiuju

    2017-01-01

    Harmony Search (HS) and Teaching-Learning-Based Optimization (TLBO) as new swarm intelligent optimization algorithms have received much attention in recent years. Both of them have shown outstanding performance for solving NP-Hard optimization problems. However, they also suffer dramatic performance degradation for some complex high-dimensional optimization problems. Through a lot of experiments, we find that the HS and TLBO have strong complementarity each other. The HS has strong global exploration power but low convergence speed. Reversely, the TLBO has much fast convergence speed but it is easily trapped into local search. In this work, we propose a hybrid search algorithm named HSTLBO that merges the two algorithms together for synergistically solving complex optimization problems using a self-adaptive selection strategy. In the HSTLBO, both HS and TLBO are modified with the aim of balancing the global exploration and exploitation abilities, where the HS aims mainly to explore the unknown regions and the TLBO aims to rapidly exploit high-precision solutions in the known regions. Our experimental results demonstrate better performance and faster speed than five state-of-the-art HS variants and show better exploration power than five good TLBO variants with similar run time, which illustrates that our method is promising in solving complex high-dimensional optimization problems. The experiment on portfolio optimization problems also demonstrate that the HSTLBO is effective in solving complex read-world application.

  17. Extremal Optimization for Quadratic Unconstrained Binary Problems

    NASA Astrophysics Data System (ADS)

    Boettcher, S.

    We present an implementation of τ-EO for quadratic unconstrained binary optimization (QUBO) problems. To this end, we transform modify QUBO from its conventional Boolean presentation into a spin glass with a random external field on each site. These fields tend to be rather large compared to the typical coupling, presenting EO with a challenging two-scale problem, exploring smaller differences in couplings effectively while sufficiently aligning with those strong external fields. However, we also find a simple solution to that problem that indicates that those external fields apparently tilt the energy landscape to a such a degree such that global minima become more easy to find than those of spin glasses without (or very small) fields. We explore the impact of the weight distribution of the QUBO formulation in the operations research literature and analyze their meaning in a spin-glass language. This is significant because QUBO problems are considered among the main contenders for NP-hard problems that could be solved efficiently on a quantum computer such as D-Wave.

  18. Discrete Optimization Model for Vehicle Routing Problem with Scheduling Side Cosntraints

    NASA Astrophysics Data System (ADS)

    Juliandri, Dedy; Mawengkang, Herman; Bu'ulolo, F.

    2018-01-01

    Vehicle Routing Problem (VRP) is an important element of many logistic systems which involve routing and scheduling of vehicles from a depot to a set of customers node. This is a hard combinatorial optimization problem with the objective to find an optimal set of routes used by a fleet of vehicles to serve the demands a set of customers It is required that these vehicles return to the depot after serving customers’ demand. The problem incorporates time windows, fleet and driver scheduling, pick-up and delivery in the planning horizon. The goal is to determine the scheduling of fleet and driver and routing policies of the vehicles. The objective is to minimize the overall costs of all routes over the planning horizon. We model the problem as a linear mixed integer program. We develop a combination of heuristics and exact method for solving the model.

  19. Deaf and hard of hearing students' problem-solving strategies with signed arithmetic story problems.

    PubMed

    Pagliaro, Claudia M; Ansell, Ellen

    2012-01-01

    The use of problem-solving strategies by 59 deaf and hard of hearing children, grades K-3, was investigated. The children were asked to solve 9 arithmetic story problems presented to them in American Sign Language. The researchers found that while the children used the same general types of strategies that are used by hearing children (i.e., modeling, counting, and fact-based strategies), they showed an overwhelming use of counting strategies for all types of problems and at all ages. This difference may have its roots in language or instruction (or in both), and calls attention to the need for conceptual rather than procedural mathematics instruction for deaf and hard of hearing students.

  20. Discrete particle swarm optimization to solve multi-objective limited-wait hybrid flow shop scheduling problem

    NASA Astrophysics Data System (ADS)

    Santosa, B.; Siswanto, N.; Fiqihesa

    2018-04-01

    This paper proposes a discrete Particle Swam Optimization (PSO) to solve limited-wait hybrid flowshop scheduing problem with multi objectives. Flow shop schedulimg represents the condition when several machines are arranged in series and each job must be processed at each machine with same sequence. The objective functions are minimizing completion time (makespan), total tardiness time, and total machine idle time. Flow shop scheduling model always grows to cope with the real production system accurately. Since flow shop scheduling is a NP-Hard problem then the most suitable method to solve is metaheuristics. One of metaheuristics algorithm is Particle Swarm Optimization (PSO), an algorithm which is based on the behavior of a swarm. Originally, PSO was intended to solve continuous optimization problems. Since flow shop scheduling is a discrete optimization problem, then, we need to modify PSO to fit the problem. The modification is done by using probability transition matrix mechanism. While to handle multi objectives problem, we use Pareto Optimal (MPSO). The results of MPSO is better than the PSO because the MPSO solution set produced higher probability to find the optimal solution. Besides the MPSO solution set is closer to the optimal solution

  1. New Hardness Results for Diophantine Approximation

    NASA Astrophysics Data System (ADS)

    Eisenbrand, Friedrich; Rothvoß, Thomas

    We revisit simultaneous Diophantine approximation, a classical problem from the geometry of numbers which has many applications in algorithms and complexity. The input to the decision version of this problem consists of a rational vector α ∈ ℚ n , an error bound ɛ and a denominator bound N ∈ ℕ + . One has to decide whether there exists an integer, called the denominator Q with 1 ≤ Q ≤ N such that the distance of each number Q ·α i to its nearest integer is bounded by ɛ. Lagarias has shown that this problem is NP-complete and optimization versions have been shown to be hard to approximate within a factor n c/ loglogn for some constant c > 0. We strengthen the existing hardness results and show that the optimization problem of finding the smallest denominator Q ∈ ℕ + such that the distances of Q·α i to the nearest integer are bounded by ɛ is hard to approximate within a factor 2 n unless {textrm{P}} = NP.

  2. HSTLBO: A hybrid algorithm based on Harmony Search and Teaching-Learning-Based Optimization for complex high-dimensional optimization problems

    PubMed Central

    Tuo, Shouheng; Yong, Longquan; Deng, Fang’an; Li, Yanhai; Lin, Yong; Lu, Qiuju

    2017-01-01

    Harmony Search (HS) and Teaching-Learning-Based Optimization (TLBO) as new swarm intelligent optimization algorithms have received much attention in recent years. Both of them have shown outstanding performance for solving NP-Hard optimization problems. However, they also suffer dramatic performance degradation for some complex high-dimensional optimization problems. Through a lot of experiments, we find that the HS and TLBO have strong complementarity each other. The HS has strong global exploration power but low convergence speed. Reversely, the TLBO has much fast convergence speed but it is easily trapped into local search. In this work, we propose a hybrid search algorithm named HSTLBO that merges the two algorithms together for synergistically solving complex optimization problems using a self-adaptive selection strategy. In the HSTLBO, both HS and TLBO are modified with the aim of balancing the global exploration and exploitation abilities, where the HS aims mainly to explore the unknown regions and the TLBO aims to rapidly exploit high-precision solutions in the known regions. Our experimental results demonstrate better performance and faster speed than five state-of-the-art HS variants and show better exploration power than five good TLBO variants with similar run time, which illustrates that our method is promising in solving complex high-dimensional optimization problems. The experiment on portfolio optimization problems also demonstrate that the HSTLBO is effective in solving complex read-world application. PMID:28403224

  3. Guaranteed Discrete Energy Optimization on Large Protein Design Problems.

    PubMed

    Simoncini, David; Allouche, David; de Givry, Simon; Delmas, Céline; Barbe, Sophie; Schiex, Thomas

    2015-12-08

    In Computational Protein Design (CPD), assuming a rigid backbone and amino-acid rotamer library, the problem of finding a sequence with an optimal conformation is NP-hard. In this paper, using Dunbrack's rotamer library and Talaris2014 decomposable energy function, we use an exact deterministic method combining branch and bound, arc consistency, and tree-decomposition to provenly identify the global minimum energy sequence-conformation on full-redesign problems, defining search spaces of size up to 10(234). This is achieved on a single core of a standard computing server, requiring a maximum of 66GB RAM. A variant of the algorithm is able to exhaustively enumerate all sequence-conformations within an energy threshold of the optimum. These proven optimal solutions are then used to evaluate the frequencies and amplitudes, in energy and sequence, at which an existing CPD-dedicated simulated annealing implementation may miss the optimum on these full redesign problems. The probability of finding an optimum drops close to 0 very quickly. In the worst case, despite 1,000 repeats, the annealing algorithm remained more than 1 Rosetta unit away from the optimum, leading to design sequences that could differ from the optimal sequence by more than 30% of their amino acids.

  4. A Biogeography-Based Optimization Algorithm Hybridized with Tabu Search for the Quadratic Assignment Problem

    PubMed Central

    Lim, Wee Loon; Wibowo, Antoni; Desa, Mohammad Ishak; Haron, Habibollah

    2016-01-01

    The quadratic assignment problem (QAP) is an NP-hard combinatorial optimization problem with a wide variety of applications. Biogeography-based optimization (BBO), a relatively new optimization technique based on the biogeography concept, uses the idea of migration strategy of species to derive algorithm for solving optimization problems. It has been shown that BBO provides performance on a par with other optimization methods. A classical BBO algorithm employs the mutation operator as its diversification strategy. However, this process will often ruin the quality of solutions in QAP. In this paper, we propose a hybrid technique to overcome the weakness of classical BBO algorithm to solve QAP, by replacing the mutation operator with a tabu search procedure. Our experiments using the benchmark instances from QAPLIB show that the proposed hybrid method is able to find good solutions for them within reasonable computational times. Out of 61 benchmark instances tested, the proposed method is able to obtain the best known solutions for 57 of them. PMID:26819585

  5. A Biogeography-Based Optimization Algorithm Hybridized with Tabu Search for the Quadratic Assignment Problem.

    PubMed

    Lim, Wee Loon; Wibowo, Antoni; Desa, Mohammad Ishak; Haron, Habibollah

    2016-01-01

    The quadratic assignment problem (QAP) is an NP-hard combinatorial optimization problem with a wide variety of applications. Biogeography-based optimization (BBO), a relatively new optimization technique based on the biogeography concept, uses the idea of migration strategy of species to derive algorithm for solving optimization problems. It has been shown that BBO provides performance on a par with other optimization methods. A classical BBO algorithm employs the mutation operator as its diversification strategy. However, this process will often ruin the quality of solutions in QAP. In this paper, we propose a hybrid technique to overcome the weakness of classical BBO algorithm to solve QAP, by replacing the mutation operator with a tabu search procedure. Our experiments using the benchmark instances from QAPLIB show that the proposed hybrid method is able to find good solutions for them within reasonable computational times. Out of 61 benchmark instances tested, the proposed method is able to obtain the best known solutions for 57 of them.

  6. A hybrid algorithm optimization approach for machine loading problem in flexible manufacturing system

    NASA Astrophysics Data System (ADS)

    Kumar, Vijay M.; Murthy, ANN; Chandrashekara, K.

    2012-05-01

    The production planning problem of flexible manufacturing system (FMS) concerns with decisions that have to be made before an FMS begins to produce parts according to a given production plan during an upcoming planning horizon. The main aspect of production planning deals with machine loading problem in which selection of a subset of jobs to be manufactured and assignment of their operations to the relevant machines are made. Such problems are not only combinatorial optimization problems, but also happen to be non-deterministic polynomial-time-hard, making it difficult to obtain satisfactory solutions using traditional optimization techniques. In this paper, an attempt has been made to address the machine loading problem with objectives of minimization of system unbalance and maximization of throughput simultaneously while satisfying the system constraints related to available machining time and tool slot designing and using a meta-hybrid heuristic technique based on genetic algorithm and particle swarm optimization. The results reported in this paper demonstrate the model efficiency and examine the performance of the system with respect to measures such as throughput and system utilization.

  7. People efficiently explore the solution space of the computationally intractable traveling salesman problem to find near-optimal tours.

    PubMed

    Acuña, Daniel E; Parada, Víctor

    2010-07-29

    Humans need to solve computationally intractable problems such as visual search, categorization, and simultaneous learning and acting, yet an increasing body of evidence suggests that their solutions to instantiations of these problems are near optimal. Computational complexity advances an explanation to this apparent paradox: (1) only a small portion of instances of such problems are actually hard, and (2) successful heuristics exploit structural properties of the typical instance to selectively improve parts that are likely to be sub-optimal. We hypothesize that these two ideas largely account for the good performance of humans on computationally hard problems. We tested part of this hypothesis by studying the solutions of 28 participants to 28 instances of the Euclidean Traveling Salesman Problem (TSP). Participants were provided feedback on the cost of their solutions and were allowed unlimited solution attempts (trials). We found a significant improvement between the first and last trials and that solutions are significantly different from random tours that follow the convex hull and do not have self-crossings. More importantly, we found that participants modified their current better solutions in such a way that edges belonging to the optimal solution ("good" edges) were significantly more likely to stay than other edges ("bad" edges), a hallmark of structural exploitation. We found, however, that more trials harmed the participants' ability to tell good from bad edges, suggesting that after too many trials the participants "ran out of ideas." In sum, we provide the first demonstration of significant performance improvement on the TSP under repetition and feedback and evidence that human problem-solving may exploit the structure of hard problems paralleling behavior of state-of-the-art heuristics.

  8. Mathematical Problem-Solving Styles in the Education of Deaf and Hard-of-Hearing Individuals

    ERIC Educational Resources Information Center

    Erickson, Elizabeth E. A.

    2012-01-01

    This study explored the mathematical problem-solving styles of middle school and high school deaf and hard-of-hearing students and the mathematical problem-solving styles of the mathematics teachers of middle school and high school deaf and hard-of-hearing students. The research involved 45 deaf and hard-of-hearing students and 19 teachers from a…

  9. Firefly algorithm for cardinality constrained mean-variance portfolio optimization problem with entropy diversity constraint.

    PubMed

    Bacanin, Nebojsa; Tuba, Milan

    2014-01-01

    Portfolio optimization (selection) problem is an important and hard optimization problem that, with the addition of necessary realistic constraints, becomes computationally intractable. Nature-inspired metaheuristics are appropriate for solving such problems; however, literature review shows that there are very few applications of nature-inspired metaheuristics to portfolio optimization problem. This is especially true for swarm intelligence algorithms which represent the newer branch of nature-inspired algorithms. No application of any swarm intelligence metaheuristics to cardinality constrained mean-variance (CCMV) portfolio problem with entropy constraint was found in the literature. This paper introduces modified firefly algorithm (FA) for the CCMV portfolio model with entropy constraint. Firefly algorithm is one of the latest, very successful swarm intelligence algorithm; however, it exhibits some deficiencies when applied to constrained problems. To overcome lack of exploration power during early iterations, we modified the algorithm and tested it on standard portfolio benchmark data sets used in the literature. Our proposed modified firefly algorithm proved to be better than other state-of-the-art algorithms, while introduction of entropy diversity constraint further improved results.

  10. Firefly Algorithm for Cardinality Constrained Mean-Variance Portfolio Optimization Problem with Entropy Diversity Constraint

    PubMed Central

    2014-01-01

    Portfolio optimization (selection) problem is an important and hard optimization problem that, with the addition of necessary realistic constraints, becomes computationally intractable. Nature-inspired metaheuristics are appropriate for solving such problems; however, literature review shows that there are very few applications of nature-inspired metaheuristics to portfolio optimization problem. This is especially true for swarm intelligence algorithms which represent the newer branch of nature-inspired algorithms. No application of any swarm intelligence metaheuristics to cardinality constrained mean-variance (CCMV) portfolio problem with entropy constraint was found in the literature. This paper introduces modified firefly algorithm (FA) for the CCMV portfolio model with entropy constraint. Firefly algorithm is one of the latest, very successful swarm intelligence algorithm; however, it exhibits some deficiencies when applied to constrained problems. To overcome lack of exploration power during early iterations, we modified the algorithm and tested it on standard portfolio benchmark data sets used in the literature. Our proposed modified firefly algorithm proved to be better than other state-of-the-art algorithms, while introduction of entropy diversity constraint further improved results. PMID:24991645

  11. On the asymptotic optimality and improved strategies of SPTB heuristic for open-shop scheduling problem

    NASA Astrophysics Data System (ADS)

    Bai, Danyu; Zhang, Zhihai

    2014-08-01

    This article investigates the open-shop scheduling problem with the optimal criterion of minimising the sum of quadratic completion times. For this NP-hard problem, the asymptotic optimality of the shortest processing time block (SPTB) heuristic is proven in the sense of limit. Moreover, three different improvements, namely, the job-insert scheme, tabu search and genetic algorithm, are introduced to enhance the quality of the original solution generated by the SPTB heuristic. At the end of the article, a series of numerical experiments demonstrate the convergence of the heuristic, the performance of the improvements and the effectiveness of the quadratic objective.

  12. People Efficiently Explore the Solution Space of the Computationally Intractable Traveling Salesman Problem to Find Near-Optimal Tours

    PubMed Central

    Acuña, Daniel E.; Parada, Víctor

    2010-01-01

    Humans need to solve computationally intractable problems such as visual search, categorization, and simultaneous learning and acting, yet an increasing body of evidence suggests that their solutions to instantiations of these problems are near optimal. Computational complexity advances an explanation to this apparent paradox: (1) only a small portion of instances of such problems are actually hard, and (2) successful heuristics exploit structural properties of the typical instance to selectively improve parts that are likely to be sub-optimal. We hypothesize that these two ideas largely account for the good performance of humans on computationally hard problems. We tested part of this hypothesis by studying the solutions of 28 participants to 28 instances of the Euclidean Traveling Salesman Problem (TSP). Participants were provided feedback on the cost of their solutions and were allowed unlimited solution attempts (trials). We found a significant improvement between the first and last trials and that solutions are significantly different from random tours that follow the convex hull and do not have self-crossings. More importantly, we found that participants modified their current better solutions in such a way that edges belonging to the optimal solution (“good” edges) were significantly more likely to stay than other edges (“bad” edges), a hallmark of structural exploitation. We found, however, that more trials harmed the participants' ability to tell good from bad edges, suggesting that after too many trials the participants “ran out of ideas.” In sum, we provide the first demonstration of significant performance improvement on the TSP under repetition and feedback and evidence that human problem-solving may exploit the structure of hard problems paralleling behavior of state-of-the-art heuristics. PMID:20686597

  13. Improved Fractal Space Filling Curves Hybrid Optimization Algorithm for Vehicle Routing Problem.

    PubMed

    Yue, Yi-xiang; Zhang, Tong; Yue, Qun-xing

    2015-01-01

    Vehicle Routing Problem (VRP) is one of the key issues in optimization of modern logistics system. In this paper, a modified VRP model with hard time window is established and a Hybrid Optimization Algorithm (HOA) based on Fractal Space Filling Curves (SFC) method and Genetic Algorithm (GA) is introduced. By incorporating the proposed algorithm, SFC method can find an initial and feasible solution very fast; GA is used to improve the initial solution. Thereafter, experimental software was developed and a large number of experimental computations from Solomon's benchmark have been studied. The experimental results demonstrate the feasibility and effectiveness of the HOA.

  14. NP-hardness of the cluster minimization problem revisited

    NASA Astrophysics Data System (ADS)

    Adib, Artur B.

    2005-10-01

    The computational complexity of the 'cluster minimization problem' is revisited (Wille and Vennik 1985 J. Phys. A: Math. Gen. 18 L419). It is argued that the original NP-hardness proof does not apply to pairwise potentials of physical interest, such as those that depend on the geometric distance between the particles. A geometric analogue of the original problem is formulated, and a new proof for such potentials is provided by polynomial time transformation from the independent set problem for unit disk graphs. Limitations of this formulation are pointed out, and new subproblems that bear more direct consequences to the numerical study of clusters are suggested.

  15. Hybrid Self-Adaptive Evolution Strategies Guided by Neighborhood Structures for Combinatorial Optimization Problems.

    PubMed

    Coelho, V N; Coelho, I M; Souza, M J F; Oliveira, T A; Cota, L P; Haddad, M N; Mladenovic, N; Silva, R C P; Guimarães, F G

    2016-01-01

    This article presents an Evolution Strategy (ES)--based algorithm, designed to self-adapt its mutation operators, guiding the search into the solution space using a Self-Adaptive Reduced Variable Neighborhood Search procedure. In view of the specific local search operators for each individual, the proposed population-based approach also fits into the context of the Memetic Algorithms. The proposed variant uses the Greedy Randomized Adaptive Search Procedure with different greedy parameters for generating its initial population, providing an interesting exploration-exploitation balance. To validate the proposal, this framework is applied to solve three different [Formula: see text]-Hard combinatorial optimization problems: an Open-Pit-Mining Operational Planning Problem with dynamic allocation of trucks, an Unrelated Parallel Machine Scheduling Problem with Setup Times, and the calibration of a hybrid fuzzy model for Short-Term Load Forecasting. Computational results point out the convergence of the proposed model and highlight its ability in combining the application of move operations from distinct neighborhood structures along the optimization. The results gathered and reported in this article represent a collective evidence of the performance of the method in challenging combinatorial optimization problems from different application domains. The proposed evolution strategy demonstrates an ability of adapting the strength of the mutation disturbance during the generations of its evolution process. The effectiveness of the proposal motivates the application of this novel evolutionary framework for solving other combinatorial optimization problems.

  16. Parallel Optimization of Polynomials for Large-scale Problems in Stability and Control

    NASA Astrophysics Data System (ADS)

    Kamyar, Reza

    In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems --- in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) --- whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning that improving the accuracy of the solutions requires solving SDPs with tens of thousands of decision variables and constraints. Setting up and solving such problems is a significant challenge. The existing optimization algorithms and software are only designed to use desktop computers or small cluster computers --- machines which do not have sufficient memory for solving such large SDPs. Moreover, the speed-up of these algorithms does not scale beyond dozens of processors. This in fact is the reason we seek parallel algorithms for setting-up and solving large SDPs on large cluster- and/or super-computers. We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to

  17. Robust quantum optimizer with full connectivity

    PubMed Central

    Nigg, Simon E.; Lörch, Niels; Tiwari, Rakesh P.

    2017-01-01

    Quantum phenomena have the potential to speed up the solution of hard optimization problems. For example, quantum annealing, based on the quantum tunneling effect, has recently been shown to scale exponentially better with system size than classical simulated annealing. However, current realizations of quantum annealers with superconducting qubits face two major challenges. First, the connectivity between the qubits is limited, excluding many optimization problems from a direct implementation. Second, decoherence degrades the success probability of the optimization. We address both of these shortcomings and propose an architecture in which the qubits are robustly encoded in continuous variable degrees of freedom. By leveraging the phenomenon of flux quantization, all-to-all connectivity with sufficient tunability to implement many relevant optimization problems is obtained without overhead. Furthermore, we demonstrate the robustness of this architecture by simulating the optimal solution of a small instance of the nondeterministic polynomial-time hard (NP-hard) and fully connected number partitioning problem in the presence of dissipation. PMID:28435880

  18. Robust quantum optimizer with full connectivity.

    PubMed

    Nigg, Simon E; Lörch, Niels; Tiwari, Rakesh P

    2017-04-01

    Quantum phenomena have the potential to speed up the solution of hard optimization problems. For example, quantum annealing, based on the quantum tunneling effect, has recently been shown to scale exponentially better with system size than classical simulated annealing. However, current realizations of quantum annealers with superconducting qubits face two major challenges. First, the connectivity between the qubits is limited, excluding many optimization problems from a direct implementation. Second, decoherence degrades the success probability of the optimization. We address both of these shortcomings and propose an architecture in which the qubits are robustly encoded in continuous variable degrees of freedom. By leveraging the phenomenon of flux quantization, all-to-all connectivity with sufficient tunability to implement many relevant optimization problems is obtained without overhead. Furthermore, we demonstrate the robustness of this architecture by simulating the optimal solution of a small instance of the nondeterministic polynomial-time hard (NP-hard) and fully connected number partitioning problem in the presence of dissipation.

  19. Improved Fractal Space Filling Curves Hybrid Optimization Algorithm for Vehicle Routing Problem

    PubMed Central

    Yue, Yi-xiang; Zhang, Tong; Yue, Qun-xing

    2015-01-01

    Vehicle Routing Problem (VRP) is one of the key issues in optimization of modern logistics system. In this paper, a modified VRP model with hard time window is established and a Hybrid Optimization Algorithm (HOA) based on Fractal Space Filling Curves (SFC) method and Genetic Algorithm (GA) is introduced. By incorporating the proposed algorithm, SFC method can find an initial and feasible solution very fast; GA is used to improve the initial solution. Thereafter, experimental software was developed and a large number of experimental computations from Solomon's benchmark have been studied. The experimental results demonstrate the feasibility and effectiveness of the HOA. PMID:26167171

  20. Deaf and Hard of Hearing Students' Problem-Solving Strategies with Signed Arithmetic Story Problems

    ERIC Educational Resources Information Center

    Pagliaro, Claudia M.; Ansell, Ellen

    2011-01-01

    The use of problem-solving strategies by 59 deaf and hard of hearing children, grades K-3, was investigated. The children were asked to solve 9 arithmetic story problems presented to them in American Sign Language. The researchers found that while the children used the same general types of strategies that are used by hearing children (i.e.,…

  1. Class and Home Problems: Optimization Problems

    ERIC Educational Resources Information Center

    Anderson, Brian J.; Hissam, Robin S.; Shaeiwitz, Joseph A.; Turton, Richard

    2011-01-01

    Optimization problems suitable for all levels of chemical engineering students are available. These problems do not require advanced mathematical techniques, since they can be solved using typical software used by students and practitioners. The method used to solve these problems forces students to understand the trends for the different terms…

  2. Selecting Optimal Random Forest Predictive Models: A Case Study on Predicting the Spatial Distribution of Seabed Hardness

    PubMed Central

    Li, Jin; Tran, Maggie; Siwabessy, Justy

    2016-01-01

    Spatially continuous predictions of seabed hardness are important baseline environmental information for sustainable management of Australia’s marine jurisdiction. Seabed hardness is often inferred from multibeam backscatter data with unknown accuracy and can be inferred from underwater video footage at limited locations. In this study, we classified the seabed into four classes based on two new seabed hardness classification schemes (i.e., hard90 and hard70). We developed optimal predictive models to predict seabed hardness using random forest (RF) based on the point data of hardness classes and spatially continuous multibeam data. Five feature selection (FS) methods that are variable importance (VI), averaged variable importance (AVI), knowledge informed AVI (KIAVI), Boruta and regularized RF (RRF) were tested based on predictive accuracy. Effects of highly correlated, important and unimportant predictors on the accuracy of RF predictive models were examined. Finally, spatial predictions generated using the most accurate models were visually examined and analysed. This study confirmed that: 1) hard90 and hard70 are effective seabed hardness classification schemes; 2) seabed hardness of four classes can be predicted with a high degree of accuracy; 3) the typical approach used to pre-select predictive variables by excluding highly correlated variables needs to be re-examined; 4) the identification of the important and unimportant predictors provides useful guidelines for further improving predictive models; 5) FS methods select the most accurate predictive model(s) instead of the most parsimonious ones, and AVI and Boruta are recommended for future studies; and 6) RF is an effective modelling method with high predictive accuracy for multi-level categorical data and can be applied to ‘small p and large n’ problems in environmental sciences. Additionally, automated computational programs for AVI need to be developed to increase its computational efficiency and

  3. Selecting Optimal Random Forest Predictive Models: A Case Study on Predicting the Spatial Distribution of Seabed Hardness.

    PubMed

    Li, Jin; Tran, Maggie; Siwabessy, Justy

    2016-01-01

    Spatially continuous predictions of seabed hardness are important baseline environmental information for sustainable management of Australia's marine jurisdiction. Seabed hardness is often inferred from multibeam backscatter data with unknown accuracy and can be inferred from underwater video footage at limited locations. In this study, we classified the seabed into four classes based on two new seabed hardness classification schemes (i.e., hard90 and hard70). We developed optimal predictive models to predict seabed hardness using random forest (RF) based on the point data of hardness classes and spatially continuous multibeam data. Five feature selection (FS) methods that are variable importance (VI), averaged variable importance (AVI), knowledge informed AVI (KIAVI), Boruta and regularized RF (RRF) were tested based on predictive accuracy. Effects of highly correlated, important and unimportant predictors on the accuracy of RF predictive models were examined. Finally, spatial predictions generated using the most accurate models were visually examined and analysed. This study confirmed that: 1) hard90 and hard70 are effective seabed hardness classification schemes; 2) seabed hardness of four classes can be predicted with a high degree of accuracy; 3) the typical approach used to pre-select predictive variables by excluding highly correlated variables needs to be re-examined; 4) the identification of the important and unimportant predictors provides useful guidelines for further improving predictive models; 5) FS methods select the most accurate predictive model(s) instead of the most parsimonious ones, and AVI and Boruta are recommended for future studies; and 6) RF is an effective modelling method with high predictive accuracy for multi-level categorical data and can be applied to 'small p and large n' problems in environmental sciences. Additionally, automated computational programs for AVI need to be developed to increase its computational efficiency and

  4. COPS: Large-scale nonlinearly constrained optimization problems

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

    Bondarenko, A.S.; Bortz, D.M.; More, J.J.

    2000-02-10

    The authors have started the development of COPS, a collection of large-scale nonlinearly Constrained Optimization Problems. The primary purpose of this collection is to provide difficult test cases for optimization software. Problems in the current version of the collection come from fluid dynamics, population dynamics, optimal design, and optimal control. For each problem they provide a short description of the problem, notes on the formulation of the problem, and results of computational experiments with general optimization solvers. They currently have results for DONLP2, LANCELOT, MINOS, SNOPT, and LOQO.

  5. A modified generalized extremal optimization algorithm for the quay crane scheduling problem with interference constraints

    NASA Astrophysics Data System (ADS)

    Guo, Peng; Cheng, Wenming; Wang, Yi

    2014-10-01

    The quay crane scheduling problem (QCSP) determines the handling sequence of tasks at ship bays by a set of cranes assigned to a container vessel such that the vessel's service time is minimized. A number of heuristics or meta-heuristics have been proposed to obtain the near-optimal solutions to overcome the NP-hardness of the problem. In this article, the idea of generalized extremal optimization (GEO) is adapted to solve the QCSP with respect to various interference constraints. The resulting GEO is termed the modified GEO. A randomized searching method for neighbouring task-to-QC assignments to an incumbent task-to-QC assignment is developed in executing the modified GEO. In addition, a unidirectional search decoding scheme is employed to transform a task-to-QC assignment to an active quay crane schedule. The effectiveness of the developed GEO is tested on a suite of benchmark problems introduced by K.H. Kim and Y.M. Park in 2004 (European Journal of Operational Research, Vol. 156, No. 3). Compared with other well-known existing approaches, the experiment results show that the proposed modified GEO is capable of obtaining the optimal or near-optimal solution in a reasonable time, especially for large-sized problems.

  6. Social Emotional Optimization Algorithm for Nonlinear Constrained Optimization Problems

    NASA Astrophysics Data System (ADS)

    Xu, Yuechun; Cui, Zhihua; Zeng, Jianchao

    Nonlinear programming problem is one important branch in operational research, and has been successfully applied to various real-life problems. In this paper, a new approach called Social emotional optimization algorithm (SEOA) is used to solve this problem which is a new swarm intelligent technique by simulating the human behavior guided by emotion. Simulation results show that the social emotional optimization algorithm proposed in this paper is effective and efficiency for the nonlinear constrained programming problems.

  7. Optimization of lipid profile and hardness of low-fat mortadella following a sequential strategy of experimental design.

    PubMed

    Saldaña, Erick; Siche, Raúl; da Silva Pinto, Jair Sebastião; de Almeida, Marcio Aurélio; Selani, Miriam Mabel; Rios-Mera, Juan; Contreras-Castillo, Carmen J

    2018-02-01

    This study aims to optimize simultaneously the lipid profile and instrumental hardness of low-fat mortadella. For lipid mixture optimization, the overlapping of surface boundaries was used to select the quantities of canola, olive, and fish oils, in order to maximize PUFAs, specifically the long-chain n-3 fatty acids (eicosapentaenoic-EPA, docosahexaenoic acids-DHA) using the minimum content of fish oil. Increased quantities of canola oil were associated with higher PUFA/SFA ratios. The presence of fish oil, even in small amounts, was effective in improving the nutritional quality of the mixture, showing lower n-6/n-3 ratios and significant levels of EPA and DHA. Thus, the optimal lipid mixture comprised of 20, 30 and 50% fish, olive and canola oils, respectively, which present PUFA/SFA (2.28) and n-6/n-3 (2.30) ratios within the recommendations of a healthy diet. Once the lipid mixture was optimized, components of the pre-emulsion used as fat replacer in the mortadella, such as lipid mixture (LM), sodium alginate (SA), and milk protein concentrate (PC), were studied to optimize hardness and springiness to target ranges of 13-16 N and 0.86-0.87, respectively. Results showed that springiness was not significantly affected by these variables. However, as the concentration of the three components increased, hardness decreased. Through the desirability function, the optimal proportions were 30% LM, 0.5% SA, and 0.5% PC. This study showed that the pre-emulsion decreases hardness of mortadella. In addition, response surface methodology was efficient to model lipid mixture and hardness, resulting in a product with improved texture and lipid quality.

  8. When students can choose easy, medium, or hard homework problems

    NASA Astrophysics Data System (ADS)

    Teodorescu, Raluca E.; Seaton, Daniel T.; Cardamone, Caroline N.; Rayyan, Saif; Abbott, Jonathan E.; Barrantes, Analia; Pawl, Andrew; Pritchard, David E.

    2012-02-01

    We investigate student-chosen, multi-level homework in our Integrated Learning Environment for Mechanics [1] built using the LON-CAPA [2] open-source learning system. Multi-level refers to problems categorized as easy, medium, and hard. Problem levels were determined a priori based on the knowledge needed to solve them [3]. We analyze these problems using three measures: time-per-problem, LON-CAPA difficulty, and item difficulty measured by item response theory. Our analysis of student behavior in this environment suggests that time-per-problem is strongly dependent on problem category, unlike either score-based measures. We also found trends in student choice of problems, overall effort, and efficiency across the student population. Allowing students choice in problem solving seems to improve their motivation; 70% of students worked additional problems for which no credit was given.

  9. Structural qualia: a solution to the hard problem of consciousness.

    PubMed

    Loorits, Kristjan

    2014-01-01

    The hard problem of consciousness has been often claimed to be unsolvable by the methods of traditional empirical sciences. It has been argued that all the objects of empirical sciences can be fully analyzed in structural terms but that consciousness is (or has) something over and above its structure. However, modern neuroscience has introduced a theoretical framework in which also the apparently non-structural aspects of consciousness, namely the so called qualia or qualitative properties, can be analyzed in structural terms. That framework allows us to see qualia as something compositional with internal structures that fully determine their qualitative nature. Moreover, those internal structures can be identified which certain neural patterns. Thus consciousness as a whole can be seen as a complex neural pattern that misperceives some of its own highly complex structural properties as monadic and qualitative. Such neural pattern is analyzable in fully structural terms and thereby the hard problem is solved.

  10. Structural qualia: a solution to the hard problem of consciousness

    PubMed Central

    Loorits, Kristjan

    2014-01-01

    The hard problem of consciousness has been often claimed to be unsolvable by the methods of traditional empirical sciences. It has been argued that all the objects of empirical sciences can be fully analyzed in structural terms but that consciousness is (or has) something over and above its structure. However, modern neuroscience has introduced a theoretical framework in which also the apparently non-structural aspects of consciousness, namely the so called qualia or qualitative properties, can be analyzed in structural terms. That framework allows us to see qualia as something compositional with internal structures that fully determine their qualitative nature. Moreover, those internal structures can be identified which certain neural patterns. Thus consciousness as a whole can be seen as a complex neural pattern that misperceives some of its own highly complex structural properties as monadic and qualitative. Such neural pattern is analyzable in fully structural terms and thereby the hard problem is solved. PMID:24672510

  11. A Problem on Optimal Transportation

    ERIC Educational Resources Information Center

    Cechlarova, Katarina

    2005-01-01

    Mathematical optimization problems are not typical in the classical curriculum of mathematics. In this paper we show how several generalizations of an easy problem on optimal transportation were solved by gifted secondary school pupils in a correspondence mathematical seminar, how they can be used in university courses of linear programming and…

  12. The "Hard Problem" and the Quantum Physicists. Part 1: The First Generation

    ERIC Educational Resources Information Center

    Smith, C. U. M.

    2006-01-01

    All four of the most important figures in the early twentieth-century development of quantum physics--Niels Bohr, Erwin Schroedinger, Werner Heisenberg and Wolfgang Pauli--had strong interests in the traditional mind--brain, or "hard," problem. This paper reviews their approach to this problem, showing the influence of Bohr's complementarity…

  13. On the Parameterized Complexity of Some Optimization Problems Related to Multiple-Interval Graphs

    NASA Astrophysics Data System (ADS)

    Jiang, Minghui

    We show that for any constant t ≥ 2, K -Independent Set and K-Dominating Set in t-track interval graphs are W[1]-hard. This settles an open question recently raised by Fellows, Hermelin, Rosamond, and Vialette. We also give an FPT algorithm for K-Clique in t-interval graphs, parameterized by both k and t, with running time max { t O(k), 2 O(klogk) } ·poly(n), where n is the number of vertices in the graph. This slightly improves the previous FPT algorithm by Fellows, Hermelin, Rosamond, and Vialette. Finally, we use the W[1]-hardness of K-Independent Set in t-track interval graphs to obtain the first parameterized intractability result for a recent bioinformatics problem called Maximal Strip Recovery (MSR). We show that MSR-d is W[1]-hard for any constant d ≥ 4 when the parameter is either the total length of the strips, or the total number of adjacencies in the strips, or the number of strips in the optimal solution.

  14. Optimization of Smart Structure for Improving Servo Performance of Hard Disk Drive

    NASA Astrophysics Data System (ADS)

    Kajiwara, Itsuro; Takahashi, Masafumi; Arisaka, Toshihiro

    Head positioning accuracy of the hard disk drive should be improved to meet today's increasing performance demands. Vibration suppression of the arm in the hard disk drive is very important to enhance the servo bandwidth of the head positioning system. In this study, smart structure technology is introduced into the hard disk drive to suppress the vibration of the head actuator. It has been expected that the smart structure technology will contribute to the development of small and light-weight mechatronics devices with the required performance. First, modeling of the system is conducted with finite element method and modal analysis. Next, the actuator location and the control system are simultaneously optimized using genetic algorithm. Vibration control effect with the proposed vibration control mechanisms has been evaluated by some simulations.

  15. Binary Bees Algorithm - bioinspiration from the foraging mechanism of honeybees to optimize a multiobjective multidimensional assignment problem

    NASA Astrophysics Data System (ADS)

    Xu, Shuo; Ji, Ze; Truong Pham, Duc; Yu, Fan

    2011-11-01

    The simultaneous mission assignment and home allocation for hospital service robots studied is a Multidimensional Assignment Problem (MAP) with multiobjectives and multiconstraints. A population-based metaheuristic, the Binary Bees Algorithm (BBA), is proposed to optimize this NP-hard problem. Inspired by the foraging mechanism of honeybees, the BBA's most important feature is an explicit functional partitioning between global search and local search for exploration and exploitation, respectively. Its key parts consist of adaptive global search, three-step elitism selection (constraint handling, non-dominated solutions selection, and diversity preservation), and elites-centred local search within a Hamming neighbourhood. Two comparative experiments were conducted to investigate its single objective optimization, optimization effectiveness (indexed by the S-metric and C-metric) and optimization efficiency (indexed by computational burden and CPU time) in detail. The BBA outperformed its competitors in almost all the quantitative indices. Hence, the above overall scheme, and particularly the searching history-adapted global search strategy was validated.

  16. 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

  17. On the Hardness of Subset Sum Problem from Different Intervals

    NASA Astrophysics Data System (ADS)

    Kogure, Jun; Kunihiro, Noboru; Yamamoto, Hirosuke

    The subset sum problem, which is often called as the knapsack problem, is known as an NP-hard problem, and there are several cryptosystems based on the problem. Assuming an oracle for shortest vector problem of lattice, the low-density attack algorithm by Lagarias and Odlyzko and its variants solve the subset sum problem efficiently, when the “density” of the given problem is smaller than some threshold. When we define the density in the context of knapsack-type cryptosystems, weights are usually assumed to be chosen uniformly at random from the same interval. In this paper, we focus on general subset sum problems, where this assumption may not hold. We assume that weights are chosen from different intervals, and make analysis of the effect on the success probability of above algorithms both theoretically and experimentally. Possible application of our result in the context of knapsack cryptosystems is the security analysis when we reduce the data size of public keys.

  18. Problem Solving through an Optimization Problem in Geometry

    ERIC Educational Resources Information Center

    Poon, Kin Keung; Wong, Hang-Chi

    2011-01-01

    This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect…

  19. An evolutionary strategy based on partial imitation for solving optimization problems

    NASA Astrophysics Data System (ADS)

    Javarone, Marco Alberto

    2016-12-01

    In this work we introduce an evolutionary strategy to solve combinatorial optimization tasks, i.e. problems characterized by a discrete search space. In particular, we focus on the Traveling Salesman Problem (TSP), i.e. a famous problem whose search space grows exponentially, increasing the number of cities, up to becoming NP-hard. The solutions of the TSP can be codified by arrays of cities, and can be evaluated by fitness, computed according to a cost function (e.g. the length of a path). Our method is based on the evolution of an agent population by means of an imitative mechanism, we define 'partial imitation'. In particular, agents receive a random solution and then, interacting among themselves, may imitate the solutions of agents with a higher fitness. Since the imitation mechanism is only partial, agents copy only one entry (randomly chosen) of another array (i.e. solution). In doing so, the population converges towards a shared solution, behaving like a spin system undergoing a cooling process, i.e. driven towards an ordered phase. We highlight that the adopted 'partial imitation' mechanism allows the population to generate solutions over time, before reaching the final equilibrium. Results of numerical simulations show that our method is able to find, in a finite time, both optimal and suboptimal solutions, depending on the size of the considered search space.

  20. Improved understanding of the searching behavior of ant colony optimization algorithms applied to the water distribution design problem

    NASA Astrophysics Data System (ADS)

    Zecchin, A. C.; Simpson, A. R.; Maier, H. R.; Marchi, A.; Nixon, J. B.

    2012-09-01

    Evolutionary algorithms (EAs) have been applied successfully to many water resource problems, such as system design, management decision formulation, and model calibration. The performance of an EA with respect to a particular problem type is dependent on how effectively its internal operators balance the exploitation/exploration trade-off to iteratively find solutions of an increasing quality. For a given problem, different algorithms are observed to produce a variety of different final performances, but there have been surprisingly few investigations into characterizing how the different internal mechanisms alter the algorithm's searching behavior, in both the objective and decision space, to arrive at this final performance. This paper presents metrics for analyzing the searching behavior of ant colony optimization algorithms, a particular type of EA, for the optimal water distribution system design problem, which is a classical NP-hard problem in civil engineering. Using the proposed metrics, behavior is characterized in terms of three different attributes: (1) the effectiveness of the search in improving its solution quality and entering into optimal or near-optimal regions of the search space, (2) the extent to which the algorithm explores as it converges to solutions, and (3) the searching behavior with respect to the feasible and infeasible regions. A range of case studies is considered, where a number of ant colony optimization variants are applied to a selection of water distribution system optimization problems. The results demonstrate the utility of the proposed metrics to give greater insight into how the internal operators affect each algorithm's searching behavior.

  1. Unraveling Quantum Annealers using Classical Hardness

    PubMed Central

    Martin-Mayor, Victor; Hen, Itay

    2015-01-01

    Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealing optimizers that contain hundreds of quantum bits. These optimizers, commonly referred to as ‘D-Wave’ chips, promise to solve practical optimization problems potentially faster than conventional ‘classical’ computers. Attempts to quantify the quantum nature of these chips have been met with both excitement and skepticism but have also brought up numerous fundamental questions pertaining to the distinguishability of experimental quantum annealers from their classical thermal counterparts. Inspired by recent results in spin-glass theory that recognize ‘temperature chaos’ as the underlying mechanism responsible for the computational intractability of hard optimization problems, we devise a general method to quantify the performance of quantum annealers on optimization problems suffering from varying degrees of temperature chaos: A superior performance of quantum annealers over classical algorithms on these may allude to the role that quantum effects play in providing speedup. We utilize our method to experimentally study the D-Wave Two chip on different temperature-chaotic problems and find, surprisingly, that its performance scales unfavorably as compared to several analogous classical algorithms. We detect, quantify and discuss several purely classical effects that possibly mask the quantum behavior of the chip. PMID:26483257

  2. A Mathematical Optimization Problem in Bioinformatics

    ERIC Educational Resources Information Center

    Heyer, Laurie J.

    2008-01-01

    This article describes the sequence alignment problem in bioinformatics. Through examples, we formulate sequence alignment as an optimization problem and show how to compute the optimal alignment with dynamic programming. The examples and sample exercises have been used by the author in a specialized course in bioinformatics, but could be adapted…

  3. Optimizing a realistic large-scale frequency assignment problem using a new parallel evolutionary approach

    NASA Astrophysics Data System (ADS)

    Chaves-González, José M.; Vega-Rodríguez, Miguel A.; Gómez-Pulido, Juan A.; Sánchez-Pérez, Juan M.

    2011-08-01

    This article analyses the use of a novel parallel evolutionary strategy to solve complex optimization problems. The work developed here has been focused on a relevant real-world problem from the telecommunication domain to verify the effectiveness of the approach. The problem, known as frequency assignment problem (FAP), basically consists of assigning a very small number of frequencies to a very large set of transceivers used in a cellular phone network. Real data FAP instances are very difficult to solve due to the NP-hard nature of the problem, therefore using an efficient parallel approach which makes the most of different evolutionary strategies can be considered as a good way to obtain high-quality solutions in short periods of time. Specifically, a parallel hyper-heuristic based on several meta-heuristics has been developed. After a complete experimental evaluation, results prove that the proposed approach obtains very high-quality solutions for the FAP and beats any other result published.

  4. Graphical models for optimal power flow

    DOE PAGES

    Dvijotham, Krishnamurthy; Chertkov, Michael; Van Hentenryck, Pascal; ...

    2016-09-13

    Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In this paper, we formulate the optimal power flow problem over tree networks as an inference problem over a tree-structured graphical model where the nodal variables are low-dimensional vectors. We adapt the standard dynamic programming algorithm for inference over a tree-structured graphical model to the OPF problem. Combining this with an interval discretization of the nodal variables, we develop an approximation algorithmmore » for the OPF problem. Further, we use techniques from constraint programming (CP) to perform interval computations and adaptive bound propagation to obtain practically efficient algorithms. Compared to previous algorithms that solve OPF with optimality guarantees using convex relaxations, our approach is able to work for arbitrary tree-structured distribution networks and handle mixed-integer optimization problems. Further, it can be implemented in a distributed message-passing fashion that is scalable and is suitable for “smart grid” applications like control of distributed energy resources. In conclusion, numerical evaluations on several benchmark networks show that practical OPF problems can be solved effectively using this approach.« less

  5. Performance of Grey Wolf Optimizer on large scale problems

    NASA Astrophysics Data System (ADS)

    Gupta, Shubham; Deep, Kusum

    2017-01-01

    For solving nonlinear continuous problems of optimization numerous nature inspired optimization techniques are being proposed in literature which can be implemented to solve real life problems wherein the conventional techniques cannot be applied. Grey Wolf Optimizer is one of such technique which is gaining popularity since the last two years. The objective of this paper is to investigate the performance of Grey Wolf Optimization Algorithm on large scale optimization problems. The Algorithm is implemented on 5 common scalable problems appearing in literature namely Sphere, Rosenbrock, Rastrigin, Ackley and Griewank Functions. The dimensions of these problems are varied from 50 to 1000. The results indicate that Grey Wolf Optimizer is a powerful nature inspired Optimization Algorithm for large scale problems, except Rosenbrock which is a unimodal function.

  6. Target: Alcohol Abuse in the Hard-to-Reach Work Force. Ideas and Resources for Responding to Problems of the Hard-to-Reach Work Force.

    ERIC Educational Resources Information Center

    Informatics, Inc., Rockville, MD.

    This guide is designed as a source of ideas and information for individuals and organizations interested in occupational alcoholism programs for the hard-to-reach work force. Following a brief overview of the problem and a report on progress in occupational alcoholism programming, a working definition of the hard-to-reach work force is offered;…

  7. A new chaotic multi-verse optimization algorithm for solving engineering optimization problems

    NASA Astrophysics Data System (ADS)

    Sayed, Gehad Ismail; Darwish, Ashraf; Hassanien, Aboul Ella

    2018-03-01

    Multi-verse optimization algorithm (MVO) is one of the recent meta-heuristic optimization algorithms. The main inspiration of this algorithm came from multi-verse theory in physics. However, MVO like most optimization algorithms suffers from low convergence rate and entrapment in local optima. In this paper, a new chaotic multi-verse optimization algorithm (CMVO) is proposed to overcome these problems. The proposed CMVO is applied on 13 benchmark functions and 7 well-known design problems in the engineering and mechanical field; namely, three-bar trust, speed reduce design, pressure vessel problem, spring design, welded beam, rolling element-bearing and multiple disc clutch brake. In the current study, a modified feasible-based mechanism is employed to handle constraints. In this mechanism, four rules were used to handle the specific constraint problem through maintaining a balance between feasible and infeasible solutions. Moreover, 10 well-known chaotic maps are used to improve the performance of MVO. The experimental results showed that CMVO outperforms other meta-heuristic optimization algorithms on most of the optimization problems. Also, the results reveal that sine chaotic map is the most appropriate map to significantly boost MVO's performance.

  8. Socio-Emotional Problems Experienced by Deaf and Hard of Hearing Students in Ethiopia

    ERIC Educational Resources Information Center

    Mekonnen, Mulat; Hannu, Savolainen; Elina, Lehtomäki; Matti, Kuorelahti

    2015-01-01

    This study compares the socio-emotional problems experienced by deaf and hard of hearing (DHH) students with those of hearing students in Ethiopia. The research involved a sample of 103 grade 4 students attending a special school for the deaf, a special class for the deaf and a regular school. Socio-emotional problems were measured using Goodman's…

  9. A hybrid binary particle swarm optimization for large capacitated multi item multi level lot sizing (CMIMLLS) problem

    NASA Astrophysics Data System (ADS)

    Mishra, S. K.; Sahithi, V. V. D.; Rao, C. S. P.

    2016-09-01

    The lot sizing problem deals with finding optimal order quantities which minimizes the ordering and holding cost of product mix. when multiple items at multiple levels with all capacity restrictions are considered, the lot sizing problem become NP hard. Many heuristics were developed in the past have inevitably failed due to size, computational complexity and time. However the authors were successful in the development of PSO based technique namely iterative improvement binary particles swarm technique to address very large capacitated multi-item multi level lot sizing (CMIMLLS) problem. First binary particle Swarm Optimization algorithm is used to find a solution in a reasonable time and iterative improvement local search mechanism is employed to improvise the solution obtained by BPSO algorithm. This hybrid mechanism of using local search on the global solution is found to improve the quality of solutions with respect to time thus IIBPSO method is found best and show excellent results.

  10. Parameterized Complexity of k-Anonymity: Hardness and Tractability

    NASA Astrophysics Data System (ADS)

    Bonizzoni, Paola; Della Vedova, Gianluca; Dondi, Riccardo; Pirola, Yuri

    The problem of publishing personal data without giving up privacy is becoming increasingly important. A precise formalization that has been recently proposed is the k-anonymity, where the rows of a table are partitioned in clusters of size at least k and all rows in a cluster become the same tuple after the suppression of some entries. The natural optimization problem, where the goal is to minimize the number of suppressed entries, is hard even when the stored values are over a binary alphabet or the table consists of a bounded number of columns. In this paper we study how the complexity of the problem is influenced by different parameters. First we show that the problem is W[1]-hard when parameterized by the value of the solution (and k). Then we exhibit a fixed-parameter algorithm when the problem is parameterized by the number of columns and the number of different values in any column.

  11. Solving optimization problems on computational grids.

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

    Wright, S. J.; Mathematics and Computer Science

    2001-05-01

    Multiprocessor computing platforms, which have become more and more widely available since the mid-1980s, are now heavily used by organizations that need to solve very demanding computational problems. Parallel computing is now central to the culture of many research communities. Novel parallel approaches were developed for global optimization, network optimization, and direct-search methods for nonlinear optimization. Activity was particularly widespread in parallel branch-and-bound approaches for various problems in combinatorial and network optimization. As the cost of personal computers and low-end workstations has continued to fall, while the speed and capacity of processors and networks have increased dramatically, 'cluster' platforms havemore » become popular in many settings. A somewhat different type of parallel computing platform know as a computational grid (alternatively, metacomputer) has arisen in comparatively recent times. Broadly speaking, this term refers not to a multiprocessor with identical processing nodes but rather to a heterogeneous collection of devices that are widely distributed, possibly around the globe. The advantage of such platforms is obvious: they have the potential to deliver enormous computing power. Just as obviously, however, the complexity of grids makes them very difficult to use. The Condor team, headed by Miron Livny at the University of Wisconsin, were among the pioneers in providing infrastructure for grid computations. More recently, the Globus project has developed technologies to support computations on geographically distributed platforms consisting of high-end computers, storage and visualization devices, and other scientific instruments. In 1997, we started the metaneos project as a collaborative effort between optimization specialists and the Condor and Globus groups. Our aim was to address complex, difficult optimization problems in several areas, designing and implementing the algorithms and the software

  12. Comparison of Optimal Design Methods in Inverse Problems

    PubMed Central

    Banks, H. T.; Holm, Kathleen; Kappel, Franz

    2011-01-01

    Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher Information Matrix (FIM). A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criteria with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model [13], the standard harmonic oscillator model [13] and a popular glucose regulation model [16, 19, 29]. PMID:21857762

  13. Optimality conditions for the numerical solution of optimization problems with PDE constraints :

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

    Aguilo Valentin, Miguel Alejandro; Ridzal, Denis

    2014-03-01

    A theoretical framework for the numerical solution of partial di erential equation (PDE) constrained optimization problems is presented in this report. This theoretical framework embodies the fundamental infrastructure required to e ciently implement and solve this class of problems. Detail derivations of the optimality conditions required to accurately solve several parameter identi cation and optimal control problems are also provided in this report. This will allow the reader to further understand how the theoretical abstraction presented in this report translates to the application.

  14. Some insights on hard quadratic assignment problem instances

    NASA Astrophysics Data System (ADS)

    Hussin, Mohamed Saifullah

    2017-11-01

    Since the formal introduction of metaheuristics, a huge number Quadratic Assignment Problem (QAP) instances have been introduced. Those instances however are loosely-structured, and therefore made it difficult to perform any systematic analysis. The QAPLIB for example, is a library that contains a huge number of QAP benchmark instances that consists of instances with different size and structure, but with a very limited availability for every instance type. This prevents researchers from performing organized study on those instances, such as parameter tuning and testing. In this paper, we will discuss several hard instances that have been introduced over the years, and algorithms that have been used for solving them.

  15. Supervised learning from human performance at the computationally hard problem of optimal traffic signal control on a network of junctions

    PubMed Central

    Box, Simon

    2014-01-01

    Optimal switching of traffic lights on a network of junctions is a computationally intractable problem. In this research, road traffic networks containing signallized junctions are simulated. A computer game interface is used to enable a human ‘player’ to control the traffic light settings on the junctions within the simulation. A supervised learning approach, based on simple neural network classifiers can be used to capture human player's strategies in the game and thus develop a human-trained machine control (HuTMaC) system that approaches human levels of performance. Experiments conducted within the simulation compare the performance of HuTMaC to two well-established traffic-responsive control systems that are widely deployed in the developed world and also to a temporal difference learning-based control method. In all experiments, HuTMaC outperforms the other control methods in terms of average delay and variance over delay. The conclusion is that these results add weight to the suggestion that HuTMaC may be a viable alternative, or supplemental method, to approximate optimization for some practical engineering control problems where the optimal strategy is computationally intractable. PMID:26064570

  16. Supervised learning from human performance at the computationally hard problem of optimal traffic signal control on a network of junctions.

    PubMed

    Box, Simon

    2014-12-01

    Optimal switching of traffic lights on a network of junctions is a computationally intractable problem. In this research, road traffic networks containing signallized junctions are simulated. A computer game interface is used to enable a human 'player' to control the traffic light settings on the junctions within the simulation. A supervised learning approach, based on simple neural network classifiers can be used to capture human player's strategies in the game and thus develop a human-trained machine control (HuTMaC) system that approaches human levels of performance. Experiments conducted within the simulation compare the performance of HuTMaC to two well-established traffic-responsive control systems that are widely deployed in the developed world and also to a temporal difference learning-based control method. In all experiments, HuTMaC outperforms the other control methods in terms of average delay and variance over delay. The conclusion is that these results add weight to the suggestion that HuTMaC may be a viable alternative, or supplemental method, to approximate optimization for some practical engineering control problems where the optimal strategy is computationally intractable.

  17. The "Hard Problem" and the Quantum Physicists. Part 2: Modern Times

    ERIC Educational Resources Information Center

    Smith, C. U. M.

    2009-01-01

    This is the second part of a review of the work of quantum physicists on the "hard part" of the problem of mind. After an introduction which sets the scene and a brief review of contemporary work on the neural correlates of consciousness (NCC) the work of four prominent modern investigators is examined: J.C. Eccles/Friedrich Beck; Henry Stapp;…

  18. Comparative Assessment of Cutting Inserts and Optimization during Hard Turning: Taguchi-Based Grey Relational Analysis

    NASA Astrophysics Data System (ADS)

    Venkata Subbaiah, K.; Raju, Ch.; Suresh, Ch.

    2017-08-01

    The present study aims to compare the conventional cutting inserts with wiper cutting inserts during the hard turning of AISI 4340 steel at different workpiece hardness. Type of insert, hardness, cutting speed, feed, and depth of cut are taken as process parameters. Taguchi’s L18 orthogonal array was used to conduct the experimental tests. Parametric analysis carried in order to know the influence of each process parameter on the three important Surface Roughness Characteristics (Ra, Rz, and Rt) and Material Removal Rate. Taguchi based Grey Relational Analysis (GRA) used to optimize the process parameters for individual response and multi-response outputs. Additionally, the analysis of variance (ANOVA) is also applied to identify the most significant factor.

  19. Improved teaching-learning-based and JAYA optimization algorithms for solving flexible flow shop scheduling problems

    NASA Astrophysics Data System (ADS)

    Buddala, Raviteja; Mahapatra, Siba Sankar

    2017-11-01

    Flexible flow shop (or a hybrid flow shop) scheduling problem is an extension of classical flow shop scheduling problem. In a simple flow shop configuration, a job having `g' operations is performed on `g' operation centres (stages) with each stage having only one machine. If any stage contains more than one machine for providing alternate processing facility, then the problem becomes a flexible flow shop problem (FFSP). FFSP which contains all the complexities involved in a simple flow shop and parallel machine scheduling problems is a well-known NP-hard (Non-deterministic polynomial time) problem. Owing to high computational complexity involved in solving these problems, it is not always possible to obtain an optimal solution in a reasonable computation time. To obtain near-optimal solutions in a reasonable computation time, a large variety of meta-heuristics have been proposed in the past. However, tuning algorithm-specific parameters for solving FFSP is rather tricky and time consuming. To address this limitation, teaching-learning-based optimization (TLBO) and JAYA algorithm are chosen for the study because these are not only recent meta-heuristics but they do not require tuning of algorithm-specific parameters. Although these algorithms seem to be elegant, they lose solution diversity after few iterations and get trapped at the local optima. To alleviate such drawback, a new local search procedure is proposed in this paper to improve the solution quality. Further, mutation strategy (inspired from genetic algorithm) is incorporated in the basic algorithm to maintain solution diversity in the population. Computational experiments have been conducted on standard benchmark problems to calculate makespan and computational time. It is found that the rate of convergence of TLBO is superior to JAYA. From the results, it is found that TLBO and JAYA outperform many algorithms reported in the literature and can be treated as efficient methods for solving the FFSP.

  20. Quadratic constrained mixed discrete optimization with an adiabatic quantum optimizer

    NASA Astrophysics Data System (ADS)

    Chandra, Rishabh; Jacobson, N. Tobias; Moussa, Jonathan E.; Frankel, Steven H.; Kais, Sabre

    2014-07-01

    We extend the family of problems that may be implemented on an adiabatic quantum optimizer (AQO). When a quadratic optimization problem has at least one set of discrete controls and the constraints are linear, we call this a quadratic constrained mixed discrete optimization (QCMDO) problem. QCMDO problems are NP-hard, and no efficient classical algorithm for their solution is known. Included in the class of QCMDO problems are combinatorial optimization problems constrained by a linear partial differential equation (PDE) or system of linear PDEs. An essential complication commonly encountered in solving this type of problem is that the linear constraint may introduce many intermediate continuous variables into the optimization while the computational cost grows exponentially with problem size. We resolve this difficulty by developing a constructive mapping from QCMDO to quadratic unconstrained binary optimization (QUBO) such that the size of the QUBO problem depends only on the number of discrete control variables. With a suitable embedding, taking into account the physical constraints of the realizable coupling graph, the resulting QUBO problem can be implemented on an existing AQO. The mapping itself is efficient, scaling cubically with the number of continuous variables in the general case and linearly in the PDE case if an efficient preconditioner is available.

  1. A general optimality criteria algorithm for a class of engineering optimization problems

    NASA Astrophysics Data System (ADS)

    Belegundu, Ashok D.

    2015-05-01

    An optimality criteria (OC)-based algorithm for optimization of a general class of nonlinear programming (NLP) problems is presented. The algorithm is only applicable to problems where the objective and constraint functions satisfy certain monotonicity properties. For multiply constrained problems which satisfy these assumptions, the algorithm is attractive compared with existing NLP methods as well as prevalent OC methods, as the latter involve computationally expensive active set and step-size control strategies. The fixed point algorithm presented here is applicable not only to structural optimization problems but also to certain problems as occur in resource allocation and inventory models. Convergence aspects are discussed. The fixed point update or resizing formula is given physical significance, which brings out a strength and trim feature. The number of function evaluations remains independent of the number of variables, allowing the efficient solution of problems with large number of variables.

  2. 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.

  3. Representations in Problem Solving: A Case Study with Optimization Problems

    ERIC Educational Resources Information Center

    Villegas, Jose L.; Castro, Enrique; Gutierrez, Jose

    2009-01-01

    Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and…

  4. Learning With Mixed Hard/Soft Pointwise Constraints.

    PubMed

    Gnecco, Giorgio; Gori, Marco; Melacci, Stefano; Sanguineti, Marcello

    2015-09-01

    A learning paradigm is proposed and investigated, in which the classical framework of learning from examples is enhanced by the introduction of hard pointwise constraints, i.e., constraints imposed on a finite set of examples that cannot be violated. Such constraints arise, e.g., when requiring coherent decisions of classifiers acting on different views of the same pattern. The classical examples of supervised learning, which can be violated at the cost of some penalization (quantified by the choice of a suitable loss function) play the role of soft pointwise constraints. Constrained variational calculus is exploited to derive a representer theorem that provides a description of the functional structure of the optimal solution to the proposed learning paradigm. It is shown that such an optimal solution can be represented in terms of a set of support constraints, which generalize the concept of support vectors and open the doors to a novel learning paradigm, called support constraint machines. The general theory is applied to derive the representation of the optimal solution to the problem of learning from hard linear pointwise constraints combined with soft pointwise constraints induced by supervised examples. In some cases, closed-form optimal solutions are obtained.

  5. Direct Multiple Shooting Optimization with Variable Problem Parameters

    NASA Technical Reports Server (NTRS)

    Whitley, Ryan J.; Ocampo, Cesar A.

    2009-01-01

    Taking advantage of a novel approach to the design of the orbital transfer optimization problem and advanced non-linear programming algorithms, several optimal transfer trajectories are found for problems with and without known analytic solutions. This method treats the fixed known gravitational constants as optimization variables in order to reduce the need for an advanced initial guess. Complex periodic orbits are targeted with very simple guesses and the ability to find optimal transfers in spite of these bad guesses is successfully demonstrated. Impulsive transfers are considered for orbits in both the 2-body frame as well as the circular restricted three-body problem (CRTBP). The results with this new approach demonstrate the potential for increasing robustness for all types of orbit transfer problems.

  6. LDRD Final Report: Global Optimization for Engineering Science Problems

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

    HART,WILLIAM E.

    1999-12-01

    For a wide variety of scientific and engineering problems the desired solution corresponds to an optimal set of objective function parameters, where the objective function measures a solution's quality. The main goal of the LDRD ''Global Optimization for Engineering Science Problems'' was the development of new robust and efficient optimization algorithms that can be used to find globally optimal solutions to complex optimization problems. This SAND report summarizes the technical accomplishments of this LDRD, discusses lessons learned and describes open research issues.

  7. Exact solution for an optimal impermeable parachute problem

    NASA Astrophysics Data System (ADS)

    Lupu, Mircea; Scheiber, Ernest

    2002-10-01

    In the paper there are solved direct and inverse boundary problems and analytical solutions are obtained for optimization problems in the case of some nonlinear integral operators. It is modeled the plane potential flow of an inviscid, incompressible and nonlimited fluid jet, witch encounters a symmetrical, curvilinear obstacle--the deflector of maximal drag. There are derived integral singular equations, for direct and inverse problems and the movement in the auxiliary canonical half-plane is obtained. Next, the optimization problem is solved in an analytical manner. The design of the optimal airfoil is performed and finally, numerical computations concerning the drag coefficient and other geometrical and aerodynamical parameters are carried out. This model corresponds to the Helmholtz impermeable parachute problem.

  8. An Optimal Static Scheduling Algorithm for Hard Real-Time Systems Specified in a Prototyping Language

    DTIC Science & Technology

    1989-12-01

    to construct because the mechanism is a dispatching procedure. Since all nonpreemptive schedules are contained in the set of all preemptive schedules...the optimal value of T’.. in the preemptive case is at least a lower bound on the optimal T., for the nonpreemptive schedules. This principle is the...adapt to changes in the enviro.nment. In hard real-time systems, tasks are also distinguished as preemptable and nonpreemptable . A task is preemptable

  9. Analog Processor To Solve Optimization Problems

    NASA Technical Reports Server (NTRS)

    Duong, Tuan A.; Eberhardt, Silvio P.; Thakoor, Anil P.

    1993-01-01

    Proposed analog processor solves "traveling-salesman" problem, considered paradigm of global-optimization problems involving routing or allocation of resources. Includes electronic neural network and auxiliary circuitry based partly on concepts described in "Neural-Network Processor Would Allocate Resources" (NPO-17781) and "Neural Network Solves 'Traveling-Salesman' Problem" (NPO-17807). Processor based on highly parallel computing solves problem in significantly less time.

  10. FRANOPP: Framework for analysis and optimization problems user's guide

    NASA Technical Reports Server (NTRS)

    Riley, K. M.

    1981-01-01

    Framework for analysis and optimization problems (FRANOPP) is a software aid for the study and solution of design (optimization) problems which provides the driving program and plotting capability for a user generated programming system. In addition to FRANOPP, the programming system also contains the optimization code CONMIN, and two user supplied codes, one for analysis and one for output. With FRANOPP the user is provided with five options for studying a design problem. Three of the options utilize the plot capability and present an indepth study of the design problem. The study can be focused on a history of the optimization process or on the interaction of variables within the design problem.

  11. Weak Hamiltonian finite element method for optimal control problems

    NASA Technical Reports Server (NTRS)

    Hodges, Dewey H.; Bless, Robert R.

    1991-01-01

    A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

  12. The 'hard problem' and the quantum physicists. Part 1: the first generation.

    PubMed

    Smith, C U M

    2006-07-01

    All four of the most important figures in the early twentieth-century development of quantum physics-Niels Bohr, Erwin Schroedinger, Werner Heisenberg and Wolfgang Pauli-had strong interests in the traditional mind-brain, or 'hard,' problem. This paper reviews their approach to this problem, showing the influence of Bohr's complementarity thesis, the significance of Schroedinger's small book, 'What is life?,' the updated Platonism of Heisenberg and, perhaps most interesting of all, the interaction of Carl Jung and Wolfgang Pauli in the latter's search for a unification of mind and matter.

  13. Finding Minimal Addition Chains with a Particle Swarm Optimization Algorithm

    NASA Astrophysics Data System (ADS)

    León-Javier, Alejandro; Cruz-Cortés, Nareli; Moreno-Armendáriz, Marco A.; Orantes-Jiménez, Sandra

    The addition chains with minimal length are the basic block to the optimal computation of finite field exponentiations. It has very important applications in the areas of error-correcting codes and cryptography. However, obtaining the shortest addition chains for a given exponent is a NP-hard problem. In this work we propose the adaptation of a Particle Swarm Optimization algorithm to deal with this problem. Our proposal is tested on several exponents whose addition chains are considered hard to find. We obtained very promising results.

  14. The checkpoint ordering problem

    PubMed Central

    Hungerländer, P.

    2017-01-01

    Abstract We suggest a new variant of a row layout problem: Find an ordering of n departments with given lengths such that the total weighted sum of their distances to a given checkpoint is minimized. The Checkpoint Ordering Problem (COP) is both of theoretical and practical interest. It has several applications and is conceptually related to some well-studied combinatorial optimization problems, namely the Single-Row Facility Layout Problem, the Linear Ordering Problem and a variant of parallel machine scheduling. In this paper we study the complexity of the (COP) and its special cases. The general version of the (COP) with an arbitrary but fixed number of checkpoints is NP-hard in the weak sense. We propose both a dynamic programming algorithm and an integer linear programming approach for the (COP) . Our computational experiments indicate that the (COP) is hard to solve in practice. While the run time of the dynamic programming algorithm strongly depends on the length of the departments, the integer linear programming approach is able to solve instances with up to 25 departments to optimality. PMID:29170574

  15. Comparison of optimal design methods in inverse problems

    NASA Astrophysics Data System (ADS)

    Banks, H. T.; Holm, K.; Kappel, F.

    2011-07-01

    Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667-77 De Gaetano A and Arino O 2000 J. Math. Biol. 40 136-68 Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979-90).

  16. An Enhanced Memetic Algorithm for Single-Objective Bilevel Optimization Problems.

    PubMed

    Islam, Md Monjurul; Singh, Hemant Kumar; Ray, Tapabrata; Sinha, Ankur

    2017-01-01

    Bilevel optimization, as the name reflects, deals with optimization at two interconnected hierarchical levels. The aim is to identify the optimum of an upper-level  leader problem, subject to the optimality of a lower-level follower problem. Several problems from the domain of engineering, logistics, economics, and transportation have an inherent nested structure which requires them to be modeled as bilevel optimization problems. Increasing size and complexity of such problems has prompted active theoretical and practical interest in the design of efficient algorithms for bilevel optimization. Given the nested nature of bilevel problems, the computational effort (number of function evaluations) required to solve them is often quite high. In this article, we explore the use of a Memetic Algorithm (MA) to solve bilevel optimization problems. While MAs have been quite successful in solving single-level optimization problems, there have been relatively few studies exploring their potential for solving bilevel optimization problems. MAs essentially attempt to combine advantages of global and local search strategies to identify optimum solutions with low computational cost (function evaluations). The approach introduced in this article is a nested Bilevel Memetic Algorithm (BLMA). At both upper and lower levels, either a global or a local search method is used during different phases of the search. The performance of BLMA is presented on twenty-five standard test problems and two real-life applications. The results are compared with other established algorithms to demonstrate the efficacy of the proposed approach.

  17. Performance of Quantum Annealers on Hard Scheduling Problems

    NASA Astrophysics Data System (ADS)

    Pokharel, Bibek; Venturelli, Davide; Rieffel, Eleanor

    Quantum annealers have been employed to attack a variety of optimization problems. We compared the performance of the current D-Wave 2X quantum annealer to that of the previous generation D-Wave Two quantum annealer on scheduling-type planning problems. Further, we compared the effect of different anneal times, embeddings of the logical problem, and different settings of the ferromagnetic coupling JF across the logical vertex-model on the performance of the D-Wave 2X quantum annealer. Our results show that at the best settings, the scaling of expected anneal time to solution for D-WAVE 2X is better than that of the DWave Two, but still inferior to that of state of the art classical solvers on these problems. We discuss the implication of our results for the design and programming of future quantum annealers. Supported by NASA Ames Research Center.

  18. Probing for quantum speedup in spin-glass problems with planted solutions

    NASA Astrophysics Data System (ADS)

    Hen, Itay; Job, Joshua; Albash, Tameem; Rønnow, Troels F.; Troyer, Matthias; Lidar, Daniel A.

    2015-10-01

    The availability of quantum annealing devices with hundreds of qubits has made the experimental demonstration of a quantum speedup for optimization problems a coveted, albeit elusive goal. Going beyond earlier studies of random Ising problems, here we introduce a method to construct a set of frustrated Ising-model optimization problems with tunable hardness. We study the performance of a D-Wave Two device (DW2) with up to 503 qubits on these problems and compare it to a suite of classical algorithms, including a highly optimized algorithm designed to compete directly with the DW2. The problems are generated around predetermined ground-state configurations, called planted solutions, which makes them particularly suitable for benchmarking purposes. The problem set exhibits properties familiar from constraint satisfaction (SAT) problems, such as a peak in the typical hardness of the problems, determined by a tunable clause density parameter. We bound the hardness regime where the DW2 device either does not or might exhibit a quantum speedup for our problem set. While we do not find evidence for a speedup for the hardest and most frustrated problems in our problem set, we cannot rule out that a speedup might exist for some of the easier, less frustrated problems. Our empirical findings pertain to the specific D-Wave processor and problem set we studied and leave open the possibility that future processors might exhibit a quantum speedup on the same problem set.

  19. An impatient evolutionary algorithm with probabilistic tabu search for unified solution of some NP-hard problems in graph and set theory via clique finding.

    PubMed

    Guturu, Parthasarathy; Dantu, Ram

    2008-06-01

    Many graph- and set-theoretic problems, because of their tremendous application potential and theoretical appeal, have been well investigated by the researchers in complexity theory and were found to be NP-hard. Since the combinatorial complexity of these problems does not permit exhaustive searches for optimal solutions, only near-optimal solutions can be explored using either various problem-specific heuristic strategies or metaheuristic global-optimization methods, such as simulated annealing, genetic algorithms, etc. In this paper, we propose a unified evolutionary algorithm (EA) to the problems of maximum clique finding, maximum independent set, minimum vertex cover, subgraph and double subgraph isomorphism, set packing, set partitioning, and set cover. In the proposed approach, we first map these problems onto the maximum clique-finding problem (MCP), which is later solved using an evolutionary strategy. The proposed impatient EA with probabilistic tabu search (IEA-PTS) for the MCP integrates the best features of earlier successful approaches with a number of new heuristics that we developed to yield a performance that advances the state of the art in EAs for the exploration of the maximum cliques in a graph. Results of experimentation with the 37 DIMACS benchmark graphs and comparative analyses with six state-of-the-art algorithms, including two from the smaller EA community and four from the larger metaheuristics community, indicate that the IEA-PTS outperforms the EAs with respect to a Pareto-lexicographic ranking criterion and offers competitive performance on some graph instances when individually compared to the other heuristic algorithms. It has also successfully set a new benchmark on one graph instance. On another benchmark suite called Benchmarks with Hidden Optimal Solutions, IEA-PTS ranks second, after a very recent algorithm called COVER, among its peers that have experimented with this suite.

  20. Singular perturbation analysis of AOTV-related trajectory optimization problems

    NASA Technical Reports Server (NTRS)

    Calise, Anthony J.; Bae, Gyoung H.

    1990-01-01

    The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality

  1. Belief Propagation Algorithm for Portfolio Optimization Problems

    PubMed Central

    2015-01-01

    The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm. PMID:26305462

  2. Belief Propagation Algorithm for Portfolio Optimization Problems.

    PubMed

    Shinzato, Takashi; Yasuda, Muneki

    2015-01-01

    The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.

  3. Sensorless optimal sinusoidal brushless direct current for hard disk drives

    NASA Astrophysics Data System (ADS)

    Soh, C. S.; Bi, C.

    2009-04-01

    Initiated by the availability of digital signal processors and emergence of new applications, market demands for permanent magnet synchronous motors have been surging. As its back-emf is sinusoidal, the drive current should also be sinusoidal for reducing the torque ripple. However, in applications like hard disk drives, brushless direct current (BLDC) drive is adopted instead of sinusoidal drive for simplification. The adoption, however, comes at the expense of increased harmonics, losses, torque pulsations, and acoustics. In this paper, we propose a sensorless optimal sinusoidal BLDC drive. First and foremost, the derivation for an optimal sinusoidal drive is presented, and a power angle control scheme is proposed to achieve an optimal sinusoidal BLDC. The scheme maintains linear relationship between the motor speed and drive voltage. In an attempt to execute the sensorless drive, an innovative power angle measurement scheme is devised, which takes advantage of the freewheeling diodes and measures the power angle through the detection of diode voltage drops. The objectives as laid out will be presented and discussed in this paper, supported by derivations, simulations, and experimental results. The proposed scheme is straightforward, brings about the benefits of sensorless sinusoidal drive, negates the need for current sensors by utilizing the freewheeling diodes, and does not incur additional cost.

  4. A Cascade Optimization Strategy for Solution of Difficult Multidisciplinary Design Problems

    NASA Technical Reports Server (NTRS)

    Patnaik, Surya N.; Coroneos, Rula M.; Hopkins, Dale A.; Berke, Laszlo

    1996-01-01

    A research project to comparatively evaluate 10 nonlinear optimization algorithms was recently completed. A conclusion was that no single optimizer could successfully solve all 40 problems in the test bed, even though most optimizers successfully solved at least one-third of the problems. We realized that improved search directions and step lengths, available in the 10 optimizers compared, were not likely to alleviate the convergence difficulties. For the solution of those difficult problems we have devised an alternative approach called cascade optimization strategy. The cascade strategy uses several optimizers, one followed by another in a specified sequence, to solve a problem. A pseudorandom scheme perturbs design variables between the optimizers. The cascade strategy has been tested successfully in the design of supersonic and subsonic aircraft configurations and air-breathing engines for high-speed civil transport applications. These problems could not be successfully solved by an individual optimizer. The cascade optimization strategy, however, generated feasible optimum solutions for both aircraft and engine problems. This paper presents the cascade strategy and solutions to a number of these problems.

  5. Execution of Multidisciplinary Design Optimization Approaches on Common Test Problems

    NASA Technical Reports Server (NTRS)

    Balling, R. J.; Wilkinson, C. A.

    1997-01-01

    A class of synthetic problems for testing multidisciplinary design optimization (MDO) approaches is presented. These test problems are easy to reproduce because all functions are given as closed-form mathematical expressions. They are constructed in such a way that the optimal value of all variables and the objective is unity. The test problems involve three disciplines and allow the user to specify the number of design variables, state variables, coupling functions, design constraints, controlling design constraints, and the strength of coupling. Several MDO approaches were executed on two sample synthetic test problems. These approaches included single-level optimization approaches, collaborative optimization approaches, and concurrent subspace optimization approaches. Execution results are presented, and the robustness and efficiency of these approaches an evaluated for these sample problems.

  6. The optimization problems of CP operation

    NASA Astrophysics Data System (ADS)

    Kler, A. M.; Stepanova, E. L.; Maximov, A. S.

    2017-11-01

    The problem of enhancing energy and economic efficiency of CP is urgent indeed. One of the main methods for solving it is optimization of CP operation. To solve the optimization problems of CP operation, Energy Systems Institute, SB of RAS, has developed a software. The software makes it possible to make optimization calculations of CP operation. The software is based on the techniques and software tools of mathematical modeling and optimization of heat and power installations. Detailed mathematical models of new equipment have been developed in the work. They describe sufficiently accurately the processes that occur in the installations. The developed models include steam turbine models (based on the checking calculation) which take account of all steam turbine compartments and regeneration system. They also enable one to make calculations with regenerative heaters disconnected. The software for mathematical modeling of equipment and optimization of CP operation has been developed. It is based on the technique for optimization of CP operating conditions in the form of software tools and integrates them in the common user interface. The optimization of CP operation often generates the need to determine the minimum and maximum possible total useful electricity capacity of the plant at set heat loads of consumers, i.e. it is necessary to determine the interval on which the CP capacity may vary. The software has been applied to optimize the operating conditions of the Novo-Irkutskaya CP of JSC “Irkutskenergo”. The efficiency of operating condition optimization and the possibility for determination of CP energy characteristics that are necessary for optimization of power system operation are shown.

  7. The expanded invasive weed optimization metaheuristic for solving continuous and discrete optimization problems.

    PubMed

    Josiński, Henryk; Kostrzewa, Daniel; Michalczuk, Agnieszka; Switoński, Adam

    2014-01-01

    This paper introduces an expanded version of the Invasive Weed Optimization algorithm (exIWO) distinguished by the hybrid strategy of the search space exploration proposed by the authors. The algorithm is evaluated by solving three well-known optimization problems: minimization of numerical functions, feature selection, and the Mona Lisa TSP Challenge as one of the instances of the traveling salesman problem. The achieved results are compared with analogous outcomes produced by other optimization methods reported in the literature.

  8. Random Matrix Approach for Primal-Dual Portfolio Optimization Problems

    NASA Astrophysics Data System (ADS)

    Tada, Daichi; Yamamoto, Hisashi; Shinzato, Takashi

    2017-12-01

    In this paper, we revisit the portfolio optimization problems of the minimization/maximization of investment risk under constraints of budget and investment concentration (primal problem) and the maximization/minimization of investment concentration under constraints of budget and investment risk (dual problem) for the case that the variances of the return rates of the assets are identical. We analyze both optimization problems by the Lagrange multiplier method and the random matrix approach. Thereafter, we compare the results obtained from our proposed approach with the results obtained in previous work. Moreover, we use numerical experiments to validate the results obtained from the replica approach and the random matrix approach as methods for analyzing both the primal and dual portfolio optimization problems.

  9. Two combinatorial optimization problems for SNP discovery using base-specific cleavage and mass spectrometry.

    PubMed

    Chen, Xin; Wu, Qiong; Sun, Ruimin; Zhang, Louxin

    2012-01-01

    The discovery of single-nucleotide polymorphisms (SNPs) has important implications in a variety of genetic studies on human diseases and biological functions. One valuable approach proposed for SNP discovery is based on base-specific cleavage and mass spectrometry. However, it is still very challenging to achieve the full potential of this SNP discovery approach. In this study, we formulate two new combinatorial optimization problems. While both problems are aimed at reconstructing the sample sequence that would attain the minimum number of SNPs, they search over different candidate sequence spaces. The first problem, denoted as SNP - MSP, limits its search to sequences whose in silico predicted mass spectra have all their signals contained in the measured mass spectra. In contrast, the second problem, denoted as SNP - MSQ, limits its search to sequences whose in silico predicted mass spectra instead contain all the signals of the measured mass spectra. We present an exact dynamic programming algorithm for solving the SNP - MSP problem and also show that the SNP - MSQ problem is NP-hard by a reduction from a restricted variation of the 3-partition problem. We believe that an efficient solution to either problem above could offer a seamless integration of information in four complementary base-specific cleavage reactions, thereby improving the capability of the underlying biotechnology for sensitive and accurate SNP discovery.

  10. A weak Hamiltonian finite element method for optimal control problems

    NASA Technical Reports Server (NTRS)

    Hodges, Dewey H.; Bless, Robert R.

    1989-01-01

    A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

  11. A weak Hamiltonian finite element method for optimal control problems

    NASA Technical Reports Server (NTRS)

    Hodges, Dewey H.; Bless, Robert R.

    1990-01-01

    A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

  12. Optimal Price Decision Problem for Simultaneous Multi-article Auction and Its Optimal Price Searching Method by Particle Swarm Optimization

    NASA Astrophysics Data System (ADS)

    Masuda, Kazuaki; Aiyoshi, Eitaro

    We propose a method for solving optimal price decision problems for simultaneous multi-article auctions. An auction problem, originally formulated as a combinatorial problem, determines both every seller's whether or not to sell his/her article and every buyer's which article(s) to buy, so that the total utility of buyers and sellers will be maximized. Due to the duality theory, we transform it equivalently into a dual problem in which Lagrange multipliers are interpreted as articles' transaction price. As the dual problem is a continuous optimization problem with respect to the multipliers (i.e., the transaction prices), we propose a numerical method to solve it by applying heuristic global search methods. In this paper, Particle Swarm Optimization (PSO) is used to solve the dual problem, and experimental results are presented to show the validity of the proposed method.

  13. Robust optimization modelling with applications to industry and environmental problems

    NASA Astrophysics Data System (ADS)

    Chaerani, Diah; Dewanto, Stanley P.; Lesmana, Eman

    2017-10-01

    Robust Optimization (RO) modeling is one of the existing methodology for handling data uncertainty in optimization problem. The main challenge in this RO methodology is how and when we can reformulate the robust counterpart of uncertain problems as a computationally tractable optimization problem or at least approximate the robust counterpart by a tractable problem. Due to its definition the robust counterpart highly depends on how we choose the uncertainty set. As a consequence we can meet this challenge only if this set is chosen in a suitable way. The development on RO grows fast, since 2004, a new approach of RO called Adjustable Robust Optimization (ARO) is introduced to handle uncertain problems when the decision variables must be decided as a ”wait and see” decision variables. Different than the classic Robust Optimization (RO) that models decision variables as ”here and now”. In ARO, the uncertain problems can be considered as a multistage decision problem, thus decision variables involved are now become the wait and see decision variables. In this paper we present the applications of both RO and ARO. We present briefly all results to strengthen the importance of RO and ARO in many real life problems.

  14. Reply to "Comment on 'Calculations for the one-dimensional soft Coulomb problem and the hard Coulomb limit' ".

    PubMed

    Gebremedhin, Daniel H; Weatherford, Charles A

    2015-02-01

    This is a response to the comment we received on our recent paper "Calculations for the one-dimensional soft Coulomb problem and the hard Coulomb limit." In that paper, we introduced a computational algorithm that is appropriate for solving stiff initial value problems, and which we applied to the one-dimensional time-independent Schrödinger equation with a soft Coulomb potential. We solved for the eigenpairs using a shooting method and hence turned it into an initial value problem. In particular, we examined the behavior of the eigenpairs as the softening parameter approached zero (hard Coulomb limit). The commenters question the existence of the ground state of the hard Coulomb potential, which we inferred by extrapolation of the softening parameter to zero. A key distinction between the commenters' approach and ours is that they consider only the half-line while we considered the entire x axis. Based on mathematical considerations, the commenters consider only a vanishing solution function at the origin, and they question our conclusion that the ground state of the hard Coulomb potential exists. The ground state we inferred resembles a δ(x), and hence it cannot even be addressed based on their argument. For the excited states, there is agreement with the fact that the particle is always excluded from the origin. Our discussion with regard to the symmetry of the excited states is an extrapolation of the soft Coulomb case and is further explained herein.

  15. It looks easy! Heuristics for combinatorial optimization problems.

    PubMed

    Chronicle, Edward P; MacGregor, James N; Ormerod, Thomas C; Burr, Alistair

    2006-04-01

    Human performance on instances of computationally intractable optimization problems, such as the travelling salesperson problem (TSP), can be excellent. We have proposed a boundary-following heuristic to account for this finding. We report three experiments with TSPs where the capacity to employ this heuristic was varied. In Experiment 1, participants free to use the heuristic produced solutions significantly closer to optimal than did those prevented from doing so. Experiments 2 and 3 together replicated this finding in larger problems and demonstrated that a potential confound had no effect. In all three experiments, performance was closely matched by a boundary-following model. The results implicate global rather than purely local processes. Humans may have access to simple, perceptually based, heuristics that are suited to some combinatorial optimization tasks.

  16. Forecasting Electricity Prices in an Optimization Hydrothermal Problem

    NASA Astrophysics Data System (ADS)

    Matías, J. M.; Bayón, L.; Suárez, P.; Argüelles, A.; Taboada, J.

    2007-12-01

    This paper presents an economic dispatch algorithm in a hydrothermal system within the framework of a competitive and deregulated electricity market. The optimization problem of one firm is described, whose objective function can be defined as its profit maximization. Since next-day price forecasting is an aspect crucial, this paper proposes an efficient yet highly accurate next-day price new forecasting method using a functional time series approach trying to exploit the daily seasonal structure of the series of prices. For the optimization problem, an optimal control technique is applied and Pontryagin's theorem is employed.

  17. About an Optimal Visiting Problem

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

    Bagagiolo, Fabio, E-mail: bagagiol@science.unitn.it; Benetton, Michela

    In this paper we are concerned with the optimal control problem consisting in minimizing the time for reaching (visiting) a fixed number of target sets, in particular more than one target. Such a problem is of course reminiscent of the famous 'Traveling Salesman Problem' and brings all its computational difficulties. Our aim is to apply the dynamic programming technique in order to characterize the value function of the problem as the unique viscosity solution of a suitable Hamilton-Jacobi equation. We introduce some 'external' variables, one per target, which keep in memory whether the corresponding target is already visited or not,more » and we transform the visiting problem in a suitable Mayer problem. This fact allows us to overcome the lacking of the Dynamic Programming Principle for the originary problem. The external variables evolve with a hysteresis law and the Hamilton-Jacobi equation turns out to be discontinuous.« less

  18. Essays on variational approximation techniques for stochastic optimization problems

    NASA Astrophysics Data System (ADS)

    Deride Silva, Julio A.

    This dissertation presents five essays on approximation and modeling techniques, based on variational analysis, applied to stochastic optimization problems. It is divided into two parts, where the first is devoted to equilibrium problems and maxinf optimization, and the second corresponds to two essays in statistics and uncertainty modeling. Stochastic optimization lies at the core of this research as we were interested in relevant equilibrium applications that contain an uncertain component, and the design of a solution strategy. In addition, every stochastic optimization problem relies heavily on the underlying probability distribution that models the uncertainty. We studied these distributions, in particular, their design process and theoretical properties such as their convergence. Finally, the last aspect of stochastic optimization that we covered is the scenario creation problem, in which we described a procedure based on a probabilistic model to create scenarios for the applied problem of power estimation of renewable energies. In the first part, Equilibrium problems and maxinf optimization, we considered three Walrasian equilibrium problems: from economics, we studied a stochastic general equilibrium problem in a pure exchange economy, described in Chapter 3, and a stochastic general equilibrium with financial contracts, in Chapter 4; finally from engineering, we studied an infrastructure planning problem in Chapter 5. We stated these problems as belonging to the maxinf optimization class and, in each instance, we provided an approximation scheme based on the notion of lopsided convergence and non-concave duality. This strategy is the foundation of the augmented Walrasian algorithm, whose convergence is guaranteed by lopsided convergence, that was implemented computationally, obtaining numerical results for relevant examples. The second part, Essays about statistics and uncertainty modeling, contains two essays covering a convergence problem for a sequence

  19. Genetic algorithms for the vehicle routing problem

    NASA Astrophysics Data System (ADS)

    Volna, Eva

    2016-06-01

    The Vehicle Routing Problem (VRP) is one of the most challenging combinatorial optimization tasks. This problem consists in designing the optimal set of routes for fleet of vehicles in order to serve a given set of customers. Evolutionary algorithms are general iterative algorithms for combinatorial optimization. These algorithms have been found to be very effective and robust in solving numerous problems from a wide range of application domains. This problem is known to be NP-hard; hence many heuristic procedures for its solution have been suggested. For such problems it is often desirable to obtain approximate solutions, so they can be found fast enough and are sufficiently accurate for the purpose. In this paper we have performed an experimental study that indicates the suitable use of genetic algorithms for the vehicle routing problem.

  20. Music algorithm for imaging of a sound-hard arc in limited-view inverse scattering problem

    NASA Astrophysics Data System (ADS)

    Park, Won-Kwang

    2017-07-01

    MUltiple SIgnal Classification (MUSIC) algorithm for a non-iterative imaging of sound-hard arc in limited-view inverse scattering problem is considered. In order to discover mathematical structure of MUSIC, we derive a relationship between MUSIC and an infinite series of Bessel functions of integer order. This structure enables us to examine some properties of MUSIC in limited-view problem. Numerical simulations are performed to support the identified structure of MUSIC.

  1. Replica analysis for the duality of the portfolio optimization problem

    NASA Astrophysics Data System (ADS)

    Shinzato, Takashi

    2016-11-01

    In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we analyzed in a previous study, we herein consider a primal-dual problem in which the investment risk minimization problem with budget and expected return constraints is regarded as the primal problem, and the expected return maximization problem with budget and investment risk constraints is regarded as the dual problem. With respect to these optimal problems, we analyze a quenched disordered system involving both of these optimization problems using the approach developed in statistical mechanical informatics and confirm that both optimal portfolios can possess the primal-dual structure. Finally, the results of numerical simulations are shown to validate the effectiveness of the proposed method.

  2. Replica analysis for the duality of the portfolio optimization problem.

    PubMed

    Shinzato, Takashi

    2016-11-01

    In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we analyzed in a previous study, we herein consider a primal-dual problem in which the investment risk minimization problem with budget and expected return constraints is regarded as the primal problem, and the expected return maximization problem with budget and investment risk constraints is regarded as the dual problem. With respect to these optimal problems, we analyze a quenched disordered system involving both of these optimization problems using the approach developed in statistical mechanical informatics and confirm that both optimal portfolios can possess the primal-dual structure. Finally, the results of numerical simulations are shown to validate the effectiveness of the proposed method.

  3. A roadmap for optimal control: the right way to commute.

    PubMed

    Ross, I Michael

    2005-12-01

    Optimal control theory is the foundation for many problems in astrodynamics. Typical examples are trajectory design and optimization, relative motion control of distributed space systems and attitude steering. Many such problems in astrodynamics are solved by an alternative route of mathematical analysis and deep physical insight, in part because of the perception that an optimal control framework generates hard problems. Although this is indeed true of the Bellman and Pontryagin frameworks, the covector mapping principle provides a neoclassical approach that renders hard problems easy. That is, although the origins of this philosophy can be traced back to Bernoulli and Euler, it is essentially modern as a result of the strong linkage between approximation theory, set-valued analysis and computing technology. Motivated by the broad success of this approach, mission planners are now conceiving and demanding higher performance from space systems. This has resulted in new set of theoretical and computational problems. Recently, under the leadership of NASA-GRC, several workshops were held to address some of these problems. This paper outlines the theoretical issues stemming from practical problems in astrodynamics. Emphasis is placed on how it pertains to advanced mission design problems.

  4. Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem

    NASA Astrophysics Data System (ADS)

    Chen, Wei

    2015-07-01

    In this paper, we discuss the portfolio optimization problem with real-world constraints under the assumption that the returns of risky assets are fuzzy numbers. A new possibilistic mean-semiabsolute deviation model is proposed, in which transaction costs, cardinality and quantity constraints are considered. Due to such constraints the proposed model becomes a mixed integer nonlinear programming problem and traditional optimization methods fail to find the optimal solution efficiently. Thus, a modified artificial bee colony (MABC) algorithm is developed to solve the corresponding optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm.

  5. A novel comprehensive learning artificial bee colony optimizer for dynamic optimization biological problems.

    PubMed

    Su, Weixing; Chen, Hanning; Liu, Fang; Lin, Na; Jing, Shikai; Liang, Xiaodan; Liu, Wei

    2017-03-01

    There are many dynamic optimization problems in the real world, whose convergence and searching ability is cautiously desired, obviously different from static optimization cases. This requires an optimization algorithm adaptively seek the changing optima over dynamic environments, instead of only finding the global optimal solution in the static environment. This paper proposes a novel comprehensive learning artificial bee colony optimizer (CLABC) for optimization in dynamic environments problems, which employs a pool of optimal foraging strategies to balance the exploration and exploitation tradeoff. The main motive of CLABC is to enrich artificial bee foraging behaviors in the ABC model by combining Powell's pattern search method, life-cycle, and crossover-based social learning strategy. The proposed CLABC is a more bee-colony-realistic model that the bee can reproduce and die dynamically throughout the foraging process and population size varies as the algorithm runs. The experiments for evaluating CLABC are conducted on the dynamic moving peak benchmarks. Furthermore, the proposed algorithm is applied to a real-world application of dynamic RFID network optimization. Statistical analysis of all these cases highlights the significant performance improvement due to the beneficial combination and demonstrates the performance superiority of the proposed algorithm.

  6. On Evaluating Human Problem Solving of Computationally Hard Problems

    ERIC Educational Resources Information Center

    Carruthers, Sarah; Stege, Ulrike

    2013-01-01

    This article is concerned with how computer science, and more exactly computational complexity theory, can inform cognitive science. In particular, we suggest factors to be taken into account when investigating how people deal with computational hardness. This discussion will address the two upper levels of Marr's Level Theory: the computational…

  7. Exact solution for the optimal neuronal layout problem.

    PubMed

    Chklovskii, Dmitri B

    2004-10-01

    Evolution perfected brain design by maximizing its functionality while minimizing costs associated with building and maintaining it. Assumption that brain functionality is specified by neuronal connectivity, implemented by costly biological wiring, leads to the following optimal design problem. For a given neuronal connectivity, find a spatial layout of neurons that minimizes the wiring cost. Unfortunately, this problem is difficult to solve because the number of possible layouts is often astronomically large. We argue that the wiring cost may scale as wire length squared, reducing the optimal layout problem to a constrained minimization of a quadratic form. For biologically plausible constraints, this problem has exact analytical solutions, which give reasonable approximations to actual layouts in the brain. These solutions make the inverse problem of inferring neuronal connectivity from neuronal layout more tractable.

  8. Optimal rail container shipment planning problem in multimodal transportation

    NASA Astrophysics Data System (ADS)

    Cao, Chengxuan; Gao, Ziyou; Li, Keping

    2012-09-01

    The optimal rail container shipment planning problem in multimodal transportation is studied in this article. The characteristics of the multi-period planning problem is presented and the problem is formulated as a large-scale 0-1 integer programming model, which maximizes the total profit generated by all freight bookings accepted in a multi-period planning horizon subject to the limited capacities. Two heuristic algorithms are proposed to obtain an approximate optimal solution of the problem. Finally, numerical experiments are conducted to demonstrate the proposed formulation and heuristic algorithms.

  9. 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.

  10. An inverse problem for Gibbs fields with hard core potential

    NASA Astrophysics Data System (ADS)

    Koralov, Leonid

    2007-05-01

    It is well known that for a regular stable potential of pair interaction and a small value of activity one can define the corresponding Gibbs field (a measure on the space of configurations of points in Rd). In this paper we consider a converse problem. Namely, we show that for a sufficiently small constant ρ¯1 and a sufficiently small function ρ¯2(x), x ∈Rd, that is equal to zero in a neighborhood of the origin, there exist a hard core pair potential and a value of activity such that ρ¯1 is the density and ρ¯2 is the pair correlation function of the corresponding Gibbs field.

  11. A Comparison of Approaches for Solving Hard Graph-Theoretic Problems

    DTIC Science & Technology

    2015-04-29

    can be converted to a quadratic unconstrained binary optimization ( QUBO ) problem that uses 0/1-valued variables, and so they are often used...Frontiers in Physics, 2:5 (12 Feb 2014). [7] “Programming with QUBOs ,” (instructional document) D-Wave: The Quantum Computing Company, 2013. [8

  12. Solving Fuzzy Optimization Problem Using Hybrid Ls-Sa Method

    NASA Astrophysics Data System (ADS)

    Vasant, Pandian

    2011-06-01

    Fuzzy optimization problem has been one of the most and prominent topics inside the broad area of computational intelligent. It's especially relevant in the filed of fuzzy non-linear programming. It's application as well as practical realization can been seen in all the real world problems. In this paper a large scale non-linear fuzzy programming problem has been solved by hybrid optimization techniques of Line Search (LS), Simulated Annealing (SA) and Pattern Search (PS). As industrial production planning problem with cubic objective function, 8 decision variables and 29 constraints has been solved successfully using LS-SA-PS hybrid optimization techniques. The computational results for the objective function respect to vagueness factor and level of satisfaction has been provided in the form of 2D and 3D plots. The outcome is very promising and strongly suggests that the hybrid LS-SA-PS algorithm is very efficient and productive in solving the large scale non-linear fuzzy programming problem.

  13. Expectation maximization for hard X-ray count modulation profiles

    NASA Astrophysics Data System (ADS)

    Benvenuto, F.; Schwartz, R.; Piana, M.; Massone, A. M.

    2013-07-01

    Context. This paper is concerned with the image reconstruction problem when the measured data are solar hard X-ray modulation profiles obtained from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) instrument. Aims: Our goal is to demonstrate that a statistical iterative method classically applied to the image deconvolution problem is very effective when utilized to analyze count modulation profiles in solar hard X-ray imaging based on rotating modulation collimators. Methods: The algorithm described in this paper solves the maximum likelihood problem iteratively and encodes a positivity constraint into the iterative optimization scheme. The result is therefore a classical expectation maximization method this time applied not to an image deconvolution problem but to image reconstruction from count modulation profiles. The technical reason that makes our implementation particularly effective in this application is the use of a very reliable stopping rule which is able to regularize the solution providing, at the same time, a very satisfactory Cash-statistic (C-statistic). Results: The method is applied to both reproduce synthetic flaring configurations and reconstruct images from experimental data corresponding to three real events. In this second case, the performance of expectation maximization, when compared to Pixon image reconstruction, shows a comparable accuracy and a notably reduced computational burden; when compared to CLEAN, shows a better fidelity with respect to the measurements with a comparable computational effectiveness. Conclusions: If optimally stopped, expectation maximization represents a very reliable method for image reconstruction in the RHESSI context when count modulation profiles are used as input data.

  14. OPTIMIZING THROUGH CO-EVOLUTIONARY AVALANCHES

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

    S. BOETTCHER; A. PERCUS

    2000-08-01

    We explore a new general-purpose heuristic for finding high-quality solutions to hard optimization problems. The method, called extremal optimization, is inspired by ''self-organized critically,'' a concept introduced to describe emergent complexity in many physical systems. In contrast to Genetic Algorithms which operate on an entire ''gene-pool'' of possible solutions, extremal optimization successively replaces extremely undesirable elements of a sub-optimal solution with new, random ones. Large fluctuations, called ''avalanches,'' ensue that efficiently explore many local optima. Drawing upon models used to simulate far-from-equilibrium dynamics, extremal optimization complements approximation methods inspired by equilibrium statistical physics, such as simulated annealing. With only onemore » adjustable parameter, its performance has proved competitive with more elaborate methods, especially near phase transitions. Those phase transitions are found in the parameter space of most optimization problems, and have recently been conjectured to be the origin of some of the hardest instances in computational complexity. We will demonstrate how extremal optimization can be implemented for a variety of combinatorial optimization problems. We believe that extremal optimization will be a useful tool in the investigation of phase transitions in combinatorial optimization problems, hence valuable in elucidating the origin of computational complexity.« less

  15. Lessons Learned During Solutions of Multidisciplinary Design Optimization Problems

    NASA Technical Reports Server (NTRS)

    Patnaik, Suna N.; Coroneos, Rula M.; Hopkins, Dale A.; Lavelle, Thomas M.

    2000-01-01

    Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. During solution of the multidisciplinary problems several issues were encountered. This paper lists four issues and discusses the strategies adapted for their resolution: (1) The 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. (2) Optimum solutions obtained were infeasible for aircraft and air-breathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. (3) Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. (4) 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 six problems: (1) design of an engine component, (2) synthesis of a subsonic aircraft, (3) operation optimization of a supersonic engine, (4) design of a wave-rotor-topping device, (5) profile optimization of a cantilever beam, and (6) design of a cvlindrical shell. The combined effort of designers and researchers can bring the optimization method from academia to industry.

  16. A novel metaheuristic for continuous optimization problems: Virus optimization algorithm

    NASA Astrophysics Data System (ADS)

    Liang, Yun-Chia; Rodolfo Cuevas Juarez, Josue

    2016-01-01

    A novel metaheuristic for continuous optimization problems, named the virus optimization algorithm (VOA), is introduced and investigated. VOA is an iteratively population-based method that imitates the behaviour of viruses attacking a living cell. The number of viruses grows at each replication and is controlled by an immune system (a so-called 'antivirus') to prevent the explosive growth of the virus population. The viruses are divided into two classes (strong and common) to balance the exploitation and exploration effects. The performance of the VOA is validated through a set of eight benchmark functions, which are also subject to rotation and shifting effects to test its robustness. Extensive comparisons were conducted with over 40 well-known metaheuristic algorithms and their variations, such as artificial bee colony, artificial immune system, differential evolution, evolutionary programming, evolutionary strategy, genetic algorithm, harmony search, invasive weed optimization, memetic algorithm, particle swarm optimization and simulated annealing. The results showed that the VOA is a viable solution for continuous optimization.

  17. Particle swarm optimization - Genetic algorithm (PSOGA) on linear transportation problem

    NASA Astrophysics Data System (ADS)

    Rahmalia, Dinita

    2017-08-01

    Linear Transportation Problem (LTP) is the case of constrained optimization where we want to minimize cost subject to the balance of the number of supply and the number of demand. The exact method such as northwest corner, vogel, russel, minimal cost have been applied at approaching optimal solution. In this paper, we use heurisitic like Particle Swarm Optimization (PSO) for solving linear transportation problem at any size of decision variable. In addition, we combine mutation operator of Genetic Algorithm (GA) at PSO to improve optimal solution. This method is called Particle Swarm Optimization - Genetic Algorithm (PSOGA). The simulations show that PSOGA can improve optimal solution resulted by PSO.

  18. Feed Forward Neural Network and Optimal Control Problem with Control and State Constraints

    NASA Astrophysics Data System (ADS)

    Kmet', Tibor; Kmet'ová, Mária

    2009-09-01

    A feed forward neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints. The paper extends adaptive critic neural network architecture proposed by [5] to the optimal control problems with control and state constraints. The optimal control problem is transcribed into a nonlinear programming problem which is implemented with adaptive critic neural network. The proposed simulation method is illustrated by the optimal control problem of nitrogen transformation cycle model. Results show that adaptive critic based systematic approach holds promise for obtaining the optimal control with control and state constraints.

  19. Finite dimensional approximation of a class of constrained nonlinear optimal control problems

    NASA Technical Reports Server (NTRS)

    Gunzburger, Max D.; Hou, L. S.

    1994-01-01

    An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.

  20. The solution of private problems for optimization heat exchangers parameters

    NASA Astrophysics Data System (ADS)

    Melekhin, A.

    2017-11-01

    The relevance of the topic due to the decision of problems of the economy of resources in heating systems of buildings. To solve this problem we have developed an integrated method of research which allows solving tasks on optimization of parameters of heat exchangers. This method decides multicriteria optimization problem with the program nonlinear optimization on the basis of software with the introduction of an array of temperatures obtained using thermography. The author have developed a mathematical model of process of heat exchange in heat exchange surfaces of apparatuses with the solution of multicriteria optimization problem and check its adequacy to the experimental stand in the visualization of thermal fields, an optimal range of managed parameters influencing the process of heat exchange with minimal metal consumption and the maximum heat output fin heat exchanger, the regularities of heat exchange process with getting generalizing dependencies distribution of temperature on the heat-release surface of the heat exchanger vehicles, defined convergence of the results of research in the calculation on the basis of theoretical dependencies and solving mathematical model.

  1. Social interaction as a heuristic for combinatorial optimization problems

    NASA Astrophysics Data System (ADS)

    Fontanari, José F.

    2010-11-01

    We investigate the performance of a variant of Axelrod’s model for dissemination of culture—the Adaptive Culture Heuristic (ACH)—on solving an NP-Complete optimization problem, namely, the classification of binary input patterns of size F by a Boolean Binary Perceptron. In this heuristic, N agents, characterized by binary strings of length F which represent possible solutions to the optimization problem, are fixed at the sites of a square lattice and interact with their nearest neighbors only. The interactions are such that the agents’ strings (or cultures) become more similar to the low-cost strings of their neighbors resulting in the dissemination of these strings across the lattice. Eventually the dynamics freezes into a homogeneous absorbing configuration in which all agents exhibit identical solutions to the optimization problem. We find through extensive simulations that the probability of finding the optimal solution is a function of the reduced variable F/N1/4 so that the number of agents must increase with the fourth power of the problem size, N∝F4 , to guarantee a fixed probability of success. In this case, we find that the relaxation time to reach an absorbing configuration scales with F6 which can be interpreted as the overall computational cost of the ACH to find an optimal set of weights for a Boolean binary perceptron, given a fixed probability of success.

  2. Multiagent optimization system for solving the traveling salesman problem (TSP).

    PubMed

    Xie, Xiao-Feng; Liu, Jiming

    2009-04-01

    The multiagent optimization system (MAOS) is a nature-inspired method, which supports cooperative search by the self-organization of a group of compact agents situated in an environment with certain sharing public knowledge. Moreover, each agent in MAOS is an autonomous entity with personal declarative memory and behavioral components. In this paper, MAOS is refined for solving the traveling salesman problem (TSP), which is a classic hard computational problem. Based on a simplified MAOS version, in which each agent manipulates on extremely limited declarative knowledge, some simple and efficient components for solving TSP, including two improving heuristics based on a generalized edge assembly recombination, are implemented. Compared with metaheuristics in adaptive memory programming, MAOS is particularly suitable for supporting cooperative search. The experimental results on two TSP benchmark data sets show that MAOS is competitive as compared with some state-of-the-art algorithms, including the Lin-Kernighan-Helsgaun, IBGLK, PHGA, etc., although MAOS does not use any explicit local search during the runtime. The contributions of MAOS components are investigated. It indicates that certain clues can be positive for making suitable selections before time-consuming computation. More importantly, it shows that the cooperative search of agents can achieve an overall good performance with a macro rule in the switch mode, which deploys certain alternate search rules with the offline performance in negative correlations. Using simple alternate rules may prevent the high difficulty of seeking an omnipotent rule that is efficient for a large data set.

  3. Performance comparison of some evolutionary algorithms on job shop scheduling problems

    NASA Astrophysics Data System (ADS)

    Mishra, S. K.; Rao, C. S. P.

    2016-09-01

    Job Shop Scheduling as a state space search problem belonging to NP-hard category due to its complexity and combinational explosion of states. Several naturally inspire evolutionary methods have been developed to solve Job Shop Scheduling Problems. In this paper the evolutionary methods namely Particles Swarm Optimization, Artificial Intelligence, Invasive Weed Optimization, Bacterial Foraging Optimization, Music Based Harmony Search Algorithms are applied and find tuned to model and solve Job Shop Scheduling Problems. To compare about 250 Bench Mark instances have been used to evaluate the performance of these algorithms. The capabilities of each these algorithms in solving Job Shop Scheduling Problems are outlined.

  4. Discrete-time entropy formulation of optimal and adaptive control problems

    NASA Technical Reports Server (NTRS)

    Tsai, Yweting A.; Casiello, Francisco A.; Loparo, Kenneth A.

    1992-01-01

    The discrete-time version of the entropy formulation of optimal control of problems developed by G. N. Saridis (1988) is discussed. Given a dynamical system, the uncertainty in the selection of the control is characterized by the probability distribution (density) function which maximizes the total entropy. The equivalence between the optimal control problem and the optimal entropy problem is established, and the total entropy is decomposed into a term associated with the certainty equivalent control law, the entropy of estimation, and the so-called equivocation of the active transmission of information from the controller to the estimator. This provides a useful framework for studying the certainty equivalent and adaptive control laws.

  5. Analyzing the Effects of a Mathematics Problem-Solving Program, Exemplars, on Mathematics Problem-Solving Scores with Deaf and Hard-of-Hearing Students

    ERIC Educational Resources Information Center

    Chilvers, Amanda Leigh

    2013-01-01

    Researchers have noted that mathematics achievement for deaf and hard-of-hearing (d/hh) students has been a concern for many years, including the ability to problem solve. This quasi-experimental study investigates the use of the Exemplars mathematics program with students in grades 2-8 in a school for the deaf that utilizes American Sign Language…

  6. 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

  7. Finding Optimal Gains In Linear-Quadratic Control Problems

    NASA Technical Reports Server (NTRS)

    Milman, Mark H.; Scheid, Robert E., Jr.

    1990-01-01

    Analytical method based on Volterra factorization leads to new approximations for optimal control gains in finite-time linear-quadratic control problem of system having infinite number of dimensions. Circumvents need to analyze and solve Riccati equations and provides more transparent connection between dynamics of system and optimal gain.

  8. A coherent Ising machine for 2000-node optimization problems

    NASA Astrophysics Data System (ADS)

    Inagaki, Takahiro; Haribara, Yoshitaka; Igarashi, Koji; Sonobe, Tomohiro; Tamate, Shuhei; Honjo, Toshimori; Marandi, Alireza; McMahon, Peter L.; Umeki, Takeshi; Enbutsu, Koji; Tadanaga, Osamu; Takenouchi, Hirokazu; Aihara, Kazuyuki; Kawarabayashi, Ken-ichi; Inoue, Kyo; Utsunomiya, Shoko; Takesue, Hiroki

    2016-11-01

    The analysis and optimization of complex systems can be reduced to mathematical problems collectively known as combinatorial optimization. Many such problems can be mapped onto ground-state search problems of the Ising model, and various artificial spin systems are now emerging as promising approaches. However, physical Ising machines have suffered from limited numbers of spin-spin couplings because of implementations based on localized spins, resulting in severe scalability problems. We report a 2000-spin network with all-to-all spin-spin couplings. Using a measurement and feedback scheme, we coupled time-multiplexed degenerate optical parametric oscillators to implement maximum cut problems on arbitrary graph topologies with up to 2000 nodes. Our coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.

  9. Fundamental differences between optimization code test problems in engineering applications

    NASA Technical Reports Server (NTRS)

    Eason, E. D.

    1984-01-01

    The purpose here is to suggest that there is at least one fundamental difference between the problems used for testing optimization codes and the problems that engineers often need to solve; in particular, the level of precision that can be practically achieved in the numerical evaluation of the objective function, derivatives, and constraints. This difference affects the performance of optimization codes, as illustrated by two examples. Two classes of optimization problem were defined. Class One functions and constraints can be evaluated to a high precision that depends primarily on the word length of the computer. Class Two functions and/or constraints can only be evaluated to a moderate or a low level of precision for economic or modeling reasons, regardless of the computer word length. Optimization codes have not been adequately tested on Class Two problems. There are very few Class Two test problems in the literature, while there are literally hundreds of Class One test problems. The relative performance of two codes may be markedly different for Class One and Class Two problems. Less sophisticated direct search type codes may be less likely to be confused or to waste many function evaluations on Class Two problems. The analysis accuracy and minimization performance are related in a complex way that probably varies from code to code. On a problem where the analysis precision was varied over a range, the simple Hooke and Jeeves code was more efficient at low precision while the Powell code was more efficient at high precision.

  10. Topology optimization of unsteady flow problems using the lattice Boltzmann method

    NASA Astrophysics Data System (ADS)

    Nørgaard, Sebastian; Sigmund, Ole; Lazarov, Boyan

    2016-02-01

    This article demonstrates and discusses topology optimization for unsteady incompressible fluid flows. The fluid flows are simulated using the lattice Boltzmann method, and a partial bounceback model is implemented to model the transition between fluid and solid phases in the optimization problems. The optimization problem is solved with a gradient based method, and the design sensitivities are computed by solving the discrete adjoint problem. For moderate Reynolds number flows, it is demonstrated that topology optimization can successfully account for unsteady effects such as vortex shedding and time-varying boundary conditions. Such effects are relevant in several engineering applications, i.e. fluid pumps and control valves.

  11. The Sizing and Optimization Language, (SOL): Computer language for design problems

    NASA Technical Reports Server (NTRS)

    Lucas, Stephen H.; Scotti, Stephen J.

    1988-01-01

    The Sizing and Optimization Language, (SOL), a new high level, special purpose computer language was developed to expedite application of numerical optimization to design problems and to make the process less error prone. SOL utilizes the ADS optimization software and provides a clear, concise syntax for describing an optimization problem, the OPTIMIZE description, which closely parallels the mathematical description of the problem. SOL offers language statements which can be used to model a design mathematically, with subroutines or code logic, and with existing FORTRAN routines. In addition, SOL provides error checking and clear output of the optimization results. Because of these language features, SOL is best suited to model and optimize a design concept when the model consits of mathematical expressions written in SOL. For such cases, SOL's unique syntax and error checking can be fully utilized. SOL is presently available for DEC VAX/VMS systems. A SOL package is available which includes the SOL compiler, runtime library routines, and a SOL reference manual.

  12. 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.

  13. Solving mixed integer nonlinear programming problems using spiral dynamics optimization algorithm

    NASA Astrophysics Data System (ADS)

    Kania, Adhe; Sidarto, Kuntjoro Adji

    2016-02-01

    Many engineering and practical problem can be modeled by mixed integer nonlinear programming. This paper proposes to solve the problem with modified spiral dynamics inspired optimization method of Tamura and Yasuda. Four test cases have been examined, including problem in engineering and sport. This method succeeds in obtaining the optimal result in all test cases.

  14. Effective Teaching of Economics: A Constrained Optimization Problem?

    ERIC Educational Resources Information Center

    Hultberg, Patrik T.; Calonge, David Santandreu

    2017-01-01

    One of the fundamental tenets of economics is that decisions are often the result of optimization problems subject to resource constraints. Consumers optimize utility, subject to constraints imposed by prices and income. As economics faculty, instructors attempt to maximize student learning while being constrained by their own and students'…

  15. The Role of Intuition in the Solving of Optimization Problems

    ERIC Educational Resources Information Center

    Malaspina, Uldarico; Font, Vicenc

    2010-01-01

    This article presents the partial results obtained in the first stage of the research, which sought to answer the following questions: (a) What is the role of intuition in university students' solutions to optimization problems? (b) What is the role of rigor in university students' solutions to optimization problems? (c) How is the combination of…

  16. Improving multi-objective reservoir operation optimization with sensitivity-informed problem decomposition

    NASA Astrophysics Data System (ADS)

    Chu, J. G.; Zhang, C.; Fu, G. T.; Li, Y.; Zhou, H. C.

    2015-04-01

    This study investigates the effectiveness of a sensitivity-informed method for multi-objective operation of reservoir systems, which uses global sensitivity analysis as a screening tool to reduce the computational demands. Sobol's method is used to screen insensitive decision variables and guide the formulation of the optimization problems with a significantly reduced number of decision variables. This sensitivity-informed problem decomposition dramatically reduces the computational demands required for attaining high quality approximations of optimal tradeoff relationships between conflicting design objectives. The search results obtained from the reduced complexity multi-objective reservoir operation problems are then used to pre-condition the full search of the original optimization problem. In two case studies, the Dahuofang reservoir and the inter-basin multi-reservoir system in Liaoning province, China, sensitivity analysis results show that reservoir performance is strongly controlled by a small proportion of decision variables. Sensitivity-informed problem decomposition and pre-conditioning are evaluated in their ability to improve the efficiency and effectiveness of multi-objective evolutionary optimization. Overall, this study illustrates the efficiency and effectiveness of the sensitivity-informed method and the use of global sensitivity analysis to inform problem decomposition when solving the complex multi-objective reservoir operation problems.

  17. Sub-problem Optimization With Regression and Neural Network Approximators

    NASA Technical Reports Server (NTRS)

    Guptill, James D.; Hopkins, Dale A.; Patnaik, Surya N.

    2003-01-01

    Design optimization of large systems can be attempted through a sub-problem strategy. In this strategy, the original problem is divided into a number of smaller problems that are clustered together to obtain a sequence of sub-problems. Solution to the large problem is attempted iteratively through repeated solutions to the modest sub-problems. This strategy is applicable to structures and to multidisciplinary systems. For structures, clustering the substructures generates the sequence of sub-problems. For a multidisciplinary system, individual disciplines, accounting for coupling, can be considered as sub-problems. A sub-problem, if required, can be further broken down to accommodate sub-disciplines. The sub-problem strategy is being implemented into the NASA design optimization test bed, referred to as "CometBoards." Neural network and regression approximators are employed for reanalysis and sensitivity analysis calculations at the sub-problem level. The strategy has been implemented in sequential as well as parallel computational environments. This strategy, which attempts to alleviate algorithmic and reanalysis deficiencies, has the potential to become a powerful design tool. However, several issues have to be addressed before its full potential can be harnessed. This paper illustrates the strategy and addresses some issues.

  18. Adapting Experiential Learning to Develop Problem-Solving Skills in Deaf and Hard-of-Hearing Engineering Students

    ERIC Educational Resources Information Center

    Marshall, Matthew M.; Carrano, Andres L.; Dannels, Wendy A.

    2016-01-01

    Individuals who are deaf and hard-of-hearing (DHH) are underrepresented in science, technology, engineering, and mathematics (STEM) professions, and this may be due in part to their level of preparation in the development and retention of mathematical and problem-solving skills. An approach was developed that incorporates experiential learning and…

  19. 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

  20. Optimal pre-scheduling of problem remappings

    NASA Technical Reports Server (NTRS)

    Nicol, David M.; Saltz, Joel H.

    1987-01-01

    A large class of scientific computational problems can be characterized as a sequence of steps where a significant amount of computation occurs each step, but the work performed at each step is not necessarily identical. Two good examples of this type of computation are: (1) regridding methods which change the problem discretization during the course of the computation, and (2) methods for solving sparse triangular systems of linear equations. Recent work has investigated a means of mapping such computations onto parallel processors; the method defines a family of static mappings with differing degrees of importance placed on the conflicting goals of good load balance and low communication/synchronization overhead. The performance tradeoffs are controllable by adjusting the parameters of the mapping method. To achieve good performance it may be necessary to dynamically change these parameters at run-time, but such changes can impose additional costs. If the computation's behavior can be determined prior to its execution, it can be possible to construct an optimal parameter schedule using a low-order-polynomial-time dynamic programming algorithm. Since the latter can be expensive, the performance is studied of the effect of a linear-time scheduling heuristic on one of the model problems, and it is shown to be effective and nearly optimal.

  1. Redundant interferometric calibration as a complex optimization problem

    NASA Astrophysics Data System (ADS)

    Grobler, T. L.; Bernardi, G.; Kenyon, J. S.; Parsons, A. R.; Smirnov, O. M.

    2018-05-01

    Observations of the redshifted 21 cm line from the epoch of reionization have recently motivated the construction of low-frequency radio arrays with highly redundant configurations. These configurations provide an alternative calibration strategy - `redundant calibration' - and boost sensitivity on specific spatial scales. In this paper, we formulate calibration of redundant interferometric arrays as a complex optimization problem. We solve this optimization problem via the Levenberg-Marquardt algorithm. This calibration approach is more robust to initial conditions than current algorithms and, by leveraging an approximate matrix inversion, allows for further optimization and an efficient implementation (`redundant STEFCAL'). We also investigated using the preconditioned conjugate gradient method as an alternative to the approximate matrix inverse, but found that its computational performance is not competitive with respect to `redundant STEFCAL'. The efficient implementation of this new algorithm is made publicly available.

  2. Optimization-based additive decomposition of weakly coercive problems with applications

    DOE PAGES

    Bochev, Pavel B.; Ridzal, Denis

    2016-01-27

    In this study, we present an abstract mathematical framework for an optimization-based additive decomposition of a large class of variational problems into a collection of concurrent subproblems. The framework replaces a given monolithic problem by an equivalent constrained optimization formulation in which the subproblems define the optimization constraints and the objective is to minimize the mismatch between their solutions. The significance of this reformulation stems from the fact that one can solve the resulting optimality system by an iterative process involving only solutions of the subproblems. Consequently, assuming that stable numerical methods and efficient solvers are available for every subproblem,more » our reformulation leads to robust and efficient numerical algorithms for a given monolithic problem by breaking it into subproblems that can be handled more easily. An application of the framework to the Oseen equations illustrates its potential.« less

  3. Smell Detection Agent Based Optimization Algorithm

    NASA Astrophysics Data System (ADS)

    Vinod Chandra, S. S.

    2016-09-01

    In this paper, a novel nature-inspired optimization algorithm has been employed and the trained behaviour of dogs in detecting smell trails is adapted into computational agents for problem solving. The algorithm involves creation of a surface with smell trails and subsequent iteration of the agents in resolving a path. This algorithm can be applied in different computational constraints that incorporate path-based problems. Implementation of the algorithm can be treated as a shortest path problem for a variety of datasets. The simulated agents have been used to evolve the shortest path between two nodes in a graph. This algorithm is useful to solve NP-hard problems that are related to path discovery. This algorithm is also useful to solve many practical optimization problems. The extensive derivation of the algorithm can be enabled to solve shortest path problems.

  4. Magnetic hyperthermia with hard-magnetic nanoparticles

    NASA Astrophysics Data System (ADS)

    Kashevsky, Bronislav E.; Kashevsky, Sergey B.; Korenkov, Victor S.; Istomin, Yuri P.; Terpinskaya, Tatyana I.; Ulashchik, Vladimir S.

    2015-04-01

    Recent clinical trials of magnetic hyperthermia have proved, and even hardened, the Ankinson-Brezovich restriction as upon magnetic field conditions applicable to any site of human body. Subject to this restriction, which is harshly violated in numerous laboratory and small animal studies, magnetic hyperthermia can relay on rather moderate heat source, so that optimization of the whole hyperthermia system remains, after all, the basic problem predetermining its clinical perspectives. We present short account of our complex (theoretical, laboratory and small animal) studies to demonstrate that such perspectives should be related with the hyperthermia system based on hard-magnetic (Stoner-Wohlfarth type) nanoparticles and strong low-frequency fields rather than with superparamagnetic (Brownian or Neél) nanoparticles and weak high-frequency fields. This conclusion is backed by an analytical evaluation of the maximum absorption rates possible under the field restriction in the ideal hard-magnetic (Stoner-Wohlarth) and the ideal superparamagnetic (single relaxation time) systems, by theoretical and experimental studies of the dynamic magnetic hysteresis in suspensions of movable hard-magnetic particles, by producing nanoparticles with adjusted coercivity and suspensions of such particles capable of effective energy absorption and intratumoral penetration, and finally, by successful treatment of a mice model tumor under field conditions acceptable for whole human body.

  5. Solving inversion problems with neural networks

    NASA Technical Reports Server (NTRS)

    Kamgar-Parsi, Behzad; Gualtieri, J. A.

    1990-01-01

    A class of inverse problems in remote sensing can be characterized by Q = F(x), where F is a nonlinear and noninvertible (or hard to invert) operator, and the objective is to infer the unknowns, x, from the observed quantities, Q. Since the number of observations is usually greater than the number of unknowns, these problems are formulated as optimization problems, which can be solved by a variety of techniques. The feasibility of neural networks for solving such problems is presently investigated. As an example, the problem of finding the atmospheric ozone profile from measured ultraviolet radiances is studied.

  6. Expected Fitness Gains of Randomized Search Heuristics for the Traveling Salesperson Problem.

    PubMed

    Nallaperuma, Samadhi; Neumann, Frank; Sudholt, Dirk

    2017-01-01

    Randomized search heuristics are frequently applied to NP-hard combinatorial optimization problems. The runtime analysis of randomized search heuristics has contributed tremendously to our theoretical understanding. Recently, randomized search heuristics have been examined regarding their achievable progress within a fixed-time budget. We follow this approach and present a fixed-budget analysis for an NP-hard combinatorial optimization problem. We consider the well-known Traveling Salesperson Problem (TSP) and analyze the fitness increase that randomized search heuristics are able to achieve within a given fixed-time budget. In particular, we analyze Manhattan and Euclidean TSP instances and Randomized Local Search (RLS), (1+1) EA and (1+[Formula: see text]) EA algorithms for the TSP in a smoothed complexity setting, and derive the lower bounds of the expected fitness gain for a specified number of generations.

  7. Proposal of Evolutionary Simplex Method for Global Optimization Problem

    NASA Astrophysics Data System (ADS)

    Shimizu, Yoshiaki

    To make an agile decision in a rational manner, role of optimization engineering has been notified increasingly under diversified customer demand. With this point of view, in this paper, we have proposed a new evolutionary method serving as an optimization technique in the paradigm of optimization engineering. The developed method has prospects to solve globally various complicated problem appearing in real world applications. It is evolved from the conventional method known as Nelder and Mead’s Simplex method by virtue of idea borrowed from recent meta-heuristic method such as PSO. Mentioning an algorithm to handle linear inequality constraints effectively, we have validated effectiveness of the proposed method through comparison with other methods using several benchmark problems.

  8. 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

  9. Nonlinear Multidimensional Assignment Problems Efficient Conic Optimization Methods and Applications

    DTIC Science & Technology

    2015-06-24

    WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Arizona State University School of Mathematical & Statistical Sciences 901 S...SUPPLEMENTARY NOTES 14. ABSTRACT The major goals of this project were completed: the exact solution of previously unsolved challenging combinatorial optimization... combinatorial optimization problem, the Directional Sensor Problem, was solved in two ways. First, heuristically in an engineering fashion and second, exactly

  10. The application of artificial intelligence in the optimal design of mechanical systems

    NASA Astrophysics Data System (ADS)

    Poteralski, A.; Szczepanik, M.

    2016-11-01

    The paper is devoted to new computational techniques in mechanical optimization where one tries to study, model, analyze and optimize very complex phenomena, for which more precise scientific tools of the past were incapable of giving low cost and complete solution. Soft computing methods differ from conventional (hard) computing in that, unlike hard computing, they are tolerant of imprecision, uncertainty, partial truth and approximation. The paper deals with an application of the bio-inspired methods, like the evolutionary algorithms (EA), the artificial immune systems (AIS) and the particle swarm optimizers (PSO) to optimization problems. Structures considered in this work are analyzed by the finite element method (FEM), the boundary element method (BEM) and by the method of fundamental solutions (MFS). The bio-inspired methods are applied to optimize shape, topology and material properties of 2D, 3D and coupled 2D/3D structures, to optimize the termomechanical structures, to optimize parameters of composites structures modeled by the FEM, to optimize the elastic vibrating systems to identify the material constants for piezoelectric materials modeled by the BEM and to identify parameters in acoustics problem modeled by the MFS.

  11. Landscape Encodings Enhance Optimization

    PubMed Central

    Klemm, Konstantin; Mehta, Anita; Stadler, Peter F.

    2012-01-01

    Hard combinatorial optimization problems deal with the search for the minimum cost solutions (ground states) of discrete systems under strong constraints. A transformation of state variables may enhance computational tractability. It has been argued that these state encodings are to be chosen invertible to retain the original size of the state space. Here we show how redundant non-invertible encodings enhance optimization by enriching the density of low-energy states. In addition, smooth landscapes may be established on encoded state spaces to guide local search dynamics towards the ground state. PMID:22496860

  12. Guided particle swarm optimization method to solve general nonlinear optimization problems

    NASA Astrophysics Data System (ADS)

    Abdelhalim, Alyaa; Nakata, Kazuhide; El-Alem, Mahmoud; Eltawil, Amr

    2018-04-01

    The development of hybrid algorithms is becoming an important topic in the global optimization research area. This article proposes a new technique in hybridizing the particle swarm optimization (PSO) algorithm and the Nelder-Mead (NM) simplex search algorithm to solve general nonlinear unconstrained optimization problems. Unlike traditional hybrid methods, the proposed method hybridizes the NM algorithm inside the PSO to improve the velocities and positions of the particles iteratively. The new hybridization considers the PSO algorithm and NM algorithm as one heuristic, not in a sequential or hierarchical manner. The NM algorithm is applied to improve the initial random solution of the PSO algorithm and iteratively in every step to improve the overall performance of the method. The performance of the proposed method was tested over 20 optimization test functions with varying dimensions. Comprehensive comparisons with other methods in the literature indicate that the proposed solution method is promising and competitive.

  13. Quadratic Optimization in the Problems of Active Control of Sound

    NASA Technical Reports Server (NTRS)

    Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)

    2002-01-01

    We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).

  14. Two hybrid compaction algorithms for the layout optimization problem.

    PubMed

    Xiao, Ren-Bin; Xu, Yi-Chun; Amos, Martyn

    2007-01-01

    In this paper we present two new algorithms for the layout optimization problem: this concerns the placement of circular, weighted objects inside a circular container, the two objectives being to minimize imbalance of mass and to minimize the radius of the container. This problem carries real practical significance in industrial applications (such as the design of satellites), as well as being of significant theoretical interest. We present two nature-inspired algorithms for this problem, the first based on simulated annealing, and the second on particle swarm optimization. We compare our algorithms with the existing best-known algorithm, and show that our approaches out-perform it in terms of both solution quality and execution time.

  15. Applying Graph Theory to Problems in Air Traffic Management

    NASA Technical Reports Server (NTRS)

    Farrahi, Amir Hossein; Goldbert, Alan; Bagasol, Leonard Neil; Jung, Jaewoo

    2017-01-01

    Graph theory is used to investigate three different problems arising in air traffic management. First, using a polynomial reduction from a graph partitioning problem, it is shown that both the airspace sectorization problem and its incremental counterpart, the sector combination problem are NP-hard, in general, under several simple workload models. Second, using a polynomial time reduction from maximum independent set in graphs, it is shown that for any fixed e, the problem of finding a solution to the minimum delay scheduling problem in traffic flow management that is guaranteed to be within n1-e of the optimal, where n is the number of aircraft in the problem instance, is NP-hard. Finally, a problem arising in precision arrival scheduling is formulated and solved using graph reachability. These results demonstrate that graph theory provides a powerful framework for modeling, reasoning about, and devising algorithmic solutions to diverse problems arising in air traffic management.

  16. Applying Graph Theory to Problems in Air Traffic Management

    NASA Technical Reports Server (NTRS)

    Farrahi, Amir H.; Goldberg, Alan T.; Bagasol, Leonard N.; Jung, Jaewoo

    2017-01-01

    Graph theory is used to investigate three different problems arising in air traffic management. First, using a polynomial reduction from a graph partitioning problem, it isshown that both the airspace sectorization problem and its incremental counterpart, the sector combination problem are NP-hard, in general, under several simple workload models. Second, using a polynomial time reduction from maximum independent set in graphs, it is shown that for any fixed e, the problem of finding a solution to the minimum delay scheduling problem in traffic flow management that is guaranteed to be within n1-e of the optimal, where n is the number of aircraft in the problem instance, is NP-hard. Finally, a problem arising in precision arrival scheduling is formulated and solved using graph reachability. These results demonstrate that graph theory provides a powerful framework for modeling, reasoning about, and devising algorithmic solutions to diverse problems arising in air traffic management.

  17. Optimal Control Problems with Switching Points. Ph.D. Thesis, 1990 Final Report

    NASA Technical Reports Server (NTRS)

    Seywald, Hans

    1991-01-01

    The main idea of this report is to give an overview of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.

  18. Direct SQP-methods for solving optimal control problems with delays

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

    Goellmann, L.; Bueskens, C.; Maurer, H.

    The maximum principle for optimal control problems with delays leads to a boundary value problem (BVP) which is retarded in the state and advanced in the costate function. Based on shooting techniques, solution methods for this type of BVP have been proposed. In recent years, direct optimization methods have been favored for solving control problems without delays. Direct methods approximate the control and the state over a fixed mesh and solve the resulting NLP-problem with SQP-methods. These methods dispense with the costate function and have shown to be robust and efficient. In this paper, we propose a direct SQP-method formore » retarded control problems. In contrast to conventional direct methods, only the control variable is approximated by e.g. spline-functions. The state is computed via a high order Runge-Kutta type algorithm and does not enter explicitly the NLP-problem through an equation. This approach reduces the number of optimization variables considerably and is implementable even on a PC. Our method is illustrated by the numerical solution of retarded control problems with constraints. In particular, we consider the control of a continuous stirred tank reactor which has been solved by dynamic programming. This example illustrates the robustness and efficiency of the proposed method. Open questions concerning sufficient conditions and convergence of discretized NLP-problems are discussed.« less

  19. Multiresolution strategies for the numerical solution of optimal control problems

    NASA Astrophysics Data System (ADS)

    Jain, Sachin

    There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a

  20. Advantages of soft versus hard constraints in self-modeling curve resolution problems. Penalty alternating least squares (P-ALS) extension to multi-way problems.

    PubMed

    Richards, Selena; Miller, Robert; Gemperline, Paul

    2008-02-01

    An extension to the penalty alternating least squares (P-ALS) method, called multi-way penalty alternating least squares (NWAY P-ALS), is presented. Optionally, hard constraints (no deviation from predefined constraints) or soft constraints (small deviations from predefined constraints) were applied through the application of a row-wise penalty least squares function. NWAY P-ALS was applied to the multi-batch near-infrared (NIR) data acquired from the base catalyzed esterification reaction of acetic anhydride in order to resolve the concentration and spectral profiles of l-butanol with the reaction constituents. Application of the NWAY P-ALS approach resulted in the reduction of the number of active constraints at the solution point, while the batch column-wise augmentation allowed hard constraints in the spectral profiles and resolved rank deficiency problems of the measurement matrix. The results were compared with the multi-way multivariate curve resolution (MCR)-ALS results using hard and soft constraints to determine whether any advantages had been gained through using the weighted least squares function of NWAY P-ALS over the MCR-ALS resolution.

  1. Evaluation of Genetic Algorithm Concepts Using Model Problems. Part 2; Multi-Objective Optimization

    NASA Technical Reports Server (NTRS)

    Holst, Terry L.; Pulliam, Thomas H.

    2003-01-01

    A genetic algorithm approach suitable for solving multi-objective optimization problems is described and evaluated using a series of simple model problems. Several new features including a binning selection algorithm and a gene-space transformation procedure are included. The genetic algorithm is suitable for finding pareto optimal solutions in search spaces that are defined by any number of genes and that contain any number of local extrema. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all optimization problems attempted. The binning algorithm generally provides pareto front quality enhancements and moderate convergence efficiency improvements for most of the model problems. The gene-space transformation procedure provides a large convergence efficiency enhancement for problems with non-convoluted pareto fronts and a degradation in efficiency for problems with convoluted pareto fronts. The most difficult problems --multi-mode search spaces with a large number of genes and convoluted pareto fronts-- require a large number of function evaluations for GA convergence, but always converge.

  2. Optimization in First Semester Calculus: A Look at a Classic Problem

    ERIC Educational Resources Information Center

    LaRue, Renee; Infante, Nicole Engelke

    2015-01-01

    Optimization problems in first semester calculus have historically been a challenge for students. Focusing on the classic optimization problem of finding the minimum amount of fencing required to enclose a fixed area, we examine students' activity through the lens of Tall and Vinner's concept image and Carlson and Bloom's multidimensional…

  3. Optimal Planning and Problem-Solving

    NASA Technical Reports Server (NTRS)

    Clemet, Bradley; Schaffer, Steven; Rabideau, Gregg

    2008-01-01

    CTAEMS MDP Optimal Planner is a problem-solving software designed to command a single spacecraft/rover, or a team of spacecraft/rovers, to perform the best action possible at all times according to an abstract model of the spacecraft/rover and its environment. It also may be useful in solving logistical problems encountered in commercial applications such as shipping and manufacturing. The planner reasons around uncertainty according to specified probabilities of outcomes using a plan hierarchy to avoid exploring certain kinds of suboptimal actions. Also, planned actions are calculated as the state-action space is expanded, rather than afterward, to reduce by an order of magnitude the processing time and memory used. The software solves planning problems with actions that can execute concurrently, that have uncertain duration and quality, and that have functional dependencies on others that affect quality. These problems are modeled in a hierarchical planning language called C_TAEMS, a derivative of the TAEMS language for specifying domains for the DARPA Coordinators program. In realistic environments, actions often have uncertain outcomes and can have complex relationships with other tasks. The planner approaches problems by considering all possible actions that may be taken from any state reachable from a given, initial state, and from within the constraints of a given task hierarchy that specifies what tasks may be performed by which team member.

  4. Optimization of multi-objective integrated process planning and scheduling problem using a priority based optimization algorithm

    NASA Astrophysics Data System (ADS)

    Ausaf, Muhammad Farhan; Gao, Liang; Li, Xinyu

    2015-12-01

    For increasing the overall performance of modern manufacturing systems, effective integration of process planning and scheduling functions has been an important area of consideration among researchers. Owing to the complexity of handling process planning and scheduling simultaneously, most of the research work has been limited to solving the integrated process planning and scheduling (IPPS) problem for a single objective function. As there are many conflicting objectives when dealing with process planning and scheduling, real world problems cannot be fully captured considering only a single objective for optimization. Therefore considering multi-objective IPPS (MOIPPS) problem is inevitable. Unfortunately, only a handful of research papers are available on solving MOIPPS problem. In this paper, an optimization algorithm for solving MOIPPS problem is presented. The proposed algorithm uses a set of dispatching rules coupled with priority assignment to optimize the IPPS problem for various objectives like makespan, total machine load, total tardiness, etc. A fixed sized external archive coupled with a crowding distance mechanism is used to store and maintain the non-dominated solutions. To compare the results with other algorithms, a C-matric based method has been used. Instances from four recent papers have been solved to demonstrate the effectiveness of the proposed algorithm. The experimental results show that the proposed method is an efficient approach for solving the MOIPPS problem.

  5. Multigrid one shot methods for optimal control problems: Infinite dimensional control

    NASA Technical Reports Server (NTRS)

    Arian, Eyal; Taasan, Shlomo

    1994-01-01

    The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.

  6. Discrete Bat Algorithm for Optimal Problem of Permutation Flow Shop Scheduling

    PubMed Central

    Luo, Qifang; Zhou, Yongquan; Xie, Jian; Ma, Mingzhi; Li, Liangliang

    2014-01-01

    A discrete bat algorithm (DBA) is proposed for optimal permutation flow shop scheduling problem (PFSP). Firstly, the discrete bat algorithm is constructed based on the idea of basic bat algorithm, which divide whole scheduling problem into many subscheduling problems and then NEH heuristic be introduced to solve subscheduling problem. Secondly, some subsequences are operated with certain probability in the pulse emission and loudness phases. An intensive virtual population neighborhood search is integrated into the discrete bat algorithm to further improve the performance. Finally, the experimental results show the suitability and efficiency of the present discrete bat algorithm for optimal permutation flow shop scheduling problem. PMID:25243220

  7. Discrete bat algorithm for optimal problem of permutation flow shop scheduling.

    PubMed

    Luo, Qifang; Zhou, Yongquan; Xie, Jian; Ma, Mingzhi; Li, Liangliang

    2014-01-01

    A discrete bat algorithm (DBA) is proposed for optimal permutation flow shop scheduling problem (PFSP). Firstly, the discrete bat algorithm is constructed based on the idea of basic bat algorithm, which divide whole scheduling problem into many subscheduling problems and then NEH heuristic be introduced to solve subscheduling problem. Secondly, some subsequences are operated with certain probability in the pulse emission and loudness phases. An intensive virtual population neighborhood search is integrated into the discrete bat algorithm to further improve the performance. Finally, the experimental results show the suitability and efficiency of the present discrete bat algorithm for optimal permutation flow shop scheduling problem.

  8. Analysis of a Two-Dimensional Thermal Cloaking Problem on the Basis of Optimization

    NASA Astrophysics Data System (ADS)

    Alekseev, G. V.

    2018-04-01

    For a two-dimensional model of thermal scattering, inverse problems arising in the development of tools for cloaking material bodies on the basis of a mixed thermal cloaking strategy are considered. By applying the optimization approach, these problems are reduced to optimization ones in which the role of controls is played by variable parameters of the medium occupying the cloaking shell and by the heat flux through a boundary segment of the basic domain. The solvability of the direct and optimization problems is proved, and an optimality system is derived. Based on its analysis, sufficient conditions on the input data are established that ensure the uniqueness and stability of optimal solutions.

  9. Designing area optimized application-specific network-on-chip architectures while providing hard QoS guarantees.

    PubMed

    Khawaja, Sajid Gul; Mushtaq, Mian Hamza; Khan, Shoab A; Akram, M Usman; Jamal, Habib Ullah

    2015-01-01

    With the increase of transistors' density, popularity of System on Chip (SoC) has increased exponentially. As a communication module for SoC, Network on Chip (NoC) framework has been adapted as its backbone. In this paper, we propose a methodology for designing area-optimized application specific NoC while providing hard Quality of Service (QoS) guarantees for real time flows. The novelty of the proposed system lies in derivation of a Mixed Integer Linear Programming model which is then used to generate a resource optimal Network on Chip (NoC) topology and architecture while considering traffic and QoS requirements. We also present the micro-architectural design features used for enabling traffic and latency guarantees and discuss how the solution adapts for dynamic variations in the application traffic. The paper highlights the effectiveness of proposed method by generating resource efficient NoC solutions for both industrial and benchmark applications. The area-optimized results are generated in few seconds by proposed technique, without resorting to heuristics, even for an application with 48 traffic flows.

  10. Designing Area Optimized Application-Specific Network-On-Chip Architectures while Providing Hard QoS Guarantees

    PubMed Central

    Khawaja, Sajid Gul; Mushtaq, Mian Hamza; Khan, Shoab A.; Akram, M. Usman; Jamal, Habib ullah

    2015-01-01

    With the increase of transistors' density, popularity of System on Chip (SoC) has increased exponentially. As a communication module for SoC, Network on Chip (NoC) framework has been adapted as its backbone. In this paper, we propose a methodology for designing area-optimized application specific NoC while providing hard Quality of Service (QoS) guarantees for real time flows. The novelty of the proposed system lies in derivation of a Mixed Integer Linear Programming model which is then used to generate a resource optimal Network on Chip (NoC) topology and architecture while considering traffic and QoS requirements. We also present the micro-architectural design features used for enabling traffic and latency guarantees and discuss how the solution adapts for dynamic variations in the application traffic. The paper highlights the effectiveness of proposed method by generating resource efficient NoC solutions for both industrial and benchmark applications. The area-optimized results are generated in few seconds by proposed technique, without resorting to heuristics, even for an application with 48 traffic flows. PMID:25898016

  11. Improved multi-objective ant colony optimization algorithm and its application in complex reasoning

    NASA Astrophysics Data System (ADS)

    Wang, Xinqing; Zhao, Yang; Wang, Dong; Zhu, Huijie; Zhang, Qing

    2013-09-01

    The problem of fault reasoning has aroused great concern in scientific and engineering fields. However, fault investigation and reasoning of complex system is not a simple reasoning decision-making problem. It has become a typical multi-constraint and multi-objective reticulate optimization decision-making problem under many influencing factors and constraints. So far, little research has been carried out in this field. This paper transforms the fault reasoning problem of complex system into a paths-searching problem starting from known symptoms to fault causes. Three optimization objectives are considered simultaneously: maximum probability of average fault, maximum average importance, and minimum average complexity of test. Under the constraints of both known symptoms and the causal relationship among different components, a multi-objective optimization mathematical model is set up, taking minimizing cost of fault reasoning as the target function. Since the problem is non-deterministic polynomial-hard(NP-hard), a modified multi-objective ant colony algorithm is proposed, in which a reachability matrix is set up to constrain the feasible search nodes of the ants and a new pseudo-random-proportional rule and a pheromone adjustment mechinism are constructed to balance conflicts between the optimization objectives. At last, a Pareto optimal set is acquired. Evaluation functions based on validity and tendency of reasoning paths are defined to optimize noninferior set, through which the final fault causes can be identified according to decision-making demands, thus realize fault reasoning of the multi-constraint and multi-objective complex system. Reasoning results demonstrate that the improved multi-objective ant colony optimization(IMACO) can realize reasoning and locating fault positions precisely by solving the multi-objective fault diagnosis model, which provides a new method to solve the problem of multi-constraint and multi-objective fault diagnosis and

  12. Analysis of Hard Thin Film Coating

    NASA Technical Reports Server (NTRS)

    Shen, Dashen

    1998-01-01

    Marshall Space Flight Center (MSFC) is interested in developing hard thin film coating for bearings. The wearing of the bearing is an important problem for space flight engine. Hard thin film coating can drastically improve the surface of the bearing and improve the wear-endurance of the bearing. However, many fundamental problems in surface physics, plasma deposition, etc, need further research. The approach is using Electron Cyclotron Resonance Chemical Vapor Deposition (ECRCVD) to deposit hard thin film on stainless steel bearing. The thin films in consideration include SiC, SiN and other materials. An ECRCVD deposition system is being assembled at MSFC.

  13. Analysis of Hard Thin Film Coating

    NASA Technical Reports Server (NTRS)

    Shen, Dashen

    1998-01-01

    MSFC is interested in developing hard thin film coating for bearings. The wearing of the bearing is an important problem for space flight engine. Hard thin film coating can drastically improve the surface of the bearing and improve the wear-endurance of the bearing. However, many fundamental problems in surface physics, plasma deposition, etc, need further research. The approach is using electron cyclotron resonance chemical vapor deposition (ECRCVD) to deposit hard thin film an stainless steel bearing. The thin films in consideration include SiC, SiN and other materials. An ECRCVD deposition system is being assembled at MSFC.

  14. Theoretical Analysis of Local Search and Simple Evolutionary Algorithms for the Generalized Travelling Salesperson Problem.

    PubMed

    Pourhassan, Mojgan; Neumann, Frank

    2018-06-22

    The generalized travelling salesperson problem is an important NP-hard combinatorial optimization problem for which meta-heuristics, such as local search and evolutionary algorithms, have been used very successfully. Two hierarchical approaches with different neighbourhood structures, namely a Cluster-Based approach and a Node-Based approach, have been proposed by Hu and Raidl (2008) for solving this problem. In this paper, local search algorithms and simple evolutionary algorithms based on these approaches are investigated from a theoretical perspective. For local search algorithms, we point out the complementary abilities of the two approaches by presenting instances where they mutually outperform each other. Afterwards, we introduce an instance which is hard for both approaches when initialized on a particular point of the search space, but where a variable neighbourhood search combining them finds the optimal solution in polynomial time. Then we turn our attention to analysing the behaviour of simple evolutionary algorithms that use these approaches. We show that the Node-Based approach solves the hard instance of the Cluster-Based approach presented in Corus et al. (2016) in polynomial time. Furthermore, we prove an exponential lower bound on the optimization time of the Node-Based approach for a class of Euclidean instances.

  15. Application of Particle Swarm Optimization Algorithm in the Heating System Planning Problem

    PubMed Central

    Ma, Rong-Jiang; Yu, Nan-Yang; Hu, Jun-Yi

    2013-01-01

    Based on the life cycle cost (LCC) approach, this paper presents an integral mathematical model and particle swarm optimization (PSO) algorithm for the heating system planning (HSP) problem. The proposed mathematical model minimizes the cost of heating system as the objective for a given life cycle time. For the particularity of HSP problem, the general particle swarm optimization algorithm was improved. An actual case study was calculated to check its feasibility in practical use. The results show that the improved particle swarm optimization (IPSO) algorithm can more preferably solve the HSP problem than PSO algorithm. Moreover, the results also present the potential to provide useful information when making decisions in the practical planning process. Therefore, it is believed that if this approach is applied correctly and in combination with other elements, it can become a powerful and effective optimization tool for HSP problem. PMID:23935429

  16. Genetic algorithm parameters tuning for resource-constrained project scheduling problem

    NASA Astrophysics Data System (ADS)

    Tian, Xingke; Yuan, Shengrui

    2018-04-01

    Project Scheduling Problem (RCPSP) is a kind of important scheduling problem. To achieve a certain optimal goal such as the shortest duration, the smallest cost, the resource balance and so on, it is required to arrange the start and finish of all tasks under the condition of satisfying project timing constraints and resource constraints. In theory, the problem belongs to the NP-hard problem, and the model is abundant. Many combinatorial optimization problems are special cases of RCPSP, such as job shop scheduling, flow shop scheduling and so on. At present, the genetic algorithm (GA) has been used to deal with the classical RCPSP problem and achieved remarkable results. Vast scholars have also studied the improved genetic algorithm for the RCPSP problem, which makes it to solve the RCPSP problem more efficiently and accurately. However, for the selection of the main parameters of the genetic algorithm, there is no parameter optimization in these studies. Generally, we used the empirical method, but it cannot ensure to meet the optimal parameters. In this paper, the problem was carried out, which is the blind selection of parameters in the process of solving the RCPSP problem. We made sampling analysis, the establishment of proxy model and ultimately solved the optimal parameters.

  17. A Mixed Integer Linear Programming Approach to Electrical Stimulation Optimization Problems.

    PubMed

    Abouelseoud, Gehan; Abouelseoud, Yasmine; Shoukry, Amin; Ismail, Nour; Mekky, Jaidaa

    2018-02-01

    Electrical stimulation optimization is a challenging problem. Even when a single region is targeted for excitation, the problem remains a constrained multi-objective optimization problem. The constrained nature of the problem results from safety concerns while its multi-objectives originate from the requirement that non-targeted regions should remain unaffected. In this paper, we propose a mixed integer linear programming formulation that can successfully address the challenges facing this problem. Moreover, the proposed framework can conclusively check the feasibility of the stimulation goals. This helps researchers to avoid wasting time trying to achieve goals that are impossible under a chosen stimulation setup. The superiority of the proposed framework over alternative methods is demonstrated through simulation examples.

  18. Set-Based Discrete Particle Swarm Optimization Based on Decomposition for Permutation-Based Multiobjective Combinatorial Optimization Problems.

    PubMed

    Yu, Xue; Chen, Wei-Neng; Gu, Tianlong; Zhang, Huaxiang; Yuan, Huaqiang; Kwong, Sam; Zhang, Jun

    2018-07-01

    This paper studies a specific class of multiobjective combinatorial optimization problems (MOCOPs), namely the permutation-based MOCOPs. Many commonly seen MOCOPs, e.g., multiobjective traveling salesman problem (MOTSP), multiobjective project scheduling problem (MOPSP), belong to this problem class and they can be very different. However, as the permutation-based MOCOPs share the inherent similarity that the structure of their search space is usually in the shape of a permutation tree, this paper proposes a generic multiobjective set-based particle swarm optimization methodology based on decomposition, termed MS-PSO/D. In order to coordinate with the property of permutation-based MOCOPs, MS-PSO/D utilizes an element-based representation and a constructive approach. Through this, feasible solutions under constraints can be generated step by step following the permutation-tree-shaped structure. And problem-related heuristic information is introduced in the constructive approach for efficiency. In order to address the multiobjective optimization issues, the decomposition strategy is employed, in which the problem is converted into multiple single-objective subproblems according to a set of weight vectors. Besides, a flexible mechanism for diversity control is provided in MS-PSO/D. Extensive experiments have been conducted to study MS-PSO/D on two permutation-based MOCOPs, namely the MOTSP and the MOPSP. Experimental results validate that the proposed methodology is promising.

  19. A constraint optimization based virtual network mapping method

    NASA Astrophysics Data System (ADS)

    Li, Xiaoling; Guo, Changguo; Wang, Huaimin; Li, Zhendong; Yang, Zhiwen

    2013-03-01

    Virtual network mapping problem, maps different virtual networks onto the substrate network is an extremely challenging work. This paper proposes a constraint optimization based mapping method for solving virtual network mapping problem. This method divides the problem into two phases, node mapping phase and link mapping phase, which are all NP-hard problems. Node mapping algorithm and link mapping algorithm are proposed for solving node mapping phase and link mapping phase, respectively. Node mapping algorithm adopts the thinking of greedy algorithm, mainly considers two factors, available resources which are supplied by the nodes and distance between the nodes. Link mapping algorithm is based on the result of node mapping phase, adopts the thinking of distributed constraint optimization method, which can guarantee to obtain the optimal mapping with the minimum network cost. Finally, simulation experiments are used to validate the method, and results show that the method performs very well.

  20. An optimization method for the problems of thermal cloaking of material bodies

    NASA Astrophysics Data System (ADS)

    Alekseev, G. V.; Levin, V. A.

    2016-11-01

    Inverse heat-transfer problems related to constructing special thermal devices such as cloaking shells, thermal-illusion or thermal-camouflage devices, and heat-flux concentrators are studied. The heatdiffusion equation with a variable heat-conductivity coefficient is used as the initial heat-transfer model. An optimization method is used to reduce the above inverse problems to the respective control problem. The solvability of the above control problem is proved, an optimality system that describes necessary extremum conditions is derived, and a numerical algorithm for solving the control problem is proposed.

  1. Hybrid intelligent optimization methods for engineering problems

    NASA Astrophysics Data System (ADS)

    Pehlivanoglu, Yasin Volkan

    The purpose of optimization is to obtain the best solution under certain conditions. There are numerous optimization methods because different problems need different solution methodologies; therefore, it is difficult to construct patterns. Also mathematical modeling of a natural phenomenon is almost based on differentials. Differential equations are constructed with relative increments among the factors related to yield. Therefore, the gradients of these increments are essential to search the yield space. However, the landscape of yield is not a simple one and mostly multi-modal. Another issue is differentiability. Engineering design problems are usually nonlinear and they sometimes exhibit discontinuous derivatives for the objective and constraint functions. Due to these difficulties, non-gradient-based algorithms have become more popular in recent decades. Genetic algorithms (GA) and particle swarm optimization (PSO) algorithms are popular, non-gradient based algorithms. Both are population-based search algorithms and have multiple points for initiation. A significant difference from a gradient-based method is the nature of the search methodologies. For example, randomness is essential for the search in GA or PSO. Hence, they are also called stochastic optimization methods. These algorithms are simple, robust, and have high fidelity. However, they suffer from similar defects, such as, premature convergence, less accuracy, or large computational time. The premature convergence is sometimes inevitable due to the lack of diversity. As the generations of particles or individuals in the population evolve, they may lose their diversity and become similar to each other. To overcome this issue, we studied the diversity concept in GA and PSO algorithms. Diversity is essential for a healthy search, and mutations are the basic operators to provide the necessary variety within a population. After having a close scrutiny of the diversity concept based on qualification and

  2. The 2-D magnetotelluric inverse problem solved with optimization

    NASA Astrophysics Data System (ADS)

    van Beusekom, Ashley E.; Parker, Robert L.; Bank, Randolph E.; Gill, Philip E.; Constable, Steven

    2011-02-01

    The practical 2-D magnetotelluric inverse problem seeks to determine the shallow-Earth conductivity structure using finite and uncertain data collected on the ground surface. We present an approach based on using PLTMG (Piecewise Linear Triangular MultiGrid), a special-purpose code for optimization with second-order partial differential equation (PDE) constraints. At each frequency, the electromagnetic field and conductivity are treated as unknowns in an optimization problem in which the data misfit is minimized subject to constraints that include Maxwell's equations and the boundary conditions. Within this framework it is straightforward to accommodate upper and lower bounds or other conditions on the conductivity. In addition, as the underlying inverse problem is ill-posed, constraints may be used to apply various kinds of regularization. We discuss some of the advantages and difficulties associated with using PDE-constrained optimization as the basis for solving large-scale nonlinear geophysical inverse problems. Combined transverse electric and transverse magnetic complex admittances from the COPROD2 data are inverted. First, we invert penalizing size and roughness giving solutions that are similar to those found previously. In a second example, conventional regularization is replaced by a technique that imposes upper and lower bounds on the model. In both examples the data misfit is better than that obtained previously, without any increase in model complexity.

  3. 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.

  4. A Measure Approximation for Distributionally Robust PDE-Constrained Optimization Problems

    DOE PAGES

    Kouri, Drew Philip

    2017-12-19

    In numerous applications, scientists and engineers acquire varied forms of data that partially characterize the inputs to an underlying physical system. This data is then used to inform decisions such as controls and designs. Consequently, it is critical that the resulting control or design is robust to the inherent uncertainties associated with the unknown probabilistic characterization of the model inputs. Here in this work, we consider optimal control and design problems constrained by partial differential equations with uncertain inputs. We do not assume a known probabilistic model for the inputs, but rather we formulate the problem as a distributionally robustmore » optimization problem where the outer minimization problem determines the control or design, while the inner maximization problem determines the worst-case probability measure that matches desired characteristics of the data. We analyze the inner maximization problem in the space of measures and introduce a novel measure approximation technique, based on the approximation of continuous functions, to discretize the unknown probability measure. Finally, we prove consistency of our approximated min-max problem and conclude with numerical results.« less

  5. L^1 -optimality conditions for the circular restricted three-body problem

    NASA Astrophysics Data System (ADS)

    Chen, Zheng

    2016-11-01

    In this paper, the L^1 -minimization for the translational motion of a spacecraft in the circular restricted three-body problem (CRTBP) is considered. Necessary conditions are derived by using the Pontryagin Maximum Principle (PMP), revealing the existence of bang-bang and singular controls. Singular extremals are analyzed, recalling the existence of the Fuller phenomenon according to the theories developed in (Marchal in J Optim Theory Appl 11(5):441-486, 1973; Zelikin and Borisov in Theory of Chattering Control with Applications to Astronautics, Robotics, Economics, and Engineering. Birkhäuser, Basal 1994; in J Math Sci 114(3):1227-1344, 2003). The sufficient optimality conditions for the L^1 -minimization problem with fixed endpoints have been developed in (Chen et al. in SIAM J Control Optim 54(3):1245-1265, 2016). In the current paper, we establish second-order conditions for optimal control problems with more general final conditions defined by a smooth submanifold target. In addition, the numerical implementation to check these optimality conditions is given. Finally, approximating the Earth-Moon-Spacecraft system by the CRTBP, an L^1 -minimization trajectory for the translational motion of a spacecraft is computed by combining a shooting method with a continuation method in (Caillau et al. in Celest Mech Dyn Astron 114:137-150, 2012; Caillau and Daoud in SIAM J Control Optim 50(6):3178-3202, 2012). The local optimality of the computed trajectory is asserted thanks to the second-order optimality conditions developed.

  6. Parallel-vector computation for structural analysis and nonlinear unconstrained optimization problems

    NASA Technical Reports Server (NTRS)

    Nguyen, Duc T.

    1990-01-01

    Practical engineering application can often be formulated in the form of a constrained optimization problem. There are several solution algorithms for solving a constrained optimization problem. One approach is to convert a constrained problem into a series of unconstrained problems. Furthermore, unconstrained solution algorithms can be used as part of the constrained solution algorithms. Structural optimization is an iterative process where one starts with an initial design, a finite element structure analysis is then performed to calculate the response of the system (such as displacements, stresses, eigenvalues, etc.). Based upon the sensitivity information on the objective and constraint functions, an optimizer such as ADS or IDESIGN, can be used to find the new, improved design. For the structural analysis phase, the equation solver for the system of simultaneous, linear equations plays a key role since it is needed for either static, or eigenvalue, or dynamic analysis. For practical, large-scale structural analysis-synthesis applications, computational time can be excessively large. Thus, it is necessary to have a new structural analysis-synthesis code which employs new solution algorithms to exploit both parallel and vector capabilities offered by modern, high performance computers such as the Convex, Cray-2 and Cray-YMP computers. The objective of this research project is, therefore, to incorporate the latest development in the parallel-vector equation solver, PVSOLVE into the widely popular finite-element production code, such as the SAP-4. Furthermore, several nonlinear unconstrained optimization subroutines have also been developed and tested under a parallel computer environment. The unconstrained optimization subroutines are not only useful in their own right, but they can also be incorporated into a more popular constrained optimization code, such as ADS.

  7. Multimaterial topology optimization of contact problems using phase field regularization

    NASA Astrophysics Data System (ADS)

    Myśliński, Andrzej

    2018-01-01

    The numerical method to solve multimaterial topology optimization problems for elastic bodies in unilateral contact with Tresca friction is developed in the paper. The displacement of the elastic body in contact is governed by elliptic equation with inequality boundary conditions. The body is assumed to consists from more than two distinct isotropic elastic materials. The materials distribution function is chosen as the design variable. Since high contact stress appears during the contact phenomenon the aim of the structural optimization problem is to find such topology of the domain occupied by the body that the normal contact stress along the boundary of the body is minimized. The original cost functional is regularized using the multiphase volume constrained Ginzburg-Landau energy functional rather than the perimeter functional. The first order necessary optimality condition is recalled and used to formulate the generalized gradient flow equations of Allen-Cahn type. The optimal topology is obtained as the steady state of the phase transition governed by the generalized Allen-Cahn equation. As the interface width parameter tends to zero the transition of the phase field model to the level set model is studied. The optimization problem is solved numerically using the operator splitting approach combined with the projection gradient method. Numerical examples confirming the applicability of the proposed method are provided and discussed.

  8. Neighboring extremals of dynamic optimization problems with path equality constraints

    NASA Technical Reports Server (NTRS)

    Lee, A. Y.

    1988-01-01

    Neighboring extremals of dynamic optimization problems with path equality constraints and with an unknown parameter vector are considered in this paper. With some simplifications, the problem is reduced to solving a linear, time-varying two-point boundary-value problem with integral path equality constraints. A modified backward sweep method is used to solve this problem. Two example problems are solved to illustrate the validity and usefulness of the solution technique.

  9. A methodology to find the elementary landscape decomposition of combinatorial optimization problems.

    PubMed

    Chicano, Francisco; Whitley, L Darrell; Alba, Enrique

    2011-01-01

    A small number of combinatorial optimization problems have search spaces that correspond to elementary landscapes, where the objective function f is an eigenfunction of the Laplacian that describes the neighborhood structure of the search space. Many problems are not elementary; however, the objective function of a combinatorial optimization problem can always be expressed as a superposition of multiple elementary landscapes if the underlying neighborhood used is symmetric. This paper presents theoretical results that provide the foundation for algebraic methods that can be used to decompose the objective function of an arbitrary combinatorial optimization problem into a sum of subfunctions, where each subfunction is an elementary landscape. Many steps of this process can be automated, and indeed a software tool could be developed that assists the researcher in finding a landscape decomposition. This methodology is then used to show that the subset sum problem is a superposition of two elementary landscapes, and to show that the quadratic assignment problem is a superposition of three elementary landscapes.

  10. Evaluation of Genetic Algorithm Concepts using Model Problems. Part 1; Single-Objective Optimization

    NASA Technical Reports Server (NTRS)

    Holst, Terry L.; Pulliam, Thomas H.

    2003-01-01

    A genetic-algorithm-based optimization approach is described and evaluated using a simple hill-climbing model problem. The model problem utilized herein allows for the broad specification of a large number of search spaces including spaces with an arbitrary number of genes or decision variables and an arbitrary number hills or modes. In the present study, only single objective problems are considered. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all problems attempted. The most difficult problems - those with large hyper-volumes and multi-mode search spaces containing a large number of genes - require a large number of function evaluations for GA convergence, but they always converge.

  11. Pseudo-time methods for constrained optimization problems governed by PDE

    NASA Technical Reports Server (NTRS)

    Taasan, Shlomo

    1995-01-01

    In this paper we present a novel method for solving optimization problems governed by partial differential equations. Existing methods are gradient information in marching toward the minimum, where the constrained PDE is solved once (sometimes only approximately) per each optimization step. Such methods can be viewed as a marching techniques on the intersection of the state and costate hypersurfaces while improving the residuals of the design equations per each iteration. In contrast, the method presented here march on the design hypersurface and at each iteration improve the residuals of the state and costate equations. The new method is usually much less expensive per iteration step since, in most problems of practical interest, the design equation involves much less unknowns that that of either the state or costate equations. Convergence is shown using energy estimates for the evolution equations governing the iterative process. Numerical tests show that the new method allows the solution of the optimization problem in a cost of solving the analysis problems just a few times, independent of the number of design parameters. The method can be applied using single grid iterations as well as with multigrid solvers.

  12. Relaxations to Sparse Optimization Problems and Applications

    NASA Astrophysics Data System (ADS)

    Skau, Erik West

    Parsimony is a fundamental property that is applied to many characteristics in a variety of fields. Of particular interest are optimization problems that apply rank, dimensionality, or support in a parsimonious manner. In this thesis we study some optimization problems and their relaxations, and focus on properties and qualities of the solutions of these problems. The Gramian tensor decomposition problem attempts to decompose a symmetric tensor as a sum of rank one tensors.We approach the Gramian tensor decomposition problem with a relaxation to a semidefinite program. We study conditions which ensure that the solution of the relaxed semidefinite problem gives the minimal Gramian rank decomposition. Sparse representations with learned dictionaries are one of the leading image modeling techniques for image restoration. When learning these dictionaries from a set of training images, the sparsity parameter of the dictionary learning algorithm strongly influences the content of the dictionary atoms.We describe geometrically the content of trained dictionaries and how it changes with the sparsity parameter.We use statistical analysis to characterize how the different content is used in sparse representations. Finally, a method to control the structure of the dictionaries is demonstrated, allowing us to learn a dictionary which can later be tailored for specific applications. Variations of dictionary learning can be broadly applied to a variety of applications.We explore a pansharpening problem with a triple factorization variant of coupled dictionary learning. Another application of dictionary learning is computer vision. Computer vision relies heavily on object detection, which we explore with a hierarchical convolutional dictionary learning model. Data fusion of disparate modalities is a growing topic of interest.We do a case study to demonstrate the benefit of using social media data with satellite imagery to estimate hazard extents. In this case study analysis we

  13. Control and System Theory, Optimization, Inverse and Ill-Posed Problems

    DTIC Science & Technology

    1988-09-14

    Justlfleatlen Distribut ion/ Availability Codes # AFOSR-87-0350 Avat’ and/or1987-1988 Dist Special *CONTROL AND SYSTEM THEORY , ~ * OPTIMIZATION, * INVERSE...considerable va- riety of research investigations within the grant areas (Control and system theory , Optimization, and Ill-posed problems]. The

  14. Quantum Heterogeneous Computing for Satellite Positioning Optimization

    NASA Astrophysics Data System (ADS)

    Bass, G.; Kumar, V.; Dulny, J., III

    2016-12-01

    Hard optimization problems occur in many fields of academic study and practical situations. We present results in which quantum heterogeneous computing is used to solve a real-world optimization problem: satellite positioning. Optimization problems like this can scale very rapidly with problem size, and become unsolvable with traditional brute-force methods. Typically, such problems have been approximately solved with heuristic approaches; however, these methods can take a long time to calculate and are not guaranteed to find optimal solutions. Quantum computing offers the possibility of producing significant speed-up and improved solution quality. There are now commercially available quantum annealing (QA) devices that are designed to solve difficult optimization problems. These devices have 1000+ quantum bits, but they have significant hardware size and connectivity limitations. We present a novel heterogeneous computing stack that combines QA and classical machine learning and allows the use of QA on problems larger than the quantum hardware could solve in isolation. We begin by analyzing the satellite positioning problem with a heuristic solver, the genetic algorithm. The classical computer's comparatively large available memory can explore the full problem space and converge to a solution relatively close to the true optimum. The QA device can then evolve directly to the optimal solution within this more limited space. Preliminary experiments, using the Quantum Monte Carlo (QMC) algorithm to simulate QA hardware, have produced promising results. Working with problem instances with known global minima, we find a solution within 8% in a matter of seconds, and within 5% in a few minutes. Future studies include replacing QMC with commercially available quantum hardware and exploring more problem sets and model parameters. Our results have important implications for how heterogeneous quantum computing can be used to solve difficult optimization problems in any

  15. 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.

  16. Multiple shooting algorithms for jump-discontinuous problems in optimal control and estimation

    NASA Technical Reports Server (NTRS)

    Mook, D. J.; Lew, Jiann-Shiun

    1991-01-01

    Multiple shooting algorithms are developed for jump-discontinuous two-point boundary value problems arising in optimal control and optimal estimation. Examples illustrating the origin of such problems are given to motivate the development of the solution algorithms. The algorithms convert the necessary conditions, consisting of differential equations and transversality conditions, into algebraic equations. The solution of the algebraic equations provides exact solutions for linear problems. The existence and uniqueness of the solution are proved.

  17. Hierarchical optimization for neutron scattering problems

    DOE PAGES

    Bao, Feng; Archibald, Rick; Bansal, Dipanshu; ...

    2016-03-14

    In this study, we present a scalable optimization method for neutron scattering problems that determines confidence regions of simulation parameters in lattice dynamics models used to fit neutron scattering data for crystalline solids. The method uses physics-based hierarchical dimension reduction in both the computational simulation domain and the parameter space. We demonstrate for silicon that after a few iterations the method converges to parameters values (interatomic force-constants) computed with density functional theory simulations.

  18. Hierarchical optimization for neutron scattering problems

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

    Bao, Feng; Archibald, Rick; Bansal, Dipanshu

    In this study, we present a scalable optimization method for neutron scattering problems that determines confidence regions of simulation parameters in lattice dynamics models used to fit neutron scattering data for crystalline solids. The method uses physics-based hierarchical dimension reduction in both the computational simulation domain and the parameter space. We demonstrate for silicon that after a few iterations the method converges to parameters values (interatomic force-constants) computed with density functional theory simulations.

  19. IPDO-2007: Inverse Problems, Design and Optimization Symposium

    DTIC Science & Technology

    2007-08-01

    Kanevce, G. H., Kanevce, Lj. P., and Mitrevski , V. B.), International Symposium on Inverse Problems, Design and Optimization (IPDO-2007), (eds...107 Gligor Kanevce Ljubica Kanevce Vangelce Mitrevski George Dulikravich 108 Gligor Kanevce Ljubica Kanevce Igor Andreevski George Dulikravich

  20. Multiswarm comprehensive learning particle swarm optimization for solving multiobjective optimization problems.

    PubMed

    Yu, Xiang; Zhang, Xueqing

    2017-01-01

    Comprehensive learning particle swarm optimization (CLPSO) is a powerful state-of-the-art single-objective metaheuristic. Extending from CLPSO, this paper proposes multiswarm CLPSO (MSCLPSO) for multiobjective optimization. MSCLPSO involves multiple swarms, with each swarm associated with a separate original objective. Each particle's personal best position is determined just according to the corresponding single objective. Elitists are stored externally. MSCLPSO differs from existing multiobjective particle swarm optimizers in three aspects. First, each swarm focuses on optimizing the associated objective using CLPSO, without learning from the elitists or any other swarm. Second, mutation is applied to the elitists and the mutation strategy appropriately exploits the personal best positions and elitists. Third, a modified differential evolution (DE) strategy is applied to some extreme and least crowded elitists. The DE strategy updates an elitist based on the differences of the elitists. The personal best positions carry useful information about the Pareto set, and the mutation and DE strategies help MSCLPSO discover the true Pareto front. Experiments conducted on various benchmark problems demonstrate that MSCLPSO can find nondominated solutions distributed reasonably over the true Pareto front in a single run.

  1. 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.

  2. Analytical and numerical analysis of inverse optimization problems: conditions of uniqueness and computational methods

    PubMed Central

    Zatsiorsky, Vladimir M.

    2011-01-01

    One of the key problems of motor control is the redundancy problem, in particular how the central nervous system (CNS) chooses an action out of infinitely many possible. A promising way to address this question is to assume that the choice is made based on optimization of a certain cost function. A number of cost functions have been proposed in the literature to explain performance in different motor tasks: from force sharing in grasping to path planning in walking. However, the problem of uniqueness of the cost function(s) was not addressed until recently. In this article, we analyze two methods of finding additive cost functions in inverse optimization problems with linear constraints, so-called linear-additive inverse optimization problems. These methods are based on the Uniqueness Theorem for inverse optimization problems that we proved recently (Terekhov et al., J Math Biol 61(3):423–453, 2010). Using synthetic data, we show that both methods allow for determining the cost function. We analyze the influence of noise on the both methods. Finally, we show how a violation of the conditions of the Uniqueness Theorem may lead to incorrect solutions of the inverse optimization problem. PMID:21311907

  3. Optimal birth control of age-dependent competitive species III. Overtaking problem

    NASA Astrophysics Data System (ADS)

    He, Ze-Rong; Cheng, Ji-Shu; Zhang, Chun-Guo

    2008-01-01

    A study is made of an overtaking optimal problem for a population system consisting of two competing species, which is controlled by fertilities. The existence of optimal policy is proved and a maximum principle is carefully derived under less restrictive conditions. Weak and strong turnpike properties of optimal trajectories are established.

  4. New numerical methods for open-loop and feedback solutions to dynamic optimization problems

    NASA Astrophysics Data System (ADS)

    Ghosh, Pradipto

    The topic of the first part of this research is trajectory optimization of dynamical systems via computational swarm intelligence. Particle swarm optimization is a nature-inspired heuristic search method that relies on a group of potential solutions to explore the fitness landscape. Conceptually, each particle in the swarm uses its own memory as well as the knowledge accumulated by the entire swarm to iteratively converge on an optimal or near-optimal solution. It is relatively straightforward to implement and unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although particle swarm optimization has been successfully employed in solving static optimization problems, its application in dynamic optimization, as posed in optimal control theory, is still relatively new. In the first half of this thesis particle swarm optimization is used to generate near-optimal solutions to several nontrivial trajectory optimization problems including thrust programming for minimum fuel, multi-burn spacecraft orbit transfer, and computing minimum-time rest-to-rest trajectories for a robotic manipulator. A distinct feature of the particle swarm optimization implementation in this work is the runtime selection of the optimal solution structure. Optimal trajectories are generated by solving instances of constrained nonlinear mixed-integer programming problems with the swarming technique. For each solved optimal programming problem, the particle swarm optimization result is compared with a nearly exact solution found via a direct method using nonlinear programming. Numerical experiments indicate that swarm search can locate solutions to very great accuracy. The second half of this research develops a new extremal-field approach for synthesizing nearly optimal feedback controllers for optimal control and two-player pursuit-evasion games described by general nonlinear differential equations. A notable revelation from this development

  5. Better Decomposition Heuristics for the Maximum-Weight Connected Graph Problem Using Betweenness Centrality

    NASA Astrophysics Data System (ADS)

    Yamamoto, Takanori; Bannai, Hideo; Nagasaki, Masao; Miyano, Satoru

    We present new decomposition heuristics for finding the optimal solution for the maximum-weight connected graph problem, which is known to be NP-hard. Previous optimal algorithms for solving the problem decompose the input graph into subgraphs using heuristics based on node degree. We propose new heuristics based on betweenness centrality measures, and show through computational experiments that our new heuristics tend to reduce the number of subgraphs in the decomposition, and therefore could lead to the reduction in computational time for finding the optimal solution. The method is further applied to analysis of biological pathway data.

  6. Double hard scattering without double counting

    NASA Astrophysics Data System (ADS)

    Diehl, Markus; Gaunt, Jonathan R.; Schönwald, Kay

    2017-06-01

    Double parton scattering in proton-proton collisions includes kinematic regions in which two partons inside a proton originate from the perturbative splitting of a single parton. This leads to a double counting problem between single and double hard scattering. We present a solution to this problem, which allows for the definition of double parton distributions as operator matrix elements in a proton, and which can be used at higher orders in perturbation theory. We show how the evaluation of double hard scattering in this framework can provide a rough estimate for the size of the higher-order contributions to single hard scattering that are affected by double counting. In a numeric study, we identify situations in which these higher-order contributions must be explicitly calculated and included if one wants to attain an accuracy at which double hard scattering becomes relevant, and other situations where such contributions may be neglected.

  7. A Decision Support System for Solving Multiple Criteria Optimization Problems

    ERIC Educational Resources Information Center

    Filatovas, Ernestas; Kurasova, Olga

    2011-01-01

    In this paper, multiple criteria optimization has been investigated. A new decision support system (DSS) has been developed for interactive solving of multiple criteria optimization problems (MOPs). The weighted-sum (WS) approach is implemented to solve the MOPs. The MOPs are solved by selecting different weight coefficient values for the criteria…

  8. A noisy chaotic neural network for solving combinatorial optimization problems: stochastic chaotic simulated annealing.

    PubMed

    Wang, Lipo; Li, Sa; Tian, Fuyu; Fu, Xiuju

    2004-10-01

    Recently Chen and Aihara have demonstrated both experimentally and mathematically that their chaotic simulated annealing (CSA) has better search ability for solving combinatorial optimization problems compared to both the Hopfield-Tank approach and stochastic simulated annealing (SSA). However, CSA may not find a globally optimal solution no matter how slowly annealing is carried out, because the chaotic dynamics are completely deterministic. In contrast, SSA tends to settle down to a global optimum if the temperature is reduced sufficiently slowly. Here we combine the best features of both SSA and CSA, thereby proposing a new approach for solving optimization problems, i.e., stochastic chaotic simulated annealing, by using a noisy chaotic neural network. We show the effectiveness of this new approach with two difficult combinatorial optimization problems, i.e., a traveling salesman problem and a channel assignment problem for cellular mobile communications.

  9. Approximation algorithms for the min-power symmetric connectivity problem

    NASA Astrophysics Data System (ADS)

    Plotnikov, Roman; Erzin, Adil; Mladenovic, Nenad

    2016-10-01

    We consider the NP-hard problem of synthesis of optimal spanning communication subgraph in a given arbitrary simple edge-weighted graph. This problem occurs in the wireless networks while minimizing the total transmission power consumptions. We propose several new heuristics based on the variable neighborhood search metaheuristic for the approximation solution of the problem. We have performed a numerical experiment where all proposed algorithms have been executed on the randomly generated test samples. For these instances, on average, our algorithms outperform the previously known heuristics.

  10. Comparison of optimized algorithms in facility location allocation problems with different distance measures

    NASA Astrophysics Data System (ADS)

    Kumar, Rakesh; Chandrawat, Rajesh Kumar; Garg, B. P.; Joshi, Varun

    2017-07-01

    Opening the new firm or branch with desired execution is very relevant to facility location problem. Along the lines to locate the new ambulances and firehouses, the government desires to minimize average response time for emergencies from all residents of cities. So finding the best location is biggest challenge in day to day life. These type of problems were named as facility location problems. A lot of algorithms have been developed to handle these problems. In this paper, we review five algorithms that were applied to facility location problems. The significance of clustering in facility location problems is also presented. First we compare Fuzzy c-means clustering (FCM) algorithm with alternating heuristic (AH) algorithm, then with Particle Swarm Optimization (PSO) algorithms using different type of distance function. The data was clustered with the help of FCM and then we apply median model and min-max problem model on that data. After finding optimized locations using these algorithms we find the distance from optimized location point to the demanded point with different distance techniques and compare the results. At last, we design a general example to validate the feasibility of the five algorithms for facilities location optimization, and authenticate the advantages and drawbacks of them.

  11. A hybrid heuristic for the multiple choice multidimensional knapsack problem

    NASA Astrophysics Data System (ADS)

    Mansi, Raïd; Alves, Cláudio; Valério de Carvalho, J. M.; Hanafi, Saïd

    2013-08-01

    In this article, a new solution approach for the multiple choice multidimensional knapsack problem is described. The problem is a variant of the multidimensional knapsack problem where items are divided into classes, and exactly one item per class has to be chosen. Both problems are NP-hard. However, the multiple choice multidimensional knapsack problem appears to be more difficult to solve in part because of its choice constraints. Many real applications lead to very large scale multiple choice multidimensional knapsack problems that can hardly be addressed using exact algorithms. A new hybrid heuristic is proposed that embeds several new procedures for this problem. The approach is based on the resolution of linear programming relaxations of the problem and reduced problems that are obtained by fixing some variables of the problem. The solutions of these problems are used to update the global lower and upper bounds for the optimal solution value. A new strategy for defining the reduced problems is explored, together with a new family of cuts and a reformulation procedure that is used at each iteration to improve the performance of the heuristic. An extensive set of computational experiments is reported for benchmark instances from the literature and for a large set of hard instances generated randomly. The results show that the approach outperforms other state-of-the-art methods described so far, providing the best known solution for a significant number of benchmark instances.

  12. Using Functional Assessment to Treat Behavior Problems of Deaf and Hard of Hearing Children Diagnosed with Autism Spectrum Disorder

    ERIC Educational Resources Information Center

    Zane, Thomas; Carlson, Mark; Estep, David; Quinn, Mike

    2013-01-01

    A defining feature of autism spectrum disorders is atypical behaviors, e.g., stereotypy, noncompliance, rituals, and aggression. Deaf and hard of hearing individuals with autism present a greater challenge because of additional issues related to their hearing status. One conceptualization of problem behavior is that it serves a communication…

  13. A neuropsychoanalytical approach to the hard problem of consciousness.

    PubMed

    Solms, Mark

    2014-06-01

    A neuropsychoanalytical approach to the hard problem of consciousness revolves around the distinction between the subject of consciousness and objects of consciousness. In contrast to the mainstream of cognitive science, neuropsychoanalysis prioritizes the subject. The subject of consciousness is the indispensable page upon which consciousness of objects is inscribed. This has implications for our conception of the mental. The subjective being of consciousness is not registered in the classical exteroceptive modalities; it is not merely a cognitive representation, not only a memory trace. Rather, the exteroceptive modalities are registered in the subjective being. Cognitive representations are mental solids embedded within subjectivity, the tangible and visible (etc) properties of which are projected onto reality. It is important to recognize that mental solids (e.g., the body-as-object) are no more real than the subjective being they are inscribed in (the body-as-subject). Moreover, pure subjectivity is not without content or quality. This aspect of consciousness is conventionally described quantitatively as the level of consciousness, or wakefulness. But it feels like something to be awake. The primary modality of this aspect of consciousness is affect. Affect supplies the subjectivity that underpins all consciousness. Some implications of this approach are discussed here, in broad brush strokes.

  14. 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

  15. An Optimization-Based Method for Feature Ranking in Nonlinear Regression Problems.

    PubMed

    Bravi, Luca; Piccialli, Veronica; Sciandrone, Marco

    2017-04-01

    In this paper, we consider the feature ranking problem, where, given a set of training instances, the task is to associate a score with the features in order to assess their relevance. Feature ranking is a very important tool for decision support systems, and may be used as an auxiliary step of feature selection to reduce the high dimensionality of real-world data. We focus on regression problems by assuming that the process underlying the generated data can be approximated by a continuous function (for instance, a feedforward neural network). We formally state the notion of relevance of a feature by introducing a minimum zero-norm inversion problem of a neural network, which is a nonsmooth, constrained optimization problem. We employ a concave approximation of the zero-norm function, and we define a smooth, global optimization problem to be solved in order to assess the relevance of the features. We present the new feature ranking method based on the solution of instances of the global optimization problem depending on the available training data. Computational experiments on both artificial and real data sets are performed, and point out that the proposed feature ranking method is a valid alternative to existing methods in terms of effectiveness. The obtained results also show that the method is costly in terms of CPU time, and this may be a limitation in the solution of large-dimensional problems.

  16. Solving quantum optimal control problems using Clebsch variables and Lin constraints

    NASA Astrophysics Data System (ADS)

    Delgado-Téllez, M.; Ibort, A.; Rodríguez de la Peña, T.

    2018-01-01

    Clebsch variables (and Lin constraints) are applied to the study of a class of optimal control problems for affine-controlled quantum systems. The optimal control problem will be modelled with controls defined on an auxiliary space where the dynamical group of the system acts freely. The reciprocity between both theories: the classical theory defined by the objective functional and the quantum system, is established by using a suitable version of Lagrange’s multipliers theorem and a geometrical interpretation of the constraints of the system as defining a subspace of horizontal curves in an associated bundle. It is shown how the solutions of the variational problem defined by the objective functional determine solutions of the quantum problem. Then a new way of obtaining explicit solutions for a family of optimal control problems for affine-controlled quantum systems (finite or infinite dimensional) is obtained. One of its main advantages, is the the use of Clebsch variables allows to compute such solutions from solutions of invariant problems that can often be computed explicitly. This procedure can be presented as an algorithm that can be applied to a large class of systems. Finally, some simple examples, spin control, a simple quantum Hamiltonian with an ‘Elroy beanie’ type classical model and a controlled one-dimensional quantum harmonic oscillator, illustrating the main features of the theory, will be discussed.

  17. Classification-Assisted Memetic Algorithms for Equality-Constrained Optimization Problems

    NASA Astrophysics Data System (ADS)

    Handoko, Stephanus Daniel; Kwoh, Chee Keong; Ong, Yew Soon

    Regressions has successfully been incorporated into memetic algorithm (MA) to build surrogate models for the objective or constraint landscape of optimization problems. This helps to alleviate the needs for expensive fitness function evaluations by performing local refinements on the approximated landscape. Classifications can alternatively be used to assist MA on the choice of individuals that would experience refinements. Support-vector-assisted MA were recently proposed to alleviate needs for function evaluations in the inequality-constrained optimization problems by distinguishing regions of feasible solutions from those of the infeasible ones based on some past solutions such that search efforts can be focussed on some potential regions only. For problems having equality constraints, however, the feasible space would obviously be extremely small. It is thus extremely difficult for the global search component of the MA to produce feasible solutions. Hence, the classification of feasible and infeasible space would become ineffective. In this paper, a novel strategy to overcome such limitation is proposed, particularly for problems having one and only one equality constraint. The raw constraint value of an individual, instead of its feasibility class, is utilized in this work.

  18. Multiple-variable neighbourhood search for the single-machine total weighted tardiness problem

    NASA Astrophysics Data System (ADS)

    Chung, Tsui-Ping; Fu, Qunjie; Liao, Ching-Jong; Liu, Yi-Ting

    2017-07-01

    The single-machine total weighted tardiness (SMTWT) problem is a typical discrete combinatorial optimization problem in the scheduling literature. This problem has been proved to be NP hard and thus provides a challenging area for metaheuristics, especially the variable neighbourhood search algorithm. In this article, a multiple variable neighbourhood search (m-VNS) algorithm with multiple neighbourhood structures is proposed to solve the problem. Special mechanisms named matching and strengthening operations are employed in the algorithm, which has an auto-revising local search procedure to explore the solution space beyond local optimality. Two aspects, searching direction and searching depth, are considered, and neighbourhood structures are systematically exchanged. Experimental results show that the proposed m-VNS algorithm outperforms all the compared algorithms in solving the SMTWT problem.

  19. Finite-time convergent recurrent neural network with a hard-limiting activation function for constrained optimization with piecewise-linear objective functions.

    PubMed

    Liu, Qingshan; Wang, Jun

    2011-04-01

    This paper presents a one-layer recurrent neural network for solving a class of constrained nonsmooth optimization problems with piecewise-linear objective functions. The proposed neural network is guaranteed to be globally convergent in finite time to the optimal solutions under a mild condition on a derived lower bound of a single gain parameter in the model. The number of neurons in the neural network is the same as the number of decision variables of the optimization problem. Compared with existing neural networks for optimization, the proposed neural network has a couple of salient features such as finite-time convergence and a low model complexity. Specific models for two important special cases, namely, linear programming and nonsmooth optimization, are also presented. In addition, applications to the shortest path problem and constrained least absolute deviation problem are discussed with simulation results to demonstrate the effectiveness and characteristics of the proposed neural network.

  20. Using the PORS Problems to Examine Evolutionary Optimization of Multiscale Systems

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

    Reinhart, Zachary; Molian, Vaelan; Bryden, Kenneth

    2013-01-01

    Nearly all systems of practical interest are composed of parts assembled across multiple scales. For example, an agrodynamic system is composed of flora and fauna on one scale; soil types, slope, and water runoff on another scale; and management practice and yield on another scale. Or consider an advanced coal-fired power plant: combustion and pollutant formation occurs on one scale, the plant components on another scale, and the overall performance of the power system is measured on another. In spite of this, there are few practical tools for the optimization of multiscale systems. This paper examines multiscale optimization of systemsmore » composed of discrete elements using the plus-one-recall-store (PORS) problem as a test case or study problem for multiscale systems. From this study, it is found that by recognizing the constraints and patterns present in discrete multiscale systems, the solution time can be significantly reduced and much more complex problems can be optimized.« less

  1. Finite Optimal Stopping Problems: The Seller's Perspective

    ERIC Educational Resources Information Center

    Hemmati, Mehdi; Smith, J. Cole

    2011-01-01

    We consider a version of an optimal stopping problem, in which a customer is presented with a finite set of items, one by one. The customer is aware of the number of items in the finite set and the minimum and maximum possible value of each item, and must purchase exactly one item. When an item is presented to the customer, she or he observes its…

  2. Optimizing Value and Avoiding Problems in Building Schools.

    ERIC Educational Resources Information Center

    Brevard County School Board, Cocoa, FL.

    This report describes school design and construction delivery processes used by the School Board of Brevard County (Cocoa, Florida) that help optimize value, avoid problems, and eliminate the cost of maintaining a large facility staff. The project phases are examined from project definition through design to construction. Project delivery…

  3. A deterministic global optimization using smooth diagonal auxiliary functions

    NASA Astrophysics Data System (ADS)

    Sergeyev, Yaroslav D.; Kvasov, Dmitri E.

    2015-04-01

    In many practical decision-making problems it happens that functions involved in optimization process are black-box with unknown analytical representations and hard to evaluate. In this paper, a global optimization problem is considered where both the goal function f (x) and its gradient f‧ (x) are black-box functions. It is supposed that f‧ (x) satisfies the Lipschitz condition over the search hyperinterval with an unknown Lipschitz constant K. A new deterministic 'Divide-the-Best' algorithm based on efficient diagonal partitions and smooth auxiliary functions is proposed in its basic version, its convergence conditions are studied and numerical experiments executed on eight hundred test functions are presented.

  4. Topology optimization for nonlinear dynamic problems: Considerations for automotive crashworthiness

    NASA Astrophysics Data System (ADS)

    Kaushik, Anshul; Ramani, Anand

    2014-04-01

    Crashworthiness of automotive structures is most often engineered after an optimal topology has been arrived at using other design considerations. This study is an attempt to incorporate crashworthiness requirements upfront in the topology synthesis process using a mathematically consistent framework. It proposes the use of equivalent linear systems from the nonlinear dynamic simulation in conjunction with a discrete-material topology optimizer. Velocity and acceleration constraints are consistently incorporated in the optimization set-up. Issues specific to crash problems due to the explicit solution methodology employed, nature of the boundary conditions imposed on the structure, etc. are discussed and possible resolutions are proposed. A demonstration of the methodology on two-dimensional problems that address some of the structural requirements and the types of loading typical of frontal and side impact is provided in order to show that this methodology has the potential for topology synthesis incorporating crashworthiness requirements.

  5. Optimality problem of network topology in stocks market analysis

    NASA Astrophysics Data System (ADS)

    Djauhari, Maman Abdurachman; Gan, Siew Lee

    2015-02-01

    Since its introduction fifteen years ago, minimal spanning tree has become an indispensible tool in econophysics. It is to filter the important economic information contained in a complex system of financial markets' commodities. Here we show that, in general, that tool is not optimal in terms of topological properties. Consequently, the economic interpretation of the filtered information might be misleading. To overcome that non-optimality problem, a set of criteria and a selection procedure of an optimal minimal spanning tree will be developed. By using New York Stock Exchange data, the advantages of the proposed method will be illustrated in terms of the power-law of degree distribution.

  6. The individual time trial as an optimal control problem

    PubMed Central

    de Jong, Jenny; Fokkink, Robbert; Olsder, Geert Jan; Schwab, AL

    2017-01-01

    In a cycling time trial, the rider needs to distribute his power output optimally to minimize the time between start and finish. Mathematically, this is an optimal control problem. Even for a straight and flat course, its solution is non-trivial and involves a singular control, which corresponds to a power that is slightly above the aerobic level. The rider must start at full anaerobic power to reach an optimal speed and maintain that speed for the rest of the course. If the course is flat but not straight, then the speed at which the rider can round the bends becomes crucial. PMID:29388631

  7. Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm

    PubMed Central

    Sidky, Emil Y.; Jørgensen, Jakob H.; Pan, Xiaochuan

    2012-01-01

    The primal-dual optimization algorithm developed in Chambolle and Pock (CP), 2011 is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems for the purpose of designing iterative image reconstruction algorithms for CT. The primal-dual algorithm is briefly summarized in the article, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application modeling breast CT with low-intensity X-ray illumination is presented. PMID:22538474

  8. Tunneling and speedup in quantum optimization for permutation-symmetric problems

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

    Muthukrishnan, Siddharth; Albash, Tameem; Lidar, Daniel A.

    Tunneling is often claimed to be the key mechanism underlying possible speedups in quantum optimization via quantum annealing (QA), especially for problems featuring a cost function with tall and thin barriers. We present and analyze several counterexamples from the class of perturbed Hamming weight optimization problems with qubit permutation symmetry. We first show that, for these problems, the adiabatic dynamics that make tunneling possible should be understood not in terms of the cost function but rather the semiclassical potential arising from the spin-coherent path-integral formalism. We then provide an example where the shape of the barrier in the final costmore » function is short and wide, which might suggest no quantum advantage for QA, yet where tunneling renders QA superior to simulated annealing in the adiabatic regime. However, the adiabatic dynamics turn out not be optimal. Instead, an evolution involving a sequence of diabatic transitions through many avoided-level crossings, involving no tunneling, is optimal and outperforms adiabatic QA. We show that this phenomenon of speedup by diabatic transitions is not unique to this example, and we provide an example where it provides an exponential speedup over adiabatic QA. In yet another twist, we show that a classical algorithm, spin-vector dynamics, is at least as efficient as diabatic QA. Lastly, in a different example with a convex cost function, the diabatic transitions result in a speedup relative to both adiabatic QA with tunneling and classical spin-vector dynamics.« less

  9. Tunneling and speedup in quantum optimization for permutation-symmetric problems

    DOE PAGES

    Muthukrishnan, Siddharth; Albash, Tameem; Lidar, Daniel A.

    2016-07-21

    Tunneling is often claimed to be the key mechanism underlying possible speedups in quantum optimization via quantum annealing (QA), especially for problems featuring a cost function with tall and thin barriers. We present and analyze several counterexamples from the class of perturbed Hamming weight optimization problems with qubit permutation symmetry. We first show that, for these problems, the adiabatic dynamics that make tunneling possible should be understood not in terms of the cost function but rather the semiclassical potential arising from the spin-coherent path-integral formalism. We then provide an example where the shape of the barrier in the final costmore » function is short and wide, which might suggest no quantum advantage for QA, yet where tunneling renders QA superior to simulated annealing in the adiabatic regime. However, the adiabatic dynamics turn out not be optimal. Instead, an evolution involving a sequence of diabatic transitions through many avoided-level crossings, involving no tunneling, is optimal and outperforms adiabatic QA. We show that this phenomenon of speedup by diabatic transitions is not unique to this example, and we provide an example where it provides an exponential speedup over adiabatic QA. In yet another twist, we show that a classical algorithm, spin-vector dynamics, is at least as efficient as diabatic QA. Lastly, in a different example with a convex cost function, the diabatic transitions result in a speedup relative to both adiabatic QA with tunneling and classical spin-vector dynamics.« less

  10. An Optimization Model for Scheduling Problems with Two-Dimensional Spatial Resource Constraint

    NASA Technical Reports Server (NTRS)

    Garcia, Christopher; Rabadi, Ghaith

    2010-01-01

    Traditional scheduling problems involve determining temporal assignments for a set of jobs in order to optimize some objective. Some scheduling problems also require the use of limited resources, which adds another dimension of complexity. In this paper we introduce a spatial resource-constrained scheduling problem that can arise in assembly, warehousing, cross-docking, inventory management, and other areas of logistics and supply chain management. This scheduling problem involves a twodimensional rectangular area as a limited resource. Each job, in addition to having temporal requirements, has a width and a height and utilizes a certain amount of space inside the area. We propose an optimization model for scheduling the jobs while respecting all temporal and spatial constraints.

  11. Provisional-Ideal-Point-Based Multi-objective Optimization Method for Drone Delivery Problem

    NASA Astrophysics Data System (ADS)

    Omagari, Hiroki; Higashino, Shin-Ichiro

    2018-04-01

    In this paper, we proposed a new evolutionary multi-objective optimization method for solving drone delivery problems (DDP). It can be formulated as a constrained multi-objective optimization problem. In our previous research, we proposed the "aspiration-point-based method" to solve multi-objective optimization problems. However, this method needs to calculate the optimal values of each objective function value in advance. Moreover, it does not consider the constraint conditions except for the objective functions. Therefore, it cannot apply to DDP which has many constraint conditions. To solve these issues, we proposed "provisional-ideal-point-based method." The proposed method defines a "penalty value" to search for feasible solutions. It also defines a new reference solution named "provisional-ideal point" to search for the preferred solution for a decision maker. In this way, we can eliminate the preliminary calculations and its limited application scope. The results of the benchmark test problems show that the proposed method can generate the preferred solution efficiently. The usefulness of the proposed method is also demonstrated by applying it to DDP. As a result, the delivery path when combining one drone and one truck drastically reduces the traveling distance and the delivery time compared with the case of using only one truck.

  12. Adapting Experiential Learning to Develop Problem-Solving Skills in Deaf and Hard-of-Hearing Engineering Students.

    PubMed

    Marshall, Matthew M; Carrano, Andres L; Dannels, Wendy A

    2016-10-01

    Individuals who are deaf and hard-of-hearing (DHH) are underrepresented in science, technology, engineering, and mathematics (STEM) professions, and this may be due in part to their level of preparation in the development and retention of mathematical and problem-solving skills. An approach was developed that incorporates experiential learning and best practices of STEM instruction to give first-year DHH students enrolled in a postsecondary STEM program the opportunity to develop problem-solving skills in real-world scenarios. Using an industrial engineering laboratory that provides manufacturing and warehousing environments, students were immersed in real-world scenarios in which they worked on teams to address prescribed problems encountered during the activities. The highly structured, Plan-Do-Check-Act approach commonly used in industry was adapted for the DHH student participants to document and communicate the problem-solving steps. Students who experienced the intervention realized a 14.6% improvement in problem-solving proficiency compared with a control group, and this gain was retained at 6 and 12 months, post-intervention. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

  13. Constraint Optimization Problem For The Cutting Of A Cobalt Chrome Refractory Material

    NASA Astrophysics Data System (ADS)

    Lebaal, Nadhir; Schlegel, Daniel; Folea, Milena

    2011-05-01

    This paper shows a complete approach to solve a given problem, from the experimentation to the optimization of different cutting parameters. In response to an industrial problem of slotting FSX 414, a Cobalt-based refractory material, we have implemented a design of experiment to determine the most influent parameters on the tool life, the surface roughness and the cutting forces. After theses trials, an optimization approach has been implemented to find the lowest manufacturing cost while respecting the roughness constraints and cutting force limitation constraints. The optimization approach is based on the Response Surface Method (RSM) using the Sequential Quadratic programming algorithm (SQP) for a constrained problem. To avoid a local optimum and to obtain an accurate solution at low cost, an efficient strategy, which allows improving the RSM accuracy in the vicinity of the global optimum, is presented. With these models and these trials, we could apply and compare our optimization methods in order to get the lowest cost for the best quality, i.e. a satisfying surface roughness and limited cutting forces.

  14. A linear programming approach to max-sum problem: a review.

    PubMed

    Werner, Tomás

    2007-07-01

    The max-sum labeling problem, defined as maximizing a sum of binary (i.e., pairwise) functions of discrete variables, is a general NP-hard optimization problem with many applications, such as computing the MAP configuration of a Markov random field. We review a not widely known approach to the problem, developed by Ukrainian researchers Schlesinger et al. in 1976, and show how it contributes to recent results, most importantly, those on the convex combination of trees and tree-reweighted max-product. In particular, we review Schlesinger et al.'s upper bound on the max-sum criterion, its minimization by equivalent transformations, its relation to the constraint satisfaction problem, the fact that this minimization is dual to a linear programming relaxation of the original problem, and the three kinds of consistency necessary for optimality of the upper bound. We revisit problems with Boolean variables and supermodular problems. We describe two algorithms for decreasing the upper bound. We present an example application for structural image analysis.

  15. Optimization to Develop Multiple Response Microstructure and Hardness of Ductile Iron Casting by using GRA

    NASA Astrophysics Data System (ADS)

    Kabnure, Bahubali Bhupal; Shinde, Vasudev Dhondiram; Kolhapure, Rakesh Ramchandra

    2018-05-01

    Ductile irons are important engineering materials because of its high strength to weight ratio and castability. The ductile iron castings are used widely for automobile applications due to their wide spectrum of property range. Weight reduction is important in automobile to improve its fuel efficiency which can be achieved by thinning down the casting sections without altering its functionality. Generally, automobile castings are having varying section thickness. Varying thickness castings offers different cooling rates while solidification of the casting. The solidification cooling rate decides the final microstructure of the cast components. Cooling rate was found to affect directly the amount of pearlite and ultimately the as cast properties in varying thickness ductile iron castings. In view of this, the automobile impeller casting is selected for study in the present work as it consists of varying section thickness in which small sections are connected to central hub. The casting solidification simulations were performed and analyzed. The solidification cooling rates were analyzed further to correlate the experimental processing parameters. The samples from poured castings were analyzed for microstructure and hardness at different section thickness. Multiple response optimization of microstructure and hardness was carried out by combined Taguchi and Grey Relational Analysis (GRA). Contribution of input variables on the output variables is attained using ANOVA.

  16. A linear decomposition method for large optimization problems. Blueprint for development

    NASA Technical Reports Server (NTRS)

    Sobieszczanski-Sobieski, J.

    1982-01-01

    A method is proposed for decomposing large optimization problems encountered in the design of engineering systems such as an aircraft into a number of smaller subproblems. The decomposition is achieved by organizing the problem and the subordinated subproblems in a tree hierarchy and optimizing each subsystem separately. Coupling of the subproblems is accounted for by subsequent optimization of the entire system based on sensitivities of the suboptimization problem solutions at each level of the tree to variables of the next higher level. A formalization of the procedure suitable for computer implementation is developed and the state of readiness of the implementation building blocks is reviewed showing that the ingredients for the development are on the shelf. The decomposition method is also shown to be compatible with the natural human organization of the design process of engineering systems. The method is also examined with respect to the trends in computer hardware and software progress to point out that its efficiency can be amplified by network computing using parallel processors.

  17. Optimal control problem for linear fractional-order systems, described by equations with Hadamard-type derivative

    NASA Astrophysics Data System (ADS)

    Postnov, Sergey

    2017-11-01

    Two kinds of optimal control problem are investigated for linear time-invariant fractional-order systems with lumped parameters which dynamics described by equations with Hadamard-type derivative: the problem of control with minimal norm and the problem of control with minimal time at given restriction on control norm. The problem setting with nonlocal initial conditions studied. Admissible controls allowed to be the p-integrable functions (p > 1) at half-interval. The optimal control problem studied by moment method. The correctness and solvability conditions for the corresponding moment problem are derived. For several special cases the optimal control problems stated are solved analytically. Some analogies pointed for results obtained with the results which are known for integer-order systems and fractional-order systems describing by equations with Caputo- and Riemann-Liouville-type derivatives.

  18. Influence maximization in complex networks through optimal percolation

    NASA Astrophysics Data System (ADS)

    Morone, Flaviano; Makse, Hernán A.

    2015-08-01

    The whole frame of interconnections in complex networks hinges on a specific set of structural nodes, much smaller than the total size, which, if activated, would cause the spread of information to the whole network, or, if immunized, would prevent the diffusion of a large scale epidemic. Localizing this optimal, that is, minimal, set of structural nodes, called influencers, is one of the most important problems in network science. Despite the vast use of heuristic strategies to identify influential spreaders, the problem remains unsolved. Here we map the problem onto optimal percolation in random networks to identify the minimal set of influencers, which arises by minimizing the energy of a many-body system, where the form of the interactions is fixed by the non-backtracking matrix of the network. Big data analyses reveal that the set of optimal influencers is much smaller than the one predicted by previous heuristic centralities. Remarkably, a large number of previously neglected weakly connected nodes emerges among the optimal influencers. These are topologically tagged as low-degree nodes surrounded by hierarchical coronas of hubs, and are uncovered only through the optimal collective interplay of all the influencers in the network. The present theoretical framework may hold a larger degree of universality, being applicable to other hard optimization problems exhibiting a continuous transition from a known phase.

  19. Influence maximization in complex networks through optimal percolation.

    PubMed

    Morone, Flaviano; Makse, Hernán A

    2015-08-06

    The whole frame of interconnections in complex networks hinges on a specific set of structural nodes, much smaller than the total size, which, if activated, would cause the spread of information to the whole network, or, if immunized, would prevent the diffusion of a large scale epidemic. Localizing this optimal, that is, minimal, set of structural nodes, called influencers, is one of the most important problems in network science. Despite the vast use of heuristic strategies to identify influential spreaders, the problem remains unsolved. Here we map the problem onto optimal percolation in random networks to identify the minimal set of influencers, which arises by minimizing the energy of a many-body system, where the form of the interactions is fixed by the non-backtracking matrix of the network. Big data analyses reveal that the set of optimal influencers is much smaller than the one predicted by previous heuristic centralities. Remarkably, a large number of previously neglected weakly connected nodes emerges among the optimal influencers. These are topologically tagged as low-degree nodes surrounded by hierarchical coronas of hubs, and are uncovered only through the optimal collective interplay of all the influencers in the network. The present theoretical framework may hold a larger degree of universality, being applicable to other hard optimization problems exhibiting a continuous transition from a known phase.

  20. Optimization Techniques for Design Problems in Selected Areas in WSNs: A Tutorial

    PubMed Central

    Ibrahim, Ahmed; Alfa, Attahiru

    2017-01-01

    This paper is intended to serve as an overview of, and mostly a tutorial to illustrate, the optimization techniques used in several different key design aspects that have been considered in the literature of wireless sensor networks (WSNs). It targets the researchers who are new to the mathematical optimization tool, and wish to apply it to WSN design problems. We hence divide the paper into two main parts. One part is dedicated to introduce optimization theory and an overview on some of its techniques that could be helpful in design problem in WSNs. In the second part, we present a number of design aspects that we came across in the WSN literature in which mathematical optimization methods have been used in the design. For each design aspect, a key paper is selected, and for each we explain the formulation techniques and the solution methods implemented. We also provide in-depth analyses and assessments of the problem formulations, the corresponding solution techniques and experimental procedures in some of these papers. The analyses and assessments, which are provided in the form of comments, are meant to reflect the points that we believe should be taken into account when using optimization as a tool for design purposes. PMID:28763039

  1. Optimization Techniques for Design Problems in Selected Areas in WSNs: A Tutorial.

    PubMed

    Ibrahim, Ahmed; Alfa, Attahiru

    2017-08-01

    This paper is intended to serve as an overview of, and mostly a tutorial to illustrate, the optimization techniques used in several different key design aspects that have been considered in the literature of wireless sensor networks (WSNs). It targets the researchers who are new to the mathematical optimization tool, and wish to apply it to WSN design problems. We hence divide the paper into two main parts. One part is dedicated to introduce optimization theory and an overview on some of its techniques that could be helpful in design problem in WSNs. In the second part, we present a number of design aspects that we came across in the WSN literature in which mathematical optimization methods have been used in the design. For each design aspect, a key paper is selected, and for each we explain the formulation techniques and the solution methods implemented. We also provide in-depth analyses and assessments of the problem formulations, the corresponding solution techniques and experimental procedures in some of these papers. The analyses and assessments, which are provided in the form of comments, are meant to reflect the points that we believe should be taken into account when using optimization as a tool for design purposes.

  2. Marker optimization for facial motion acquisition and deformation.

    PubMed

    Le, Binh H; Zhu, Mingyang; Deng, Zhigang

    2013-11-01

    A long-standing problem in marker-based facial motion capture is what are the optimal facial mocap marker layouts. Despite its wide range of potential applications, this problem has not yet been systematically explored to date. This paper describes an approach to compute optimized marker layouts for facial motion acquisition as optimization of characteristic control points from a set of high-resolution, ground-truth facial mesh sequences. Specifically, the thin-shell linear deformation model is imposed onto the example pose reconstruction process via optional hard constraints such as symmetry and multiresolution constraints. Through our experiments and comparisons, we validate the effectiveness, robustness, and accuracy of our approach. Besides guiding minimal yet effective placement of facial mocap markers, we also describe and demonstrate its two selected applications: marker-based facial mesh skinning and multiresolution facial performance capture.

  3. Parry-Romberg reconstruction: optimal timing for hard and soft tissue procedures.

    PubMed

    Slack, Ginger C; Tabit, Christina J; Allam, Karam A; Kawamoto, Henry K; Bradley, James P

    2012-11-01

    For the treatment of Parry-Romberg syndrome or progressive hemifacial atrophy, we studied 3 controversial issues: (1) optimal timing, (2) need for skeletal reconstruction, and (3) need for soft tissue (medial canthus/lacrimal duct) reconstruction. Patients with Parry-Romberg syndrome (>5 y follow-up) were divided into 2 groups: (1) younger than 14 years and (2) 14 years or older (n = 43). Sex, age, severity of deformity, number of procedures, operative times, and augmentation fat volumes were recorded. Physician and patient satisfaction surveys (5-point scale) were obtained, preoperative and postoperative three-dimensional computed tomographic scans were reviewed, and a digital three-dimensional photogrammetry system was used to determine volume retention. Our results indicate that the younger patient group required more procedures compared with the older patient group (4.3 versus 2.8); however, the younger group had higher patient/family satisfaction scores (3.8 versus 3.0). Skeletal and soft tissue reconstruction resulted in improved symmetry score (60% preoperatively to 93% final) and satisfaction scores (3.4 preoperatively to 3.8 final). Patients with Parry-Romberg syndrome required multiple corrective surgeries but showed improvements even when beginning before puberty. Soft and hard tissue reconstruction was beneficial.

  4. A finite element based method for solution of optimal control problems

    NASA Technical Reports Server (NTRS)

    Bless, Robert R.; Hodges, Dewey H.; Calise, Anthony J.

    1989-01-01

    A temporal finite element based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables that are expanded in terms of elemental values and simple shape functions. Unlike other variational approaches to optimal control problems, however, time derivatives of the states and costates do not appear in the governing variational equation. Instead, the only quantities whose time derivatives appear therein are virtual states and virtual costates. Also noteworthy among characteristics of the finite element formulation is the fact that in the algebraic equations which contain costates, they appear linearly. Thus, the remaining equations can be solved iteratively without initial guesses for the costates; this reduces the size of the problem by about a factor of two. Numerical results are presented herein for an elementary trajectory optimization problem which show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The goal is to evaluate the feasibility of this approach for real-time guidance applications. To this end, a simplified two-stage, four-state model for an advanced launch vehicle application is presented which is suitable for finite element solution.

  5. 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

  6. Nonexpansiveness of a linearized augmented Lagrangian operator for hierarchical convex optimization

    NASA Astrophysics Data System (ADS)

    Yamagishi, Masao; Yamada, Isao

    2017-04-01

    Hierarchical convex optimization concerns two-stage optimization problems: the first stage problem is a convex optimization; the second stage problem is the minimization of a convex function over the solution set of the first stage problem. For the hierarchical convex optimization, the hybrid steepest descent method (HSDM) can be applied, where the solution set of the first stage problem must be expressed as the fixed point set of a certain nonexpansive operator. In this paper, we propose a nonexpansive operator that yields a computationally efficient update when it is plugged into the HSDM. The proposed operator is inspired by the update of the linearized augmented Lagrangian method. It is applicable to characterize the solution set of recent sophisticated convex optimization problems found in the context of inverse problems, where the sum of multiple proximable convex functions involving linear operators must be minimized to incorporate preferable properties into the minimizers. For such a problem formulation, there has not yet been reported any nonexpansive operator that yields an update free from the inversions of linear operators in cases where it is utilized in the HSDM. Unlike previously known nonexpansive operators, the proposed operator yields an inversion-free update in such cases. As an application of the proposed operator plugged into the HSDM, we also present, in the context of the so-called superiorization, an algorithmic solution to a convex optimization problem over the generalized convex feasible set where the intersection of the hard constraints is not necessarily simple.

  7. Modified Backtracking Search Optimization Algorithm Inspired by Simulated Annealing for Constrained Engineering Optimization Problems

    PubMed Central

    Wang, Hailong; Sun, Yuqiu; Su, Qinghua; Xia, Xuewen

    2018-01-01

    The backtracking search optimization algorithm (BSA) is a population-based evolutionary algorithm for numerical optimization problems. BSA has a powerful global exploration capacity while its local exploitation capability is relatively poor. This affects the convergence speed of the algorithm. In this paper, we propose a modified BSA inspired by simulated annealing (BSAISA) to overcome the deficiency of BSA. In the BSAISA, the amplitude control factor (F) is modified based on the Metropolis criterion in simulated annealing. The redesigned F could be adaptively decreased as the number of iterations increases and it does not introduce extra parameters. A self-adaptive ε-constrained method is used to handle the strict constraints. We compared the performance of the proposed BSAISA with BSA and other well-known algorithms when solving thirteen constrained benchmarks and five engineering design problems. The simulation results demonstrated that BSAISA is more effective than BSA and more competitive with other well-known algorithms in terms of convergence speed. PMID:29666635

  8. Portfolio optimization problem with nonidentical variances of asset returns using statistical mechanical informatics.

    PubMed

    Shinzato, Takashi

    2016-12-01

    The portfolio optimization problem in which the variances of the return rates of assets are not identical is analyzed in this paper using the methodology of statistical mechanical informatics, specifically, replica analysis. We defined two characteristic quantities of an optimal portfolio, namely, minimal investment risk and investment concentration, in order to solve the portfolio optimization problem and analytically determined their asymptotical behaviors using replica analysis. Numerical experiments were also performed, and a comparison between the results of our simulation and those obtained via replica analysis validated our proposed method.

  9. Portfolio optimization problem with nonidentical variances of asset returns using statistical mechanical informatics

    NASA Astrophysics Data System (ADS)

    Shinzato, Takashi

    2016-12-01

    The portfolio optimization problem in which the variances of the return rates of assets are not identical is analyzed in this paper using the methodology of statistical mechanical informatics, specifically, replica analysis. We defined two characteristic quantities of an optimal portfolio, namely, minimal investment risk and investment concentration, in order to solve the portfolio optimization problem and analytically determined their asymptotical behaviors using replica analysis. Numerical experiments were also performed, and a comparison between the results of our simulation and those obtained via replica analysis validated our proposed method.

  10. A modified form of conjugate gradient method for unconstrained optimization problems

    NASA Astrophysics Data System (ADS)

    Ghani, Nur Hamizah Abdul; Rivaie, Mohd.; Mamat, Mustafa

    2016-06-01

    Conjugate gradient (CG) methods have been recognized as an interesting technique to solve optimization problems, due to the numerical efficiency, simplicity and low memory requirements. In this paper, we propose a new CG method based on the study of Rivaie et al. [7] (Comparative study of conjugate gradient coefficient for unconstrained Optimization, Aus. J. Bas. Appl. Sci. 5(2011) 947-951). Then, we show that our method satisfies sufficient descent condition and converges globally with exact line search. Numerical results show that our proposed method is efficient for given standard test problems, compare to other existing CG methods.

  11. Quantum Optimization of Fully Connected Spin Glasses

    NASA Astrophysics Data System (ADS)

    Venturelli, Davide; Mandrà, Salvatore; Knysh, Sergey; O'Gorman, Bryan; Biswas, Rupak; Smelyanskiy, Vadim

    2015-07-01

    Many NP-hard problems can be seen as the task of finding a ground state of a disordered highly connected Ising spin glass. If solutions are sought by means of quantum annealing, it is often necessary to represent those graphs in the annealer's hardware by means of the graph-minor embedding technique, generating a final Hamiltonian consisting of coupled chains of ferromagnetically bound spins, whose binding energy is a free parameter. In order to investigate the effect of embedding on problems of interest, the fully connected Sherrington-Kirkpatrick model with random ±1 couplings is programmed on the D-Wave TwoTM annealer using up to 270 qubits interacting on a Chimera-type graph. We present the best embedding prescriptions for encoding the Sherrington-Kirkpatrick problem in the Chimera graph. The results indicate that the optimal choice of embedding parameters could be associated with the emergence of the spin-glass phase of the embedded problem, whose presence was previously uncertain. This optimal parameter setting allows the performance of the quantum annealer to compete with (and potentially outperform, in the absence of analog control errors) optimized simulated annealing algorithms.

  12. A well-posed optimal spectral element approximation for the Stokes problem

    NASA Technical Reports Server (NTRS)

    Maday, Y.; Patera, A. T.; Ronquist, E. M.

    1987-01-01

    A method is proposed for the spectral element simulation of incompressible flow. This method constitutes in a well-posed optimal approximation of the steady Stokes problem with no spurious modes in the pressure. The resulting method is analyzed, and numerical results are presented for a model problem.

  13. A Hybrid Ant Colony Optimization Algorithm for the Extended Capacitated Arc Routing Problem.

    PubMed

    Li-Ning Xing; Rohlfshagen, P; Ying-Wu Chen; Xin Yao

    2011-08-01

    The capacitated arc routing problem (CARP) is representative of numerous practical applications, and in order to widen its scope, we consider an extended version of this problem that entails both total service time and fixed investment costs. We subsequently propose a hybrid ant colony optimization (ACO) algorithm (HACOA) to solve instances of the extended CARP. This approach is characterized by the exploitation of heuristic information, adaptive parameters, and local optimization techniques: Two kinds of heuristic information, arc cluster information and arc priority information, are obtained continuously from the solutions sampled to guide the subsequent optimization process. The adaptive parameters ease the burden of choosing initial values and facilitate improved and more robust results. Finally, local optimization, based on the two-opt heuristic, is employed to improve the overall performance of the proposed algorithm. The resulting HACOA is tested on four sets of benchmark problems containing a total of 87 instances with up to 140 nodes and 380 arcs. In order to evaluate the effectiveness of the proposed method, some existing capacitated arc routing heuristics are extended to cope with the extended version of this problem; the experimental results indicate that the proposed ACO method outperforms these heuristics.

  14. a New Hybrid Yin-Yang Swarm Optimization Algorithm for Uncapacitated Warehouse Location Problems

    NASA Astrophysics Data System (ADS)

    Heidari, A. A.; Kazemizade, O.; Hakimpour, F.

    2017-09-01

    Yin-Yang-pair optimization (YYPO) is one of the latest metaheuristic algorithms (MA) proposed in 2015 that tries to inspire the philosophy of balance between conflicting concepts. Particle swarm optimizer (PSO) is one of the first population-based MA inspired by social behaviors of birds. In spite of PSO, the YYPO is not a nature inspired optimizer. It has a low complexity and starts with only two initial positions and can produce more points with regard to the dimension of target problem. Due to unique advantages of these methodologies and to mitigate the immature convergence and local optima (LO) stagnation problems in PSO, in this work, a continuous hybrid strategy based on the behaviors of PSO and YYPO is proposed to attain the suboptimal solutions of uncapacitated warehouse location (UWL) problems. This efficient hierarchical PSO-based optimizer (PSOYPO) can improve the effectiveness of PSO on spatial optimization tasks such as the family of UWL problems. The performance of the proposed PSOYPO is verified according to some UWL benchmark cases. These test cases have been used in several works to evaluate the efficacy of different MA. Then, the PSOYPO is compared to the standard PSO, genetic algorithm (GA), harmony search (HS), modified HS (OBCHS), and evolutionary simulated annealing (ESA). The experimental results demonstrate that the PSOYPO can reveal a better or competitive efficacy compared to the PSO and other MA.

  15. Solving multi-objective optimization problems in conservation with the reference point method

    PubMed Central

    Dujardin, Yann; Chadès, Iadine

    2018-01-01

    Managing the biodiversity extinction crisis requires wise decision-making processes able to account for the limited resources available. In most decision problems in conservation biology, several conflicting objectives have to be taken into account. Most methods used in conservation either provide suboptimal solutions or use strong assumptions about the decision-maker’s preferences. Our paper reviews some of the existing approaches to solve multi-objective decision problems and presents new multi-objective linear programming formulations of two multi-objective optimization problems in conservation, allowing the use of a reference point approach. Reference point approaches solve multi-objective optimization problems by interactively representing the preferences of the decision-maker with a point in the criteria (objectives) space, called the reference point. We modelled and solved the following two problems in conservation: a dynamic multi-species management problem under uncertainty and a spatial allocation resource management problem. Results show that the reference point method outperforms classic methods while illustrating the use of an interactive methodology for solving combinatorial problems with multiple objectives. The method is general and can be adapted to a wide range of ecological combinatorial problems. PMID:29293650

  16. A parallel-machine scheduling problem with two competing agents

    NASA Astrophysics Data System (ADS)

    Lee, Wen-Chiung; Chung, Yu-Hsiang; Wang, Jen-Ya

    2017-06-01

    Scheduling with two competing agents has become popular in recent years. Most of the research has focused on single-machine problems. This article considers a parallel-machine problem, the objective of which is to minimize the total completion time of jobs from the first agent given that the maximum tardiness of jobs from the second agent cannot exceed an upper bound. The NP-hardness of this problem is also examined. A genetic algorithm equipped with local search is proposed to search for the near-optimal solution. Computational experiments are conducted to evaluate the proposed genetic algorithm.

  17. Toward a characterization of landscapes of combinatorial optimization problems, with special attention to the phylogeny problem.

    PubMed

    Charleston, M A

    1995-01-01

    This article introduces a coherent language base for describing and working with characteristics of combinatorial optimization problems, which is at once general enough to be used in all such problems and precise enough to allow subtle concepts in this field to be discussed unambiguously. An example is provided of how this nomenclature is applied to an instance of the phylogeny problem. Also noted is the beneficial effect, on the landscape of the solution space, of transforming the observed data to account for multiple changes of character state.

  18. Processing time tolerance-based ACO algorithm for solving job-shop scheduling problem

    NASA Astrophysics Data System (ADS)

    Luo, Yabo; Waden, Yongo P.

    2017-06-01

    Ordinarily, Job Shop Scheduling Problem (JSSP) is known as NP-hard problem which has uncertainty and complexity that cannot be handled by a linear method. Thus, currently studies on JSSP are concentrated mainly on applying different methods of improving the heuristics for optimizing the JSSP. However, there still exist many problems for efficient optimization in the JSSP, namely, low efficiency and poor reliability, which can easily trap the optimization process of JSSP into local optima. Therefore, to solve this problem, a study on Ant Colony Optimization (ACO) algorithm combined with constraint handling tactics is carried out in this paper. Further, the problem is subdivided into three parts: (1) Analysis of processing time tolerance-based constraint features in the JSSP which is performed by the constraint satisfying model; (2) Satisfying the constraints by considering the consistency technology and the constraint spreading algorithm in order to improve the performance of ACO algorithm. Hence, the JSSP model based on the improved ACO algorithm is constructed; (3) The effectiveness of the proposed method based on reliability and efficiency is shown through comparative experiments which are performed on benchmark problems. Consequently, the results obtained by the proposed method are better, and the applied technique can be used in optimizing JSSP.

  19. Open shop scheduling problem to minimize total weighted completion time

    NASA Astrophysics Data System (ADS)

    Bai, Danyu; Zhang, Zhihai; Zhang, Qiang; Tang, Mengqian

    2017-01-01

    A given number of jobs in an open shop scheduling environment must each be processed for given amounts of time on each of a given set of machines in an arbitrary sequence. This study aims to achieve a schedule that minimizes total weighted completion time. Owing to the strong NP-hardness of the problem, the weighted shortest processing time block (WSPTB) heuristic is presented to obtain approximate solutions for large-scale problems. Performance analysis proves the asymptotic optimality of the WSPTB heuristic in the sense of probability limits. The largest weight block rule is provided to seek optimal schedules in polynomial time for a special case. A hybrid discrete differential evolution algorithm is designed to obtain high-quality solutions for moderate-scale problems. Simulation experiments demonstrate the effectiveness of the proposed algorithms.

  20. Comparison of Genetic Algorithm, Particle Swarm Optimization and Biogeography-based Optimization for Feature Selection to Classify Clusters of Microcalcifications

    NASA Astrophysics Data System (ADS)

    Khehra, Baljit Singh; Pharwaha, Amar Partap Singh

    2017-04-01

    Ductal carcinoma in situ (DCIS) is one type of breast cancer. Clusters of microcalcifications (MCCs) are symptoms of DCIS that are recognized by mammography. Selection of robust features vector is the process of selecting an optimal subset of features from a large number of available features in a given problem domain after the feature extraction and before any classification scheme. Feature selection reduces the feature space that improves the performance of classifier and decreases the computational burden imposed by using many features on classifier. Selection of an optimal subset of features from a large number of available features in a given problem domain is a difficult search problem. For n features, the total numbers of possible subsets of features are 2n. Thus, selection of an optimal subset of features problem belongs to the category of NP-hard problems. In this paper, an attempt is made to find the optimal subset of MCCs features from all possible subsets of features using genetic algorithm (GA), particle swarm optimization (PSO) and biogeography-based optimization (BBO). For simulation, a total of 380 benign and malignant MCCs samples have been selected from mammogram images of DDSM database. A total of 50 features extracted from benign and malignant MCCs samples are used in this study. In these algorithms, fitness function is correct classification rate of classifier. Support vector machine is used as a classifier. From experimental results, it is also observed that the performance of PSO-based and BBO-based algorithms to select an optimal subset of features for classifying MCCs as benign or malignant is better as compared to GA-based algorithm.

  1. Vortex generator design for aircraft inlet distortion as a numerical optimization problem

    NASA Technical Reports Server (NTRS)

    Anderson, Bernhard H.; Levy, Ralph

    1991-01-01

    Aerodynamic compatibility of aircraft/inlet/engine systems is a difficult design problem for aircraft that must operate in many different flight regimes. Takeoff, subsonic cruise, supersonic cruise, transonic maneuvering, and high altitude loiter each place different constraints on inlet design. Vortex generators, small wing like sections mounted on the inside surfaces of the inlet duct, are used to control flow separation and engine face distortion. The design of vortex generator installations in an inlet is defined as a problem addressable by numerical optimization techniques. A performance parameter is suggested to account for both inlet distortion and total pressure loss at a series of design flight conditions. The resulting optimization problem is difficult since some of the design parameters take on integer values. If numerical procedures could be used to reduce multimillion dollar development test programs to a small set of verification tests, numerical optimization could have a significant impact on both cost and elapsed time to design new aircraft.

  2. Optimal least-squares finite element method for elliptic problems

    NASA Technical Reports Server (NTRS)

    Jiang, Bo-Nan; Povinelli, Louis A.

    1991-01-01

    An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.

  3. Overview: Applications of numerical optimization methods to helicopter design problems

    NASA Technical Reports Server (NTRS)

    Miura, H.

    1984-01-01

    There are a number of helicopter design problems that are well suited to applications of numerical design optimization techniques. Adequate implementation of this technology will provide high pay-offs. There are a number of numerical optimization programs available, and there are many excellent response/performance analysis programs developed or being developed. But integration of these programs in a form that is usable in the design phase should be recognized as important. It is also necessary to attract the attention of engineers engaged in the development of analysis capabilities and to make them aware that analysis capabilities are much more powerful if integrated into design oriented codes. Frequently, the shortcoming of analysis capabilities are revealed by coupling them with an optimization code. Most of the published work has addressed problems in preliminary system design, rotor system/blade design or airframe design. Very few published results were found in acoustics, aerodynamics and control system design. Currently major efforts are focused on vibration reduction, and aerodynamics/acoustics applications appear to be growing fast. The development of a computer program system to integrate the multiple disciplines required in helicopter design with numerical optimization technique is needed. Activities in Britain, Germany and Poland are identified, but no published results from France, Italy, the USSR or Japan were found.

  4. Patch planting of hard spin-glass problems: Getting ready for the next generation of optimization approaches

    NASA Astrophysics Data System (ADS)

    Wang, Wenlong; Mandrà, Salvatore; Katzgraber, Helmut

    We propose a patch planting heuristic that allows us to create arbitrarily-large Ising spin-glass instances on any topology and with any type of disorder, and where the exact ground-state energy of the problem is known by construction. By breaking up the problem into patches that can be treated either with exact or heuristic solvers, we can reconstruct the optimum of the original, considerably larger, problem. The scaling of the computational complexity of these instances with various patch numbers and sizes is investigated and compared with random instances using population annealing Monte Carlo and quantum annealing on the D-Wave 2X quantum annealer. The method can be useful for benchmarking of novel computing technologies and algorithms. NSF-DMR-1208046 and the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via MIT Lincoln Laboratory Air Force Contract No. FA8721-05-C-0002.

  5. An optimized treatment for algorithmic differentiation of an important glaciological fixed-point problem

    DOE PAGES

    Goldberg, Daniel N.; Narayanan, Sri Hari Krishna; Hascoet, Laurent; ...

    2016-05-20

    We apply an optimized method to the adjoint generation of a time-evolving land ice model through algorithmic differentiation (AD). The optimization involves a special treatment of the fixed-point iteration required to solve the nonlinear stress balance, which differs from a straightforward application of AD software, and leads to smaller memory requirements and in some cases shorter computation times of the adjoint. The optimization is done via implementation of the algorithm of Christianson (1994) for reverse accumulation of fixed-point problems, with the AD tool OpenAD. For test problems, the optimized adjoint is shown to have far lower memory requirements, potentially enablingmore » larger problem sizes on memory-limited machines. In the case of the land ice model, implementation of the algorithm allows further optimization by having the adjoint model solve a sequence of linear systems with identical (as opposed to varying) matrices, greatly improving performance. Finally, the methods introduced here will be of value to other efforts applying AD tools to ice models, particularly ones which solve a hybrid shallow ice/shallow shelf approximation to the Stokes equations.« less

  6. Finite element approximation of an optimal control problem for the von Karman equations

    NASA Technical Reports Server (NTRS)

    Hou, L. Steven; Turner, James C.

    1994-01-01

    This paper is concerned with optimal control problems for the von Karman equations with distributed controls. We first show that optimal solutions exist. We then show that Lagrange multipliers may be used to enforce the constraints and derive an optimality system from which optimal states and controls may be deduced. Finally we define finite element approximations of solutions for the optimality system and derive error estimates for the approximations.

  7. Formulation of image fusion as a constrained least squares optimization problem

    PubMed Central

    Dwork, Nicholas; Lasry, Eric M.; Pauly, John M.; Balbás, Jorge

    2017-01-01

    Abstract. Fusing a lower resolution color image with a higher resolution monochrome image is a common practice in medical imaging. By incorporating spatial context and/or improving the signal-to-noise ratio, it provides clinicians with a single frame of the most complete information for diagnosis. In this paper, image fusion is formulated as a convex optimization problem that avoids image decomposition and permits operations at the pixel level. This results in a highly efficient and embarrassingly parallelizable algorithm based on widely available robust and simple numerical methods that realizes the fused image as the global minimizer of the convex optimization problem. PMID:28331885

  8. Typical performance of approximation algorithms for NP-hard problems

    NASA Astrophysics Data System (ADS)

    Takabe, Satoshi; Hukushima, Koji

    2016-11-01

    Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with the presentation of a theoretical framework. Herein, three approximation algorithms are examined: linear-programming relaxation, loopy-belief propagation, and the leaf-removal algorithm. The former two algorithms are analyzed using a statistical-mechanical technique, whereas the average-case analysis of the last one is conducted using the generating function method. These algorithms have a threshold in the typical performance with increasing average degree of the random graph, below which they find true optimal solutions with high probability. Our study reveals that there exist only three cases, determined by the order of the typical performance thresholds. In addition, we provide some conditions for classification of the graph ensembles and demonstrate explicitly some examples for the difference in thresholds.

  9. A Transformation Approach to Optimal Control Problems with Bounded State Variables

    NASA Technical Reports Server (NTRS)

    Hanafy, Lawrence Hanafy

    1971-01-01

    A technique is described and utilized in the study of the solutions to various general problems in optimal control theory, which are converted in to Lagrange problems in the calculus of variations. This is accomplished by mapping certain properties in Euclidean space onto closed control and state regions. Nonlinear control problems with a unit m cube as control region and unit n cube as state region are considered.

  10. An optimal consumption and investment problem with quadratic utility and negative wealth constraints.

    PubMed

    Roh, Kum-Hwan; Kim, Ji Yeoun; Shin, Yong Hyun

    2017-01-01

    In this paper, we investigate the optimal consumption and portfolio selection problem with negative wealth constraints for an economic agent who has a quadratic utility function of consumption and receives a constant labor income. Due to the property of the quadratic utility function, we separate our problem into two cases and derive the closed-form solutions for each case. We also illustrate some numerical implications of the optimal consumption and portfolio.

  11. Calculation of Pareto-optimal solutions to multiple-objective problems using threshold-of-acceptability constraints

    NASA Technical Reports Server (NTRS)

    Giesy, D. P.

    1978-01-01

    A technique is presented for the calculation of Pareto-optimal solutions to a multiple-objective constrained optimization problem by solving a series of single-objective problems. Threshold-of-acceptability constraints are placed on the objective functions at each stage to both limit the area of search and to mathematically guarantee convergence to a Pareto optimum.

  12. An improved genetic algorithm for multidimensional optimization of precedence-constrained production planning and scheduling

    NASA Astrophysics Data System (ADS)

    Dao, Son Duy; Abhary, Kazem; Marian, Romeo

    2017-06-01

    Integration of production planning and scheduling is a class of problems commonly found in manufacturing industry. This class of problems associated with precedence constraint has been previously modeled and optimized by the authors, in which, it requires a multidimensional optimization at the same time: what to make, how many to make, where to make and the order to make. It is a combinatorial, NP-hard problem, for which no polynomial time algorithm is known to produce an optimal result on a random graph. In this paper, the further development of Genetic Algorithm (GA) for this integrated optimization is presented. Because of the dynamic nature of the problem, the size of its solution is variable. To deal with this variability and find an optimal solution to the problem, GA with new features in chromosome encoding, crossover, mutation, selection as well as algorithm structure is developed herein. With the proposed structure, the proposed GA is able to "learn" from its experience. Robustness of the proposed GA is demonstrated by a complex numerical example in which performance of the proposed GA is compared with those of three commercial optimization solvers.

  13. A time-domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems

    NASA Astrophysics Data System (ADS)

    Heinkenschloss, Matthias

    2005-01-01

    We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.

  14. Performance of a Group of Deaf and Hard-of-Hearing Students and a Comparison Group of Hearing Students on a Series of Problem-Solving Tasks.

    ERIC Educational Resources Information Center

    Luckner, John L.; McNeill, Joyce H.

    1994-01-01

    This study found that 43 school-age deaf and hard-of-hearing students did not perform as well as a matched group of hearing students on problem-solving tasks. As they got older, both groups made incremental gains in problem-solving ability, and the gap between groups narrowed. (Author/JDD)

  15. A Novel Approach to Hardness Testing

    NASA Technical Reports Server (NTRS)

    Spiegel, F. Xavier; West, Harvey A.

    1996-01-01

    This paper gives a description of the application of a simple rebound time measuring device and relates the determination of relative hardness of a variety of common engineering metals. A relation between rebound time and hardness will be sought. The effect of geometry and surface condition will also be discussed in order to acquaint the student with the problems associated with this type of method.

  16. An Optimizing Space Data-Communications Scheduling Method and Algorithm with Interference Mitigation, Generalized for a Broad Class of Optimization Problems

    NASA Technical Reports Server (NTRS)

    Rash, James L.

    2010-01-01

    NASA's space data-communications infrastructure, the Space Network and the Ground Network, provide scheduled (as well as some limited types of unscheduled) data-communications services to user spacecraft via orbiting relay satellites and ground stations. An implementation of the methods and algorithms disclosed herein will be a system that produces globally optimized schedules with not only optimized service delivery by the space data-communications infrastructure but also optimized satisfaction of all user requirements and prescribed constraints, including radio frequency interference (RFI) constraints. Evolutionary search, a class of probabilistic strategies for searching large solution spaces, constitutes the essential technology in this disclosure. Also disclosed are methods and algorithms for optimizing the execution efficiency of the schedule-generation algorithm itself. The scheduling methods and algorithms as presented are adaptable to accommodate the complexity of scheduling the civilian and/or military data-communications infrastructure. Finally, the problem itself, and the methods and algorithms, are generalized and specified formally, with applicability to a very broad class of combinatorial optimization problems.

  17. Determination of optimal self-drive tourism route using the orienteering problem method

    NASA Astrophysics Data System (ADS)

    Hashim, Zakiah; Ismail, Wan Rosmanira; Ahmad, Norfaieqah

    2013-04-01

    This paper was conducted to determine the optimal travel routes for self-drive tourism based on the allocation of time and expense by maximizing the amount of attraction scores assigned to each city involved. Self-drive tourism represents a type of tourism where tourists hire or travel by their own vehicle. It only involves a tourist destination which can be linked with a network of roads. Normally, the traveling salesman problem (TSP) and multiple traveling salesman problems (MTSP) method were used in the minimization problem such as determination the shortest time or distance traveled. This paper involved an alternative approach for maximization method which is maximize the attraction scores and tested on tourism data for ten cities in Kedah. A set of priority scores are used to set the attraction score at each city. The classical approach of the orienteering problem was used to determine the optimal travel route. This approach is extended to the team orienteering problem and the two methods were compared. These two models have been solved by using LINGO12.0 software. The results indicate that the model involving the team orienteering problem provides a more appropriate solution compared to the orienteering problem model.

  18. Models of resource allocation optimization when solving the control problems in organizational systems

    NASA Astrophysics Data System (ADS)

    Menshikh, V.; Samorokovskiy, A.; Avsentev, O.

    2018-03-01

    The mathematical model of optimizing the allocation of resources to reduce the time for management decisions and algorithms to solve the general problem of resource allocation. The optimization problem of choice of resources in organizational systems in order to reduce the total execution time of a job is solved. This problem is a complex three-level combinatorial problem, for the solving of which it is necessary to implement the solution to several specific problems: to estimate the duration of performing each action, depending on the number of performers within the group that performs this action; to estimate the total execution time of all actions depending on the quantitative composition of groups of performers; to find such a distribution of the existing resource of performers in groups to minimize the total execution time of all actions. In addition, algorithms to solve the general problem of resource allocation are proposed.

  19. Optimal dynamic voltage scaling for wireless sensor nodes with real-time constraints

    NASA Astrophysics Data System (ADS)

    Cassandras, Christos G.; Zhuang, Shixin

    2005-11-01

    Sensors are increasingly embedded in manufacturing systems and wirelessly networked to monitor and manage operations ranging from process and inventory control to tracking equipment and even post-manufacturing product monitoring. In building such sensor networks, a critical issue is the limited and hard to replenish energy in the devices involved. Dynamic voltage scaling is a technique that controls the operating voltage of a processor to provide desired performance while conserving energy and prolonging the overall network's lifetime. We consider such power-limited devices processing time-critical tasks which are non-preemptive, aperiodic and have uncertain arrival times. We treat voltage scaling as a dynamic optimization problem whose objective is to minimize energy consumption subject to hard or soft real-time execution constraints. In the case of hard constraints, we build on prior work (which engages a voltage scaling controller at task completion times) by developing an intra-task controller that acts at all arrival times of incoming tasks. We show that this optimization problem can be decomposed into two simpler ones whose solution leads to an algorithm that does not actually require solving any nonlinear programming problems. In the case of soft constraints, this decomposition must be partly relaxed, but it still leads to a scalable (linear in the number of tasks) algorithm. Simulation results are provided to illustrate performance improvements in systems with intra-task controllers compared to uncontrolled systems or those using inter-task control.

  20. Optimal solution of full fuzzy transportation problems using total integral ranking

    NASA Astrophysics Data System (ADS)

    Sam’an, M.; Farikhin; Hariyanto, S.; Surarso, B.

    2018-03-01

    Full fuzzy transportation problem (FFTP) is a transportation problem where transport costs, demand, supply and decision variables are expressed in form of fuzzy numbers. To solve fuzzy transportation problem, fuzzy number parameter must be converted to a crisp number called defuzzyfication method. In this new total integral ranking method with fuzzy numbers from conversion of trapezoidal fuzzy numbers to hexagonal fuzzy numbers obtained result of consistency defuzzyfication on symmetrical fuzzy hexagonal and non symmetrical type 2 numbers with fuzzy triangular numbers. To calculate of optimum solution FTP used fuzzy transportation algorithm with least cost method. From this optimum solution, it is found that use of fuzzy number form total integral ranking with index of optimism gives different optimum value. In addition, total integral ranking value using hexagonal fuzzy numbers has an optimal value better than the total integral ranking value using trapezoidal fuzzy numbers.

  1. Finding long chains in kidney exchange using the traveling salesman problem.

    PubMed

    Anderson, Ross; Ashlagi, Itai; Gamarnik, David; Roth, Alvin E

    2015-01-20

    As of May 2014 there were more than 100,000 patients on the waiting list for a kidney transplant from a deceased donor. Although the preferred treatment is a kidney transplant, every year there are fewer donors than new patients, so the wait for a transplant continues to grow. To address this shortage, kidney paired donation (KPD) programs allow patients with living but biologically incompatible donors to exchange donors through cycles or chains initiated by altruistic (nondirected) donors, thereby increasing the supply of kidneys in the system. In many KPD programs a centralized algorithm determines which exchanges will take place to maximize the total number of transplants performed. This optimization problem has proven challenging both in theory, because it is NP-hard, and in practice, because the algorithms previously used were unable to optimally search over all long chains. We give two new algorithms that use integer programming to optimally solve this problem, one of which is inspired by the techniques used to solve the traveling salesman problem. These algorithms provide the tools needed to find optimal solutions in practice.

  2. Finding long chains in kidney exchange using the traveling salesman problem

    PubMed Central

    Anderson, Ross; Ashlagi, Itai; Gamarnik, David; Roth, Alvin E.

    2015-01-01

    As of May 2014 there were more than 100,000 patients on the waiting list for a kidney transplant from a deceased donor. Although the preferred treatment is a kidney transplant, every year there are fewer donors than new patients, so the wait for a transplant continues to grow. To address this shortage, kidney paired donation (KPD) programs allow patients with living but biologically incompatible donors to exchange donors through cycles or chains initiated by altruistic (nondirected) donors, thereby increasing the supply of kidneys in the system. In many KPD programs a centralized algorithm determines which exchanges will take place to maximize the total number of transplants performed. This optimization problem has proven challenging both in theory, because it is NP-hard, and in practice, because the algorithms previously used were unable to optimally search over all long chains. We give two new algorithms that use integer programming to optimally solve this problem, one of which is inspired by the techniques used to solve the traveling salesman problem. These algorithms provide the tools needed to find optimal solutions in practice. PMID:25561535

  3. Parameter optimization of differential evolution algorithm for automatic playlist generation problem

    NASA Astrophysics Data System (ADS)

    Alamag, Kaye Melina Natividad B.; Addawe, Joel M.

    2017-11-01

    With the digitalization of music, the number of collection of music increased largely and there is a need to create lists of music that filter the collection according to user preferences, thus giving rise to the Automatic Playlist Generation Problem (APGP). Previous attempts to solve this problem include the use of search and optimization algorithms. If a music database is very large, the algorithm to be used must be able to search the lists thoroughly taking into account the quality of the playlist given a set of user constraints. In this paper we perform an evolutionary meta-heuristic optimization algorithm, Differential Evolution (DE) using different combination of parameter values and select the best performing set when used to solve four standard test functions. Performance of the proposed algorithm is then compared with normal Genetic Algorithm (GA) and a hybrid GA with Tabu Search. Numerical simulations are carried out to show better results from Differential Evolution approach with the optimized parameter values.

  4. On a distinctive feature of problems of calculating time-average characteristics of nuclear reactor optimal control sets

    NASA Astrophysics Data System (ADS)

    Trifonenkov, A. V.; Trifonenkov, V. P.

    2017-01-01

    This article deals with a feature of problems of calculating time-average characteristics of nuclear reactor optimal control sets. The operation of a nuclear reactor during threatened period is considered. The optimal control search problem is analysed. The xenon poisoning causes limitations on the variety of statements of the problem of calculating time-average characteristics of a set of optimal reactor power off controls. The level of xenon poisoning is limited. There is a problem of choosing an appropriate segment of the time axis to ensure that optimal control problem is consistent. Two procedures of estimation of the duration of this segment are considered. Two estimations as functions of the xenon limitation were plot. Boundaries of the interval of averaging are defined more precisely.

  5. Phase Transitions in Combinatorial Optimization Problems: Basics, Algorithms and Statistical Mechanics

    NASA Astrophysics Data System (ADS)

    Hartmann, Alexander K.; Weigt, Martin

    2005-10-01

    A concise, comprehensive introduction to the topic of statistical physics of combinatorial optimization, bringing together theoretical concepts and algorithms from computer science with analytical methods from physics. The result bridges the gap between statistical physics and combinatorial optimization, investigating problems taken from theoretical computing, such as the vertex-cover problem, with the concepts and methods of theoretical physics. The authors cover rapid developments and analytical methods that are both extremely complex and spread by word-of-mouth, providing all the necessary basics in required detail. Throughout, the algorithms are shown with examples and calculations, while the proofs are given in a way suitable for graduate students, post-docs, and researchers. Ideal for newcomers to this young, multidisciplinary field.

  6. Combinatorial optimization problem solution based on improved genetic algorithm

    NASA Astrophysics Data System (ADS)

    Zhang, Peng

    2017-08-01

    Traveling salesman problem (TSP) is a classic combinatorial optimization problem. It is a simplified form of many complex problems. In the process of study and research, it is understood that the parameters that affect the performance of genetic algorithm mainly include the quality of initial population, the population size, and crossover probability and mutation probability values. As a result, an improved genetic algorithm for solving TSP problems is put forward. The population is graded according to individual similarity, and different operations are performed to different levels of individuals. In addition, elitist retention strategy is adopted at each level, and the crossover operator and mutation operator are improved. Several experiments are designed to verify the feasibility of the algorithm. Through the experimental results analysis, it is proved that the improved algorithm can improve the accuracy and efficiency of the solution.

  7. 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

  8. An evaluation of methods for estimating the number of local optima in combinatorial optimization problems.

    PubMed

    Hernando, Leticia; Mendiburu, Alexander; Lozano, Jose A

    2013-01-01

    The solution of many combinatorial optimization problems is carried out by metaheuristics, which generally make use of local search algorithms. These algorithms use some kind of neighborhood structure over the search space. The performance of the algorithms strongly depends on the properties that the neighborhood imposes on the search space. One of these properties is the number of local optima. Given an instance of a combinatorial optimization problem and a neighborhood, the estimation of the number of local optima can help not only to measure the complexity of the instance, but also to choose the most convenient neighborhood to solve it. In this paper we review and evaluate several methods to estimate the number of local optima in combinatorial optimization problems. The methods reviewed not only come from the combinatorial optimization literature, but also from the statistical literature. A thorough evaluation in synthetic as well as real problems is given. We conclude by providing recommendations of methods for several scenarios.

  9. An Integrated Method Based on PSO and EDA for the Max-Cut Problem.

    PubMed

    Lin, Geng; Guan, Jian

    2016-01-01

    The max-cut problem is NP-hard combinatorial optimization problem with many real world applications. In this paper, we propose an integrated method based on particle swarm optimization and estimation of distribution algorithm (PSO-EDA) for solving the max-cut problem. The integrated algorithm overcomes the shortcomings of particle swarm optimization and estimation of distribution algorithm. To enhance the performance of the PSO-EDA, a fast local search procedure is applied. In addition, a path relinking procedure is developed to intensify the search. To evaluate the performance of PSO-EDA, extensive experiments were carried out on two sets of benchmark instances with 800 to 20,000 vertices from the literature. Computational results and comparisons show that PSO-EDA significantly outperforms the existing PSO-based and EDA-based algorithms for the max-cut problem. Compared with other best performing algorithms, PSO-EDA is able to find very competitive results in terms of solution quality.

  10. A proposed simulation optimization model framework for emergency department problems in public hospital

    NASA Astrophysics Data System (ADS)

    Ibrahim, Ireen Munira; Liong, Choong-Yeun; Bakar, Sakhinah Abu; Ahmad, Norazura; Najmuddin, Ahmad Farid

    2015-12-01

    The Emergency Department (ED) is a very complex system with limited resources to support increase in demand. ED services are considered as good quality if they can meet the patient's expectation. Long waiting times and length of stay is always the main problem faced by the management. The management of ED should give greater emphasis on their capacity of resources in order to increase the quality of services, which conforms to patient satisfaction. This paper is a review of work in progress of a study being conducted in a government hospital in Selangor, Malaysia. This paper proposed a simulation optimization model framework which is used to study ED operations and problems as well as to find an optimal solution to the problems. The integration of simulation and optimization is hoped can assist management in decision making process regarding their resource capacity planning in order to improve current and future ED operations.

  11. An Efficient Optimization Method for Solving Unsupervised Data Classification Problems.

    PubMed

    Shabanzadeh, Parvaneh; Yusof, Rubiyah

    2015-01-01

    Unsupervised data classification (or clustering) analysis is one of the most useful tools and a descriptive task in data mining that seeks to classify homogeneous groups of objects based on similarity and is used in many medical disciplines and various applications. In general, there is no single algorithm that is suitable for all types of data, conditions, and applications. Each algorithm has its own advantages, limitations, and deficiencies. Hence, research for novel and effective approaches for unsupervised data classification is still active. In this paper a heuristic algorithm, Biogeography-Based Optimization (BBO) algorithm, was adapted for data clustering problems by modifying the main operators of BBO algorithm, which is inspired from the natural biogeography distribution of different species. Similar to other population-based algorithms, BBO algorithm starts with an initial population of candidate solutions to an optimization problem and an objective function that is calculated for them. To evaluate the performance of the proposed algorithm assessment was carried on six medical and real life datasets and was compared with eight well known and recent unsupervised data classification algorithms. Numerical results demonstrate that the proposed evolutionary optimization algorithm is efficient for unsupervised data classification.

  12. A Memetic Algorithm for Global Optimization of Multimodal Nonseparable Problems.

    PubMed

    Zhang, Geng; Li, Yangmin

    2016-06-01

    It is a big challenging issue of avoiding falling into local optimum especially when facing high-dimensional nonseparable problems where the interdependencies among vector elements are unknown. In order to improve the performance of optimization algorithm, a novel memetic algorithm (MA) called cooperative particle swarm optimizer-modified harmony search (CPSO-MHS) is proposed in this paper, where the CPSO is used for local search and the MHS for global search. The CPSO, as a local search method, uses 1-D swarm to search each dimension separately and thus converges fast. Besides, it can obtain global optimum elements according to our experimental results and analyses. MHS implements the global search by recombining different vector elements and extracting global optimum elements. The interaction between local search and global search creates a set of local search zones, where global optimum elements reside within the search space. The CPSO-MHS algorithm is tested and compared with seven other optimization algorithms on a set of 28 standard benchmarks. Meanwhile, some MAs are also compared according to the results derived directly from their corresponding references. The experimental results demonstrate a good performance of the proposed CPSO-MHS algorithm in solving multimodal nonseparable problems.

  13. The Use of D-Optimal Mixture Design in Optimizing Development of Okara Tablet Formulation as a Dietary Supplement.

    PubMed

    Zen, Nur Izzati Mohamad; Abd Gani, Siti Salwa; Shamsudin, Rosnah; Masoumi, Hamid Reza Fard

    2015-01-01

    The usage of soy is increasing year by year. It increases the problem of financial crisis due to the limited sources of soybeans. Therefore, production of oral tablets containing the nutritious leftover of soymilk production, called okara, as the main ingredient was investigated. The okara tablets were produced using the direct compression method. The percentage of okara, guar gum, microcrystalline cellulose (Avicel PH-101), and maltodextrin influenced tablets' hardness and friability which are analyzed using a D-optimal mixture design. Composition of Avicel PH-101 had positive effects for both hardness and friability tests of the tablets. Maltodextrin and okara composition had a significant positive effect on tablets' hardness, but not on percentage of friability of tablets. However, guar gum had a negative effect on both physical tests. The optimum tablet formulation was obtained: 47.0% of okara, 2.0% of guar gum, 35.0% of Avicel PH-101, and 14.0% of maltodextrin.

  14. The Use of D-Optimal Mixture Design in Optimizing Development of Okara Tablet Formulation as a Dietary Supplement

    PubMed Central

    Mohamad Zen, Nur Izzati; Shamsudin, Rosnah

    2015-01-01

    The usage of soy is increasing year by year. It increases the problem of financial crisis due to the limited sources of soybeans. Therefore, production of oral tablets containing the nutritious leftover of soymilk production, called okara, as the main ingredient was investigated. The okara tablets were produced using the direct compression method. The percentage of okara, guar gum, microcrystalline cellulose (Avicel PH-101), and maltodextrin influenced tablets' hardness and friability which are analyzed using a D-optimal mixture design. Composition of Avicel PH-101 had positive effects for both hardness and friability tests of the tablets. Maltodextrin and okara composition had a significant positive effect on tablets' hardness, but not on percentage of friability of tablets. However, guar gum had a negative effect on both physical tests. The optimum tablet formulation was obtained: 47.0% of okara, 2.0% of guar gum, 35.0% of Avicel PH-101, and 14.0% of maltodextrin. PMID:26171418

  15. Performance comparison of genetic algorithms and particle swarm optimization for model integer programming bus timetabling problem

    NASA Astrophysics Data System (ADS)

    Wihartiko, F. D.; Wijayanti, H.; Virgantari, F.

    2018-03-01

    Genetic Algorithm (GA) is a common algorithm used to solve optimization problems with artificial intelligence approach. Similarly, the Particle Swarm Optimization (PSO) algorithm. Both algorithms have different advantages and disadvantages when applied to the case of optimization of the Model Integer Programming for Bus Timetabling Problem (MIPBTP), where in the case of MIPBTP will be found the optimal number of trips confronted with various constraints. The comparison results show that the PSO algorithm is superior in terms of complexity, accuracy, iteration and program simplicity in finding the optimal solution.

  16. Comparing hard and soft prior bounds in geophysical inverse problems

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1988-01-01

    In linear inversion of a finite-dimensional data vector y to estimate a finite-dimensional prediction vector z, prior information about X sub E is essential if y is to supply useful limits for z. The one exception occurs when all the prediction functionals are linear combinations of the data functionals. Two forms of prior information are compared: a soft bound on X sub E is a probability distribution p sub x on X which describes the observer's opinion about where X sub E is likely to be in X; a hard bound on X sub E is an inequality Q sub x(X sub E, X sub E) is equal to or less than 1, where Q sub x is a positive definite quadratic form on X. A hard bound Q sub x can be softened to many different probability distributions p sub x, but all these p sub x's carry much new information about X sub E which is absent from Q sub x, and some information which contradicts Q sub x. Both stochastic inversion (SI) and Bayesian inference (BI) estimate z from y and a soft prior bound p sub x. If that probability distribution was obtained by softening a hard prior bound Q sub x, rather than by objective statistical inference independent of y, then p sub x contains so much unsupported new information absent from Q sub x that conclusions about z obtained with SI or BI would seen to be suspect.

  17. Comparing hard and soft prior bounds in geophysical inverse problems

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1987-01-01

    In linear inversion of a finite-dimensional data vector y to estimate a finite-dimensional prediction vector z, prior information about X sub E is essential if y is to supply useful limits for z. The one exception occurs when all the prediction functionals are linear combinations of the data functionals. Two forms of prior information are compared: a soft bound on X sub E is a probability distribution p sub x on X which describeds the observer's opinion about where X sub E is likely to be in X; a hard bound on X sub E is an inequality Q sub x(X sub E, X sub E) is equal to or less than 1, where Q sub x is a positive definite quadratic form on X. A hard bound Q sub x can be softened to many different probability distributions p sub x, but all these p sub x's carry much new information about X sub E which is absent from Q sub x, and some information which contradicts Q sub x. Both stochastic inversion (SI) and Bayesian inference (BI) estimate z from y and a soft prior bound p sub x. If that probability distribution was obtained by softening a hard prior bound Q sub x, rather than by objective statistical inference independent of y, then p sub x contains so much unsupported new information absent from Q sub x that conclusions about z obtained with SI or BI would seen to be suspect.

  18. An Effective Hybrid Evolutionary Algorithm for Solving the Numerical Optimization Problems

    NASA Astrophysics Data System (ADS)

    Qian, Xiaohong; Wang, Xumei; Su, Yonghong; He, Liu

    2018-04-01

    There are many different algorithms for solving complex optimization problems. Each algorithm has been applied successfully in solving some optimization problems, but not efficiently in other problems. In this paper the Cauchy mutation and the multi-parent hybrid operator are combined to propose a hybrid evolutionary algorithm based on the communication (Mixed Evolutionary Algorithm based on Communication), hereinafter referred to as CMEA. The basic idea of the CMEA algorithm is that the initial population is divided into two subpopulations. Cauchy mutation operators and multiple paternal crossover operators are used to perform two subpopulations parallelly to evolve recursively until the downtime conditions are met. While subpopulation is reorganized, the individual is exchanged together with information. The algorithm flow is given and the performance of the algorithm is compared using a number of standard test functions. Simulation results have shown that this algorithm converges significantly faster than FEP (Fast Evolutionary Programming) algorithm, has good performance in global convergence and stability and is superior to other compared algorithms.

  19. Optimization Techniques for Clustering,Connectivity, and Flow Problems in Complex Networks

    DTIC Science & Technology

    2012-10-01

    discrete optimization and for analysis of performance of algorithm portfolios; introducing a metaheuristic framework of variable objective search that...The results of empirical evaluation of the proposed algorithm are also included. 1.3 Theoretical analysis of heuristics and designing new metaheuristic ...analysis of heuristics for inapproximable problems and designing new metaheuristic approaches for the problems of interest; (IV) Developing new models

  20. A dual method for optimal control problems with initial and final boundary constraints.

    NASA Technical Reports Server (NTRS)

    Pironneau, O.; Polak, E.

    1973-01-01

    This paper presents two new algorithms belonging to the family of dual methods of centers. The first can be used for solving fixed time optimal control problems with inequality constraints on the initial and terminal states. The second one can be used for solving fixed time optimal control problems with inequality constraints on the initial and terminal states and with affine instantaneous inequality constraints on the control. Convergence is established for both algorithms. Qualitative reasoning indicates that the rate of convergence is linear.

  1. Genetic Algorithm for Traveling Salesman Problem with Modified Cycle Crossover Operator

    PubMed Central

    Mohamd Shoukry, Alaa; Gani, Showkat

    2017-01-01

    Genetic algorithms are evolutionary techniques used for optimization purposes according to survival of the fittest idea. These methods do not ensure optimal solutions; however, they give good approximation usually in time. The genetic algorithms are useful for NP-hard problems, especially the traveling salesman problem. The genetic algorithm depends on selection criteria, crossover, and mutation operators. To tackle the traveling salesman problem using genetic algorithms, there are various representations such as binary, path, adjacency, ordinal, and matrix representations. In this article, we propose a new crossover operator for traveling salesman problem to minimize the total distance. This approach has been linked with path representation, which is the most natural way to represent a legal tour. Computational results are also reported with some traditional path representation methods like partially mapped and order crossovers along with new cycle crossover operator for some benchmark TSPLIB instances and found improvements. PMID:29209364

  2. Genetic Algorithm for Traveling Salesman Problem with Modified Cycle Crossover Operator.

    PubMed

    Hussain, Abid; Muhammad, Yousaf Shad; Nauman Sajid, M; Hussain, Ijaz; Mohamd Shoukry, Alaa; Gani, Showkat

    2017-01-01

    Genetic algorithms are evolutionary techniques used for optimization purposes according to survival of the fittest idea. These methods do not ensure optimal solutions; however, they give good approximation usually in time. The genetic algorithms are useful for NP-hard problems, especially the traveling salesman problem. The genetic algorithm depends on selection criteria, crossover, and mutation operators. To tackle the traveling salesman problem using genetic algorithms, there are various representations such as binary, path, adjacency, ordinal, and matrix representations. In this article, we propose a new crossover operator for traveling salesman problem to minimize the total distance. This approach has been linked with path representation, which is the most natural way to represent a legal tour. Computational results are also reported with some traditional path representation methods like partially mapped and order crossovers along with new cycle crossover operator for some benchmark TSPLIB instances and found improvements.

  3. A survey of methods of feasible directions for the solution of optimal control problems

    NASA Technical Reports Server (NTRS)

    Polak, E.

    1972-01-01

    Three methods of feasible directions for optimal control are reviewed. These methods are an extension of the Frank-Wolfe method, a dual method devised by Pironneau and Polack, and a Zontendijk method. The categories of continuous optimal control problems are shown as: (1) fixed time problems with fixed initial state, free terminal state, and simple constraints on the control; (2) fixed time problems with inequality constraints on both the initial and the terminal state and no control constraints; (3) free time problems with inequality constraints on the initial and terminal states and simple constraints on the control; and (4) fixed time problems with inequality state space contraints and constraints on the control. The nonlinear programming algorithms are derived for each of the methods in its associated category.

  4. Executive functions and behavioral problems in deaf and hard-of-hearing students at general and special schools.

    PubMed

    Hintermair, Manfred

    2013-01-01

    In this study, behavioral problems of deaf and hard-of-hearing (D/HH) school-aged children are discussed in the context of executive functioning and communicative competence. Teachers assessed the executive functions of a sample of 214 D/HH students from general schools and schools for the deaf, using a German version of the Behavior Rating Inventory of Executive Functions (BRIEF-D). This was complemented by a questionnaire that measured communicative competence and behavioral problems (German version of the Strengths and Difficulties Questionnaire; SDQ-D). The results in nearly all the scales show a significantly higher problem rate for executive functions in the group of D/HH students compared with a normative sample of hearing children. In the D/HH group, students at general schools had better scores on most scales than students at schools for the deaf. Regression analysis reveals the importance of executive functions and communicative competence for behavioral problems. The relevance of the findings for pedagogical work is discussed. A specific focus on competencies such as self-efficacy or self-control in educational concepts for D/HH students seems to be necessary in addition to extending language competencies.

  5. 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

  6. Process optimization for ultrasonic vibration assisted polishing of micro-structured surfaces on super hard material

    NASA Astrophysics Data System (ADS)

    Sun, Zhiyuan; Guo, Bing; Rao, Zhimin; Zhao, Qingliang

    2014-08-01

    In consideration of the excellent property of SiC, the ground micro-structured surface quality is hard to meet the requirement - consequently the ultrasonic vibration assisted polishing (UVAP) of micro-structures of molds is proposed in this paper. Through the orthogonal experiment, the parameters of UVAP of micro-structures were optimized. The experimental results show that, abrasive polishing process, the effect of the workpiece feed rate on the surface roughness (Ra), groove tip radius (R) and material removal rate (MRR) of micro-structures is significant. While, the UVAP, the most significant effect factor for Ra, R and MRR is the ultrasonic amplitude of the ultrasonic vibration. In addition, within the scope of the polishing process parameters selected by preliminary experiments, ultrasonic amplitude of 2.5μm, polishing force of 0.5N, workpiece feed rate of 5 mm·min-1, polishing wheel rotational speed of 50rpm, polishing time of 35min, abrasive size of 100nm and the polishing liquid concentration of 15% is the best technology of UVAP of micro-structures. Under the optimal parameters, the ground traces on the micro-structured surface were removed efficiently and the integrity of the edges of the micro-structure after grinding was maintained efficiently.

  7. Near-optimal alternative generation using modified hit-and-run sampling for non-linear, non-convex problems

    NASA Astrophysics Data System (ADS)

    Rosenberg, D. E.; Alafifi, A.

    2016-12-01

    Water resources systems analysis often focuses on finding optimal solutions. Yet an optimal solution is optimal only for the modelled issues and managers often seek near-optimal alternatives that address un-modelled objectives, preferences, limits, uncertainties, and other issues. Early on, Modelling to Generate Alternatives (MGA) formalized near-optimal as the region comprising the original problem constraints plus a new constraint that allowed performance within a specified tolerance of the optimal objective function value. MGA identified a few maximally-different alternatives from the near-optimal region. Subsequent work applied Markov Chain Monte Carlo (MCMC) sampling to generate a larger number of alternatives that span the near-optimal region of linear problems or select portions for non-linear problems. We extend the MCMC Hit-And-Run method to generate alternatives that span the full extent of the near-optimal region for non-linear, non-convex problems. First, start at a feasible hit point within the near-optimal region, then run a random distance in a random direction to a new hit point. Next, repeat until generating the desired number of alternatives. The key step at each iterate is to run a random distance along the line in the specified direction to a new hit point. If linear equity constraints exist, we construct an orthogonal basis and use a null space transformation to confine hits and runs to a lower-dimensional space. Linear inequity constraints define the convex bounds on the line that runs through the current hit point in the specified direction. We then use slice sampling to identify a new hit point along the line within bounds defined by the non-linear inequity constraints. This technique is computationally efficient compared to prior near-optimal alternative generation techniques such MGA, MCMC Metropolis-Hastings, evolutionary, or firefly algorithms because search at each iteration is confined to the hit line, the algorithm can move in one

  8. Two Point Exponential Approximation Method for structural optimization of problems with frequency constraints

    NASA Technical Reports Server (NTRS)

    Fadel, G. M.

    1991-01-01

    The point exponential approximation method was introduced by Fadel et al. (Fadel, 1990), and tested on structural optimization problems with stress and displacement constraints. The reports in earlier papers were promising, and the method, which consists of correcting Taylor series approximations using previous design history, is tested in this paper on optimization problems with frequency constraints. The aim of the research is to verify the robustness and speed of convergence of the two point exponential approximation method when highly non-linear constraints are used.

  9. An optimized full-configuration-interaction nuclear orbital approach to a ``hard-core'' interaction problem: Application to (3He)N-Cl2(B) clusters (N<=4)

    NASA Astrophysics Data System (ADS)

    de Lara-Castells, M. P.; Villarreal, P.; Delgado-Barrio, G.; Mitrushchenkov, A. O.

    2009-11-01

    An efficient full-configuration-interaction nuclear orbital treatment has been recently developed as a benchmark quantum-chemistry-like method to calculate ground and excited "solvent" energies and wave functions in small doped ΔEest clusters (N ≤4) [M. P. de Lara-Castells, G. Delgado-Barrio, P. Villarreal, and A. O. Mitrushchenkov, J. Chem. Phys. 125, 221101 (2006)]. Additional methodological and computational details of the implementation, which uses an iterative Jacobi-Davidson diagonalization algorithm to properly address the inherent "hard-core" He-He interaction problem, are described here. The convergence of total energies, average pair He-He interaction energies, and relevant one- and two-body properties upon increasing the angular part of the one-particle basis set (expanded in spherical harmonics) has been analyzed, considering Cl2 as the dopant and a semiempirical model (T-shaped) He-Cl2(B) potential. Converged results are used to analyze global energetic and structural aspects as well as the configuration makeup of the wave functions, associated with the ground and low-lying "solvent" excited states. Our study reveals that besides the fermionic nature of H3e atoms, key roles in determining total binding energies and wave-function structures are played by the strong repulsive core of the He-He potential as well as its very weak attractive region, the most stable arrangement somehow departing from the one of N He atoms equally spaced on equatorial "ring" around the dopant. The present results for N =4 fermions indicates the structural "pairing" of two H3e atoms at opposite sides on a broad "belt" around the dopant, executing a sort of asymmetric umbrella motion. This pairing is a compromise between maximizing the H3e-H3e and the He-dopant attractions, and suppressing at the same time the "hard-core" repulsion. Although the He-He attractive interaction is rather weak, its contribution to the total energy is found to scale as a power of three and it thus

  10. A tabu search evalutionary algorithm for multiobjective optimization: Application to a bi-criterion aircraft structural reliability problem

    NASA Astrophysics Data System (ADS)

    Long, Kim Chenming

    Real-world engineering optimization problems often require the consideration of multiple conflicting and noncommensurate objectives, subject to nonconvex constraint regions in a high-dimensional decision space. Further challenges occur for combinatorial multiobjective problems in which the decision variables are not continuous. Traditional multiobjective optimization methods of operations research, such as weighting and epsilon constraint methods, are ill-suited to solving these complex, multiobjective problems. This has given rise to the application of a wide range of metaheuristic optimization algorithms, such as evolutionary, particle swarm, simulated annealing, and ant colony methods, to multiobjective optimization. Several multiobjective evolutionary algorithms have been developed, including the strength Pareto evolutionary algorithm (SPEA) and the non-dominated sorting genetic algorithm (NSGA), for determining the Pareto-optimal set of non-dominated solutions. Although numerous researchers have developed a wide range of multiobjective optimization algorithms, there is a continuing need to construct computationally efficient algorithms with an improved ability to converge to globally non-dominated solutions along the Pareto-optimal front for complex, large-scale, multiobjective engineering optimization problems. This is particularly important when the multiple objective functions and constraints of the real-world system cannot be expressed in explicit mathematical representations. This research presents a novel metaheuristic evolutionary algorithm for complex multiobjective optimization problems, which combines the metaheuristic tabu search algorithm with the evolutionary algorithm (TSEA), as embodied in genetic algorithms. TSEA is successfully applied to bicriteria (i.e., structural reliability and retrofit cost) optimization of the aircraft tail structure fatigue life, which increases its reliability by prolonging fatigue life. A comparison for this

  11. CSOLNP: Numerical Optimization Engine for Solving Non-linearly Constrained Problems.

    PubMed

    Zahery, Mahsa; Maes, Hermine H; Neale, Michael C

    2017-08-01

    We introduce the optimizer CSOLNP, which is a C++ implementation of the R package RSOLNP (Ghalanos & Theussl, 2012, Rsolnp: General non-linear optimization using augmented Lagrange multiplier method. R package version, 1) alongside some improvements. CSOLNP solves non-linearly constrained optimization problems using a Sequential Quadratic Programming (SQP) algorithm. CSOLNP, NPSOL (a very popular implementation of SQP method in FORTRAN (Gill et al., 1986, User's guide for NPSOL (version 4.0): A Fortran package for nonlinear programming (No. SOL-86-2). Stanford, CA: Stanford University Systems Optimization Laboratory), and SLSQP (another SQP implementation available as part of the NLOPT collection (Johnson, 2014, The NLopt nonlinear-optimization package. Retrieved from http://ab-initio.mit.edu/nlopt)) are three optimizers available in OpenMx package. These optimizers are compared in terms of runtimes, final objective values, and memory consumption. A Monte Carlo analysis of the performance of the optimizers was performed on ordinal and continuous models with five variables and one or two factors. While the relative difference between the objective values is less than 0.5%, CSOLNP is in general faster than NPSOL and SLSQP for ordinal analysis. As for continuous data, none of the optimizers performs consistently faster than the others. In terms of memory usage, we used Valgrind's heap profiler tool, called Massif, on one-factor threshold models. CSOLNP and NPSOL consume the same amount of memory, while SLSQP uses 71 MB more memory than the other two optimizers.

  12. Optimization problems in natural gas transportation systems. A state-of-the-art review

    DOE PAGES

    Ríos-Mercado, Roger Z.; Borraz-Sánchez, Conrado

    2015-03-24

    Our paper provides a review on the most relevant research works conducted to solve natural gas transportation problems via pipeline systems. The literature reveals three major groups of gas pipeline systems, namely gathering, transmission, and distribution systems. In this work, we aim at presenting a detailed discussion of the efforts made in optimizing natural gas transmission lines.There is certainly a vast amount of research done over the past few years on many decision-making problems in the natural gas industry and, specifically, in pipeline network optimization. In this work, we present a state-of-the-art survey focusing on specific categories that include short-termmore » basis storage (line-packing problems), gas quality satisfaction (pooling problems), and compressor station modeling (fuel cost minimization problems). We also discuss both steady-state and transient optimization models highlighting the modeling aspects and the most relevant solution approaches known to date. Although the literature on natural gas transmission system problems is quite extensive, this is, to the best of our knowledge, the first comprehensive review or survey covering this specific research area on natural gas transmission from an operations research perspective. Furthermore, this paper includes a discussion of the most important and promising research areas in this field. Hence, our paper can serve as a useful tool to gain insight into the evolution of the many real-life applications and most recent advances in solution methodologies arising from this exciting and challenging research area of decision-making problems.« less

  13. Optimization problems in natural gas transportation systems. A state-of-the-art review

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

    Ríos-Mercado, Roger Z.; Borraz-Sánchez, Conrado

    Our paper provides a review on the most relevant research works conducted to solve natural gas transportation problems via pipeline systems. The literature reveals three major groups of gas pipeline systems, namely gathering, transmission, and distribution systems. In this work, we aim at presenting a detailed discussion of the efforts made in optimizing natural gas transmission lines.There is certainly a vast amount of research done over the past few years on many decision-making problems in the natural gas industry and, specifically, in pipeline network optimization. In this work, we present a state-of-the-art survey focusing on specific categories that include short-termmore » basis storage (line-packing problems), gas quality satisfaction (pooling problems), and compressor station modeling (fuel cost minimization problems). We also discuss both steady-state and transient optimization models highlighting the modeling aspects and the most relevant solution approaches known to date. Although the literature on natural gas transmission system problems is quite extensive, this is, to the best of our knowledge, the first comprehensive review or survey covering this specific research area on natural gas transmission from an operations research perspective. Furthermore, this paper includes a discussion of the most important and promising research areas in this field. Hence, our paper can serve as a useful tool to gain insight into the evolution of the many real-life applications and most recent advances in solution methodologies arising from this exciting and challenging research area of decision-making problems.« less

  14. Enhanced ant colony optimization for inventory routing problem

    NASA Astrophysics Data System (ADS)

    Wong, Lily; Moin, Noor Hasnah

    2015-10-01

    The inventory routing problem (IRP) integrates and coordinates two important components of supply chain management which are transportation and inventory management. We consider a one-to-many IRP network for a finite planning horizon. The demand for each product is deterministic and time varying as well as a fleet of capacitated homogeneous vehicles, housed at a depot/warehouse, delivers the products from the warehouse to meet the demand specified by the customers in each period. The inventory holding cost is product specific and is incurred at the customer sites. The objective is to determine the amount of inventory and to construct a delivery routing that minimizes both the total transportation and inventory holding cost while ensuring each customer's demand is met over the planning horizon. The problem is formulated as a mixed integer programming problem and is solved using CPLEX 12.4 to get the lower and upper bound (best integer) for each instance considered. We propose an enhanced ant colony optimization (ACO) to solve the problem and the built route is improved by using local search. The computational experiments demonstrating the effectiveness of our approach is presented.

  15. Stability of Solutions to Classes of Traveling Salesman Problems.

    PubMed

    Niendorf, Moritz; Kabamba, Pierre T; Girard, Anouck R

    2016-04-01

    By performing stability analysis on an optimal tour for problems belonging to classes of the traveling salesman problem (TSP), this paper derives margins of optimality for a solution with respect to disturbances in the problem data. Specifically, we consider the asymmetric sequence-dependent TSP, where the sequence dependence is driven by the dynamics of a stack. This is a generalization of the symmetric non sequence-dependent version of the TSP. Furthermore, we also consider the symmetric sequence-dependent variant and the asymmetric non sequence-dependent variant. Amongst others these problems have applications in logistics and unmanned aircraft mission planning. Changing external conditions such as traffic or weather may alter task costs, which can render an initially optimal itinerary suboptimal. Instead of optimizing the itinerary every time task costs change, stability criteria allow for fast evaluation of whether itineraries remain optimal. This paper develops a method to compute stability regions for the best tour in a set of tours for the symmetric TSP and extends the results to the asymmetric problem as well as their sequence-dependent counterparts. As the TSP is NP-hard, heuristic methods are frequently used to solve it. The presented approach is also applicable to analyze stability regions for a tour obtained through application of the k -opt heuristic with respect to the k -neighborhood. A dimensionless criticality metric for edges is proposed, such that a high criticality of an edge indicates that the optimal tour is more susceptible to cost changes in that edge. Multiple examples demonstrate the application of the developed stability computation method as well as the edge criticality measure that facilitates an intuitive assessment of instances of the TSP.

  16. Approximated analytical solution to an Ebola optimal control problem

    NASA Astrophysics Data System (ADS)

    Hincapié-Palacio, Doracelly; Ospina, Juan; Torres, Delfim F. M.

    2016-11-01

    An analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler-Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical methods.

  17. Designing a fuzzy scheduler for hard real-time systems

    NASA Technical Reports Server (NTRS)

    Yen, John; Lee, Jonathan; Pfluger, Nathan; Natarajan, Swami

    1992-01-01

    In hard real-time systems, tasks have to be performed not only correctly, but also in a timely fashion. If timing constraints are not met, there might be severe consequences. Task scheduling is the most important problem in designing a hard real-time system, because the scheduling algorithm ensures that tasks meet their deadlines. However, the inherent nature of uncertainty in dynamic hard real-time systems increases the problems inherent in scheduling. In an effort to alleviate these problems, we have developed a fuzzy scheduler to facilitate searching for a feasible schedule. A set of fuzzy rules are proposed to guide the search. The situation we are trying to address is the performance of the system when no feasible solution can be found, and therefore, certain tasks will not be executed. We wish to limit the number of important tasks that are not scheduled.

  18. Effective optimization using sample persistence: A case study on quantum annealers and various Monte Carlo optimization methods

    NASA Astrophysics Data System (ADS)

    Karimi, Hamed; Rosenberg, Gili; Katzgraber, Helmut G.

    2017-10-01

    We present and apply a general-purpose, multistart algorithm for improving the performance of low-energy samplers used for solving optimization problems. The algorithm iteratively fixes the value of a large portion of the variables to values that have a high probability of being optimal. The resulting problems are smaller and less connected, and samplers tend to give better low-energy samples for these problems. The algorithm is trivially parallelizable since each start in the multistart algorithm is independent, and could be applied to any heuristic solver that can be run multiple times to give a sample. We present results for several classes of hard problems solved using simulated annealing, path-integral quantum Monte Carlo, parallel tempering with isoenergetic cluster moves, and a quantum annealer, and show that the success metrics and the scaling are improved substantially. When combined with this algorithm, the quantum annealer's scaling was substantially improved for native Chimera graph problems. In addition, with this algorithm the scaling of the time to solution of the quantum annealer is comparable to the Hamze-de Freitas-Selby algorithm on the weak-strong cluster problems introduced by Boixo et al. Parallel tempering with isoenergetic cluster moves was able to consistently solve three-dimensional spin glass problems with 8000 variables when combined with our method, whereas without our method it could not solve any.

  19. Subspace-based optimization method for inverse scattering problems with an inhomogeneous background medium

    NASA Astrophysics Data System (ADS)

    Chen, Xudong

    2010-07-01

    This paper proposes a version of the subspace-based optimization method to solve the inverse scattering problem with an inhomogeneous background medium where the known inhomogeneities are bounded in a finite domain. Although the background Green's function at each discrete point in the computational domain is not directly available in an inhomogeneous background scenario, the paper uses the finite element method to simultaneously obtain the Green's function at all discrete points. The essence of the subspace-based optimization method is that part of the contrast source is determined from the spectrum analysis without using any optimization, whereas the orthogonally complementary part is determined by solving a lower dimension optimization problem. This feature significantly speeds up the convergence of the algorithm and at the same time makes it robust against noise. Numerical simulations illustrate the efficacy of the proposed algorithm. The algorithm presented in this paper finds wide applications in nondestructive evaluation, such as through-wall imaging.

  20. 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.

  1. A hybrid symbolic/finite-element algorithm for solving nonlinear optimal control problems

    NASA Technical Reports Server (NTRS)

    Bless, Robert R.; Hodges, Dewey H.

    1991-01-01

    The general code described is capable of solving difficult nonlinear optimal control problems by using finite elements and a symbolic manipulator. Quick and accurate solutions are obtained with a minimum for user interaction. Since no user programming is required for most problems, there are tremendous savings to be gained in terms of time and money.

  2. Statistical mechanical analysis of linear programming relaxation for combinatorial optimization problems

    NASA Astrophysics Data System (ADS)

    Takabe, Satoshi; Hukushima, Koji

    2016-05-01

    Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α -uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α =2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c =e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c =1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α ≥3 , minimum vertex covers on α -uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c =e /(α -1 ) where the replica symmetry is broken.

  3. Statistical mechanical analysis of linear programming relaxation for combinatorial optimization problems.

    PubMed

    Takabe, Satoshi; Hukushima, Koji

    2016-05-01

    Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α-uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α=2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c=e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c=1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α≥3, minimum vertex covers on α-uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c=e/(α-1) where the replica symmetry is broken.

  4. Free terminal time optimal control problem of an HIV model based on a conjugate gradient method.

    PubMed

    Jang, Taesoo; Kwon, Hee-Dae; Lee, Jeehyun

    2011-10-01

    The minimum duration of treatment periods and the optimal multidrug therapy for human immunodeficiency virus (HIV) type 1 infection are considered. We formulate an optimal tracking problem, attempting to drive the states of the model to a "healthy" steady state in which the viral load is low and the immune response is strong. We study an optimal time frame as well as HIV therapeutic strategies by analyzing the free terminal time optimal tracking control problem. The minimum duration of treatment periods and the optimal multidrug therapy are found by solving the corresponding optimality systems with the additional transversality condition for the terminal time. We demonstrate by numerical simulations that the optimal dynamic multidrug therapy can lead to the long-term control of HIV by the strong immune response after discontinuation of therapy.

  5. Potential Health Impacts of Hard Water

    PubMed Central

    Sengupta, Pallav

    2013-01-01

    In the past five decades or so evidence has been accumulating about an environmental factor, which appears to be influencing mortality, in particular, cardiovascular mortality, and this is the hardness of the drinking water. In addition, several epidemiological investigations have demonstrated the relation between risk for cardiovascular disease, growth retardation, reproductive failure, and other health problems and hardness of drinking water or its content of magnesium and calcium. In addition, the acidity of the water influences the reabsorption of calcium and magnesium in the renal tubule. Not only, calcium and magnesium, but other constituents also affect different health aspects. Thus, the present review attempts to explore the health effects of hard water and its constituents. PMID:24049611

  6. Potential health impacts of hard water.

    PubMed

    Sengupta, Pallav

    2013-08-01

    In the past five decades or so evidence has been accumulating about an environmental factor, which appears to be influencing mortality, in particular, cardiovascular mortality, and this is the hardness of the drinking water. In addition, several epidemiological investigations have demonstrated the relation between risk for cardiovascular disease, growth retardation, reproductive failure, and other health problems and hardness of drinking water or its content of magnesium and calcium. In addition, the acidity of the water influences the reabsorption of calcium and magnesium in the renal tubule. Not only, calcium and magnesium, but other constituents also affect different health aspects. Thus, the present review attempts to explore the health effects of hard water and its constituents.

  7. A Computationally Inexpensive Optimal Guidance via Radial-Basis-Function Neural Network for Autonomous Soft Landing on Asteroids

    PubMed Central

    Zhang, Peng; Liu, Keping; Zhao, Bo; Li, Yuanchun

    2015-01-01

    Optimal guidance is essential for the soft landing task. However, due to its high computational complexities, it is hardly applied to the autonomous guidance. In this paper, a computationally inexpensive optimal guidance algorithm based on the radial basis function neural network (RBFNN) is proposed. The optimization problem of the trajectory for soft landing on asteroids is formulated and transformed into a two-point boundary value problem (TPBVP). Combining the database of initial states with the relative initial co-states, an RBFNN is trained offline. The optimal trajectory of the soft landing is determined rapidly by applying the trained network in the online guidance. The Monte Carlo simulations of soft landing on the Eros433 are performed to demonstrate the effectiveness of the proposed guidance algorithm. PMID:26367382

  8. Permutation flow-shop scheduling problem to optimize a quadratic objective function

    NASA Astrophysics Data System (ADS)

    Ren, Tao; Zhao, Peng; Zhang, Da; Liu, Bingqian; Yuan, Huawei; Bai, Danyu

    2017-09-01

    A flow-shop scheduling model enables appropriate sequencing for each job and for processing on a set of machines in compliance with identical processing orders. The objective is to achieve a feasible schedule for optimizing a given criterion. Permutation is a special setting of the model in which the processing order of the jobs on the machines is identical for each subsequent step of processing. This article addresses the permutation flow-shop scheduling problem to minimize the criterion of total weighted quadratic completion time. With a probability hypothesis, the asymptotic optimality of the weighted shortest processing time schedule under a consistency condition (WSPT-CC) is proven for sufficiently large-scale problems. However, the worst case performance ratio of the WSPT-CC schedule is the square of the number of machines in certain situations. A discrete differential evolution algorithm, where a new crossover method with multiple-point insertion is used to improve the final outcome, is presented to obtain high-quality solutions for moderate-scale problems. A sequence-independent lower bound is designed for pruning in a branch-and-bound algorithm for small-scale problems. A set of random experiments demonstrates the performance of the lower bound and the effectiveness of the proposed algorithms.

  9. Heuristic algorithms for the minmax regret flow-shop problem with interval processing times.

    PubMed

    Ćwik, Michał; Józefczyk, Jerzy

    2018-01-01

    An uncertain version of the permutation flow-shop with unlimited buffers and the makespan as a criterion is considered. The investigated parametric uncertainty is represented by given interval-valued processing times. The maximum regret is used for the evaluation of uncertainty. Consequently, the minmax regret discrete optimization problem is solved. Due to its high complexity, two relaxations are applied to simplify the optimization procedure. First of all, a greedy procedure is used for calculating the criterion's value, as such calculation is NP-hard problem itself. Moreover, the lower bound is used instead of solving the internal deterministic flow-shop. The constructive heuristic algorithm is applied for the relaxed optimization problem. The algorithm is compared with previously elaborated other heuristic algorithms basing on the evolutionary and the middle interval approaches. The conducted computational experiments showed the advantage of the constructive heuristic algorithm with regards to both the criterion and the time of computations. The Wilcoxon paired-rank statistical test confirmed this conclusion.

  10. Optimization of the time-dependent traveling salesman problem with Monte Carlo methods.

    PubMed

    Bentner, J; Bauer, G; Obermair, G M; Morgenstern, I; Schneider, J

    2001-09-01

    A problem often considered in operations research and computational physics is the traveling salesman problem, in which a traveling salesperson has to find the shortest closed tour between a certain set of cities. This problem has been extended to more realistic scenarios, e.g., the "real" traveling salesperson has to take rush hours into consideration. We will show how this extended problem is treated with physical optimization algorithms. We will present results for a specific instance of Reinelt's library TSPLIB95, in which we define a zone with traffic jams in the afternoon.

  11. Comparison of some evolutionary algorithms for optimization of the path synthesis problem

    NASA Astrophysics Data System (ADS)

    Grabski, Jakub Krzysztof; Walczak, Tomasz; Buśkiewicz, Jacek; Michałowska, Martyna

    2018-01-01

    The paper presents comparison of the results obtained in a mechanism synthesis by means of some selected evolutionary algorithms. The optimization problem considered in the paper as an example is the dimensional synthesis of the path generating four-bar mechanism. In order to solve this problem, three different artificial intelligence algorithms are employed in this study.

  12. Optimal control of LQG problem with an explicit trade-off between mean and variance

    NASA Astrophysics Data System (ADS)

    Qian, Fucai; Xie, Guo; Liu, Ding; Xie, Wenfang

    2011-12-01

    For discrete-time linear-quadratic Gaussian (LQG) control problems, a utility function on the expectation and the variance of the conventional performance index is considered. The utility function is viewed as an overall objective of the system and can perform the optimal trade-off between the mean and the variance of performance index. The nonlinear utility function is first converted into an auxiliary parameters optimisation problem about the expectation and the variance. Then an optimal closed-loop feedback controller for the nonseparable mean-variance minimisation problem is designed by nonlinear mathematical programming. Finally, simulation results are given to verify the algorithm's effectiveness obtained in this article.

  13. Minimal investment risk of a portfolio optimization problem with budget and investment concentration constraints

    NASA Astrophysics Data System (ADS)

    Shinzato, Takashi

    2017-02-01

    In the present paper, the minimal investment risk for a portfolio optimization problem with imposed budget and investment concentration constraints is considered using replica analysis. Since the minimal investment risk is influenced by the investment concentration constraint (as well as the budget constraint), it is intuitive that the minimal investment risk for the problem with an investment concentration constraint can be larger than that without the constraint (that is, with only the budget constraint). Moreover, a numerical experiment shows the effectiveness of our proposed analysis. In contrast, the standard operations research approach failed to identify accurately the minimal investment risk of the portfolio optimization problem.

  14. A Gradient-Based Multistart Algorithm for Multimodal Aerodynamic Shape Optimization Problems Based on Free-Form Deformation

    NASA Astrophysics Data System (ADS)

    Streuber, Gregg Mitchell

    Environmental and economic factors motivate the pursuit of more fuel-efficient aircraft designs. Aerodynamic shape optimization is a powerful tool in this effort, but is hampered by the presence of multimodality in many design spaces. Gradient-based multistart optimization uses a sampling algorithm and multiple parallel optimizations to reliably apply fast gradient-based optimization to moderately multimodal problems. Ensuring that the sampled geometries remain physically realizable requires manually developing specialized linear constraints for each class of problem. Utilizing free-form deformation geometry control allows these linear constraints to be written in a geometry-independent fashion, greatly easing the process of applying the algorithm to new problems. This algorithm was used to assess the presence of multimodality when optimizing a wing in subsonic and transonic flows, under inviscid and viscous conditions, and a blended wing-body under transonic, viscous conditions. Multimodality was present in every wing case, while the blended wing-body was found to be generally unimodal.

  15. Mathematical theory of a relaxed design problem in structural optimization

    NASA Technical Reports Server (NTRS)

    Kikuchi, Noboru; Suzuki, Katsuyuki

    1990-01-01

    Various attempts have been made to construct a rigorous mathematical theory of optimization for size, shape, and topology (i.e. layout) of an elastic structure. If these are represented by a finite number of parametric functions, as Armand described, it is possible to construct an existence theory of the optimum design using compactness argument in a finite dimensional design space or a closed admissible set of a finite dimensional design space. However, if the admissible design set is a subset of non-reflexive Banach space such as L(sup infinity)(Omega), construction of the existence theory of the optimum design becomes suddenly difficult and requires to extend (i.e. generalize) the design problem to much more wider class of design that is compatible to mechanics of structures in the sense of variational principle. Starting from the study by Cheng and Olhoff, Lurie, Cherkaev, and Fedorov introduced a new concept of convergence of design variables in a generalized sense and construct the 'G-Closure' theory of an extended (relaxed) optimum design problem. A similar attempt, but independent in large extent, can also be found in Kohn and Strang in which the shape and topology optimization problem is relaxed to allow to use of perforated composites rather than restricting it to usual solid structures. An identical idea is also stated in Murat and Tartar using the notion of the homogenization theory. That is, introducing possibility of micro-scale perforation together with the theory of homogenization, the optimum design problem is relaxed to construct its mathematical theory. It is also noted that this type of relaxed design problem is perfectly matched to the variational principle in structural mechanics.

  16. A modified genetic algorithm with fuzzy roulette wheel selection for job-shop scheduling problems

    NASA Astrophysics Data System (ADS)

    Thammano, Arit; Teekeng, Wannaporn

    2015-05-01

    The job-shop scheduling problem is one of the most difficult production planning problems. Since it is in the NP-hard class, a recent trend in solving the job-shop scheduling problem is shifting towards the use of heuristic and metaheuristic algorithms. This paper proposes a novel metaheuristic algorithm, which is a modification of the genetic algorithm. This proposed algorithm introduces two new concepts to the standard genetic algorithm: (1) fuzzy roulette wheel selection and (2) the mutation operation with tabu list. The proposed algorithm has been evaluated and compared with several state-of-the-art algorithms in the literature. The experimental results on 53 JSSPs show that the proposed algorithm is very effective in solving the combinatorial optimization problems. It outperforms all state-of-the-art algorithms on all benchmark problems in terms of the ability to achieve the optimal solution and the computational time.

  17. A Comparison of Trajectory Optimization Methods for the Impulsive Minimum Fuel Rendezvous Problem

    NASA Technical Reports Server (NTRS)

    Hughes, Steven P.; Mailhe, Laurie M.; Guzman, Jose J.

    2002-01-01

    In this paper we present a comparison of optimization approaches to the minimum fuel rendezvous problem. Both indirect and direct methods are compared for a variety of test cases. The indirect approach is based on primer vector theory. The direct approaches are implemented numerically and include Sequential Quadratic Programming (SQP), Quasi-Newton, Simplex, Genetic Algorithms, and Simulated Annealing. Each method is applied to a variety of test cases including, circular to circular coplanar orbits, LEO to GEO, and orbit phasing in highly elliptic orbits. We also compare different constrained optimization routines on complex orbit rendezvous problems with complicated, highly nonlinear constraints.

  18. An Optimizing Space Data-Communications Scheduling Method and Algorithm with Interference Mitigation, Generalized for a Broad Class of Optimization Problems

    NASA Technical Reports Server (NTRS)

    Rash, James

    2014-01-01

    NASA's space data-communications infrastructure-the Space Network and the Ground Network-provide scheduled (as well as some limited types of unscheduled) data-communications services to user spacecraft. The Space Network operates several orbiting geostationary platforms (the Tracking and Data Relay Satellite System (TDRSS)), each with its own servicedelivery antennas onboard. The Ground Network operates service-delivery antennas at ground stations located around the world. Together, these networks enable data transfer between user spacecraft and their mission control centers on Earth. Scheduling data-communications events for spacecraft that use the NASA communications infrastructure-the relay satellites and the ground stations-can be accomplished today with software having an operational heritage dating from the 1980s or earlier. An implementation of the scheduling methods and algorithms disclosed and formally specified herein will produce globally optimized schedules with not only optimized service delivery by the space data-communications infrastructure but also optimized satisfaction of all user requirements and prescribed constraints, including radio frequency interference (RFI) constraints. Evolutionary algorithms, a class of probabilistic strategies for searching large solution spaces, is the essential technology invoked and exploited in this disclosure. Also disclosed are secondary methods and algorithms for optimizing the execution efficiency of the schedule-generation algorithms themselves. The scheduling methods and algorithms as presented are adaptable to accommodate the complexity of scheduling the civilian and/or military data-communications infrastructure within the expected range of future users and space- or ground-based service-delivery assets. Finally, the problem itself, and the methods and algorithms, are generalized and specified formally. The generalized methods and algorithms are applicable to a very broad class of combinatorial-optimization

  19. Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows

    PubMed Central

    Wang, Di; Kleinberg, Robert D.

    2009-01-01

    Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C2, C3, C4,…. It is known that C2 can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing Ck (k > 2) require solving a linear program. In this paper we prove that C3 can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}n, this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network. PMID:20161596

  20. Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows.

    PubMed

    Wang, Di; Kleinberg, Robert D

    2009-11-28

    Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C(2), C(3), C(4),…. It is known that C(2) can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing C(k) (k > 2) require solving a linear program. In this paper we prove that C(3) can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}(n), this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network.

  1. Solving bi-level optimization problems in engineering design using kriging models

    NASA Astrophysics Data System (ADS)

    Xia, Yi; Liu, Xiaojie; Du, Gang

    2018-05-01

    Stackelberg game-theoretic approaches are applied extensively in engineering design to handle distributed collaboration decisions. Bi-level genetic algorithms (BLGAs) and response surfaces have been used to solve the corresponding bi-level programming models. However, the computational costs for BLGAs often increase rapidly with the complexity of lower-level programs, and optimal solution functions sometimes cannot be approximated by response surfaces. This article proposes a new method, namely the optimal solution function approximation by kriging model (OSFAKM), in which kriging models are used to approximate the optimal solution functions. A detailed example demonstrates that OSFAKM can obtain better solutions than BLGAs and response surface-based methods, and at the same time reduce the workload of computation remarkably. Five benchmark problems and a case study of the optimal design of a thin-walled pressure vessel are also presented to illustrate the feasibility and potential of the proposed method for bi-level optimization in engineering design.

  2. Can linear superiorization be useful for linear optimization problems?

    NASA Astrophysics Data System (ADS)

    Censor, Yair

    2017-04-01

    Linear superiorization (LinSup) considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are: (i) does LinSup provide a feasible point whose linear target function value is lower than that obtained by running the same feasibility-seeking algorithm without superiorization under identical conditions? (ii) How does LinSup fare in comparison with the Simplex method for solving linear programming problems? Based on our computational experiments presented here, the answers to these two questions are: ‘yes’ and ‘very well’, respectively.

  3. Can Linear Superiorization Be Useful for Linear Optimization Problems?

    PubMed Central

    Censor, Yair

    2017-01-01

    Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are (i) Does linear superiorization provide a feasible point whose linear target function value is lower than that obtained by running the same feasibility-seeking algorithm without superiorization under identical conditions? and (ii) How does linear superiorization fare in comparison with the Simplex method for solving linear programming problems? Based on our computational experiments presented here, the answers to these two questions are: “yes” and “very well”, respectively. PMID:29335660

  4. A guide to multi-objective optimization for ecological problems with an application to cackling goose management

    USGS Publications Warehouse

    Williams, Perry J.; Kendall, William L.

    2017-01-01

    Choices in ecological research and management are the result of balancing multiple, often competing, objectives. Multi-objective optimization (MOO) is a formal decision-theoretic framework for solving multiple objective problems. MOO is used extensively in other fields including engineering, economics, and operations research. However, its application for solving ecological problems has been sparse, perhaps due to a lack of widespread understanding. Thus, our objective was to provide an accessible primer on MOO, including a review of methods common in other fields, a review of their application in ecology, and a demonstration to an applied resource management problem.A large class of methods for solving MOO problems can be separated into two strategies: modelling preferences pre-optimization (the a priori strategy), or modelling preferences post-optimization (the a posteriori strategy). The a priori strategy requires describing preferences among objectives without knowledge of how preferences affect the resulting decision. In the a posteriori strategy, the decision maker simultaneously considers a set of solutions (the Pareto optimal set) and makes a choice based on the trade-offs observed in the set. We describe several methods for modelling preferences pre-optimization, including: the bounded objective function method, the lexicographic method, and the weighted-sum method. We discuss modelling preferences post-optimization through examination of the Pareto optimal set. We applied each MOO strategy to the natural resource management problem of selecting a population target for cackling goose (Branta hutchinsii minima) abundance. Cackling geese provide food security to Native Alaskan subsistence hunters in the goose's nesting area, but depredate crops on private agricultural fields in wintering areas. We developed objective functions to represent the competing objectives related to the cackling goose population target and identified an optimal solution

  5. A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems.

    PubMed

    Gong, Pinghua; Zhang, Changshui; Lu, Zhaosong; Huang, Jianhua Z; Ye, Jieping

    2013-01-01

    Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterparts in several sparse learning settings. However, solving the non-convex optimization problems associated with non-convex penalties remains a big challenge. A commonly used approach is the Multi-Stage (MS) convex relaxation (or DC programming), which relaxes the original non-convex problem to a sequence of convex problems. This approach is usually not very practical for large-scale problems because its computational cost is a multiple of solving a single convex problem. In this paper, we propose a General Iterative Shrinkage and Thresholding (GIST) algorithm to solve the nonconvex optimization problem for a large class of non-convex penalties. The GIST algorithm iteratively solves a proximal operator problem, which in turn has a closed-form solution for many commonly used penalties. At each outer iteration of the algorithm, we use a line search initialized by the Barzilai-Borwein (BB) rule that allows finding an appropriate step size quickly. The paper also presents a detailed convergence analysis of the GIST algorithm. The efficiency of the proposed algorithm is demonstrated by extensive experiments on large-scale data sets.

  6. Inverse problems and optimal experiment design in unsteady heat transfer processes identification

    NASA Technical Reports Server (NTRS)

    Artyukhin, Eugene A.

    1991-01-01

    Experimental-computational methods for estimating characteristics of unsteady heat transfer processes are analyzed. The methods are based on the principles of distributed parameter system identification. The theoretical basis of such methods is the numerical solution of nonlinear ill-posed inverse heat transfer problems and optimal experiment design problems. Numerical techniques for solving problems are briefly reviewed. The results of the practical application of identification methods are demonstrated when estimating effective thermophysical characteristics of composite materials and thermal contact resistance in two-layer systems.

  7. Finite element solution of optimal control problems with state-control inequality constraints

    NASA Technical Reports Server (NTRS)

    Bless, Robert R.; Hodges, Dewey H.

    1992-01-01

    It is demonstrated that the weak Hamiltonian finite-element formulation is amenable to the solution of optimal control problems with inequality constraints which are functions of both state and control variables. Difficult problems can be treated on account of the ease with which algebraic equations can be generated before having to specify the problem. These equations yield very accurate solutions. Owing to the sparse structure of the resulting Jacobian, computer solutions can be obtained quickly when the sparsity is exploited.

  8. An iterative method for tri-level quadratic fractional programming problems using fuzzy goal programming approach

    NASA Astrophysics Data System (ADS)

    Kassa, Semu Mitiku; Tsegay, Teklay Hailay

    2017-08-01

    Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fractional objective functions at each of the three levels. A solution algorithm has been proposed by applying fuzzy goal programming approach and by reformulating the fractional constraints to equivalent but non-fractional non-linear constraints. Based on the transformed formulation, an iterative procedure is developed that can yield a satisfactory solution to the tri-level problem. The numerical results on various illustrative examples demonstrated that the proposed algorithm is very much promising and it can also be used to solve larger-sized as well as n-level problems of similar structure.

  9. Particle swarm optimization using multi-information characteristics of all personal-best information.

    PubMed

    Huang, Song; Tian, Na; Wang, Yan; Ji, Zhicheng

    2016-01-01

    Convergence stagnation is the chief difficulty to solve hard optimization problems for most particle swarm optimization variants. To address this issue, a novel particle swarm optimization using multi-information characteristics of all personal-best information is developed in our research. In the modified algorithm, two positions are defined by personal-best positions and an improved cognition term with three positions of all personal-best information is used in velocity update equation to enhance the search capability. This strategy could make particles fly to a better direction by discovering useful information from all the personal-best positions. The validity of the proposed algorithm is assessed on twenty benchmark problems including unimodal, multimodal, rotated and shifted functions, and the results are compared with that obtained by some published variants of particle swarm optimization in the literature. Computational results demonstrate that the proposed algorithm finds several global optimum and high-quality solutions in most case with a fast convergence speed.

  10. Mesh refinement strategy for optimal control problems

    NASA Astrophysics Data System (ADS)

    Paiva, L. T.; Fontes, F. A. C. C.

    2013-10-01

    Direct methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are frequently used. However, in some cases these meshes cannot cope accurately with nonlinear behavior. One way to improve the solution is to select a new mesh with a greater number of nodes. Another way, involves adaptive mesh refinement. In this case, the mesh nodes have non equidistant spacing which allow a non uniform nodes collocation. In the method presented in this paper, a time mesh refinement strategy based on the local error is developed. After computing a solution in a coarse mesh, the local error is evaluated, which gives information about the subintervals of time domain where refinement is needed. This procedure is repeated until the local error reaches a user-specified threshold. The technique is applied to solve the car-like vehicle problem aiming minimum consumption. The approach developed in this paper leads to results with greater accuracy and yet with lower overall computational time as compared to using a time meshes having equidistant spacing.

  11. On the complexity of some quadratic Euclidean 2-clustering problems

    NASA Astrophysics Data System (ADS)

    Kel'manov, A. V.; Pyatkin, A. V.

    2016-03-01

    Some problems of partitioning a finite set of points of Euclidean space into two clusters are considered. In these problems, the following criteria are minimized: (1) the sum over both clusters of the sums of squared pairwise distances between the elements of the cluster and (2) the sum of the (multiplied by the cardinalities of the clusters) sums of squared distances from the elements of the cluster to its geometric center, where the geometric center (or centroid) of a cluster is defined as the mean value of the elements in that cluster. Additionally, another problem close to (2) is considered, where the desired center of one of the clusters is given as input, while the center of the other cluster is unknown (is the variable to be optimized) as in problem (2). Two variants of the problems are analyzed, in which the cardinalities of the clusters are (1) parts of the input or (2) optimization variables. It is proved that all the considered problems are strongly NP-hard and that, in general, there is no fully polynomial-time approximation scheme for them (unless P = NP).

  12. Constrained Optimization Problems in Cost and Managerial Accounting--Spreadsheet Tools

    ERIC Educational Resources Information Center

    Amlie, Thomas T.

    2009-01-01

    A common problem addressed in Managerial and Cost Accounting classes is that of selecting an optimal production mix given scarce resources. That is, if a firm produces a number of different products, and is faced with scarce resources (e.g., limitations on labor, materials, or machine time), what combination of products yields the greatest profit…

  13. Singular optimal control and the identically non-regular problem in the calculus of variations

    NASA Technical Reports Server (NTRS)

    Menon, P. K. A.; Kelley, H. J.; Cliff, E. M.

    1985-01-01

    A small but interesting class of optimal control problems featuring a scalar control appearing linearly is equivalent to the class of identically nonregular problems in the Calculus of Variations. It is shown that a condition due to Mancill (1950) is equivalent to the generalized Legendre-Clebsch condition for this narrow class of problems.

  14. Aggregation of LoD 1 building models as an optimization problem

    NASA Astrophysics Data System (ADS)

    Guercke, R.; Götzelmann, T.; Brenner, C.; Sester, M.

    3D city models offered by digital map providers typically consist of several thousands or even millions of individual buildings. Those buildings are usually generated in an automated fashion from high resolution cadastral and remote sensing data and can be very detailed. However, not in every application such a high degree of detail is desirable. One way to remove complexity is to aggregate individual buildings, simplify the ground plan and assign an appropriate average building height. This task is computationally complex because it includes the combinatorial optimization problem of determining which subset of the original set of buildings should best be aggregated to meet the demands of an application. In this article, we introduce approaches to express different aspects of the aggregation of LoD 1 building models in the form of Mixed Integer Programming (MIP) problems. The advantage of this approach is that for linear (and some quadratic) MIP problems, sophisticated software exists to find exact solutions (global optima) with reasonable effort. We also propose two different heuristic approaches based on the region growing strategy and evaluate their potential for optimization by comparing their performance to a MIP-based approach.

  15. Collective neurodynamic optimization for economic emission dispatch problem considering valve point effect in microgrid.

    PubMed

    Wang, Tiancai; He, Xing; Huang, Tingwen; Li, Chuandong; Zhang, Wei

    2017-09-01

    The economic emission dispatch (EED) problem aims to control generation cost and reduce the impact of waste gas on the environment. It has multiple constraints and nonconvex objectives. To solve it, the collective neurodynamic optimization (CNO) method, which combines heuristic approach and projection neural network (PNN), is attempted to optimize scheduling of an electrical microgrid with ten thermal generators and minimize the plus of generation and emission cost. As the objective function has non-derivative points considering valve point effect (VPE), differential inclusion approach is employed in the PNN model introduced to deal with them. Under certain conditions, the local optimality and convergence of the dynamic model for the optimization problem is analyzed. The capability of the algorithm is verified in a complicated situation, where transmission loss and prohibited operating zones are considered. In addition, the dynamic variation of load power at demand side is considered and the optimal scheduling of generators within 24 h is described. Copyright © 2017 Elsevier Ltd. All rights reserved.

  16. A linked simulation-optimization model for solving the unknown groundwater pollution source identification problems.

    PubMed

    Ayvaz, M Tamer

    2010-09-20

    This study proposes a linked simulation-optimization model for solving the unknown groundwater pollution source identification problems. In the proposed model, MODFLOW and MT3DMS packages are used to simulate the flow and transport processes in the groundwater system. These models are then integrated with an optimization model which is based on the heuristic harmony search (HS) algorithm. In the proposed simulation-optimization model, the locations and release histories of the pollution sources are treated as the explicit decision variables and determined through the optimization model. Also, an implicit solution procedure is proposed to determine the optimum number of pollution sources which is an advantage of this model. The performance of the proposed model is evaluated on two hypothetical examples for simple and complex aquifer geometries, measurement error conditions, and different HS solution parameter sets. Identified results indicated that the proposed simulation-optimization model is an effective way and may be used to solve the inverse pollution source identification problems. Copyright (c) 2010 Elsevier B.V. All rights reserved.

  17. Electronic neural network for solving traveling salesman and similar global optimization problems

    NASA Technical Reports Server (NTRS)

    Thakoor, Anilkumar P. (Inventor); Moopenn, Alexander W. (Inventor); Duong, Tuan A. (Inventor); Eberhardt, Silvio P. (Inventor)

    1993-01-01

    This invention is a novel high-speed neural network based processor for solving the 'traveling salesman' and other global optimization problems. It comprises a novel hybrid architecture employing a binary synaptic array whose embodiment incorporates the fixed rules of the problem, such as the number of cities to be visited. The array is prompted by analog voltages representing variables such as distances. The processor incorporates two interconnected feedback networks, each of which solves part of the problem independently and simultaneously, yet which exchange information dynamically.

  18. New optimization model for routing and spectrum assignment with nodes insecurity

    NASA Astrophysics Data System (ADS)

    Xuan, Hejun; Wang, Yuping; Xu, Zhanqi; Hao, Shanshan; Wang, Xiaoli

    2017-04-01

    By adopting the orthogonal frequency division multiplexing technology, elastic optical networks can provide the flexible and variable bandwidth allocation to each connection request and get higher spectrum utilization. The routing and spectrum assignment problem in elastic optical network is a well-known NP-hard problem. In addition, information security has received worldwide attention. We combine these two problems to investigate the routing and spectrum assignment problem with the guaranteed security in elastic optical network, and establish a new optimization model to minimize the maximum index of the used frequency slots, which is used to determine an optimal routing and spectrum assignment schemes. To solve the model effectively, a hybrid genetic algorithm framework integrating a heuristic algorithm into a genetic algorithm is proposed. The heuristic algorithm is first used to sort the connection requests and then the genetic algorithm is designed to look for an optimal routing and spectrum assignment scheme. In the genetic algorithm, tailor-made crossover, mutation and local search operators are designed. Moreover, simulation experiments are conducted with three heuristic strategies, and the experimental results indicate that the effectiveness of the proposed model and algorithm framework.

  19. Hard particle effect on surface generation in nano-cutting

    NASA Astrophysics Data System (ADS)

    Xu, Feifei; Fang, Fengzhou; Zhang, Xiaodong

    2017-12-01

    The influence of the hard particle on the surface generation, plastic deformation and processing forces in nano-cutting of aluminum is investigated by means of molecular dynamics simulations. In this investigation, a hard particle which is simplified as a diamond ball is embedded under the free surface of workpiece with different depths. The influence of the position of the hard ball on the surface generation and other material removal mechanism, such as the movement of the ball under the action of cutting tool edge, is revealed. The results show that when the hard particle is removed, only a small shallow pit is left on the machined surface. Otherwise, it is pressed down to the subsurface of the workpiece left larger and deeper pit on the generated surface. Besides that, the hard particle in the workpiece would increase the processing force when the cutting tool edge or the plastic carriers interact with the hard particle. It is helpful to optimize the cutting parameters and material properties for obtaining better surface quality in nano-cutting of composites or other materials with micro/nanoscale hard particles in it.

  20. Effects of hard mask etch on final topography of advanced phase shift masks

    NASA Astrophysics Data System (ADS)

    Hortenbach, Olga; Rolff, Haiko; Lajn, Alexander; Baessler, Martin

    2017-07-01

    Continuous shrinking of the semiconductor device dimensions demands steady improvements of the lithographic resolution on wafer level. These requirements challenge the photomask industry to further improve the mask quality in all relevant printing characteristics. In this paper topography of the Phase Shift Masks (PSM) was investigated. Effects of hard mask etch on phase shift uniformity and mask absorber profile were studied. Design of experiments method (DoE) was used for the process optimization, whereas gas composition, bias power of the hard mask main etch and bias power of the over-etch were varied. In addition, influence of the over-etch time was examined at the end of the experiment. Absorber depth uniformity, sidewall angle (SWA), reactive ion etch lag (RIE lag) and through pitch (TP) dependence were analyzed. Measurements were performed by means of Atomic-force microscopy (AFM) using critical dimension (CD) mode with a boot-shaped tip. Scanning electron microscope (SEM) cross-section images were prepared to verify the profile quality. Finally CD analysis was performed to confirm the optimal etch conditions. Significant dependence of the absorber SWA on hard mask (HM) etch conditions was observed revealing an improvement potential for the mask absorber profile. It was found that hard mask etch can leave a depth footprint in the absorber layer. Thus, the etch depth uniformity of hard mask etch is crucial for achieving a uniform phase shift over the active mask area. The optimized hard mask etch process results in significantly improved mask topography without deterioration of tight CD specifications.

  1. Solving iTOUGH2 simulation and optimization problems using the PEST protocol

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

    Finsterle, S.A.; Zhang, Y.

    2011-02-01

    The PEST protocol has been implemented into the iTOUGH2 code, allowing the user to link any simulation program (with ASCII-based inputs and outputs) to iTOUGH2's sensitivity analysis, inverse modeling, and uncertainty quantification capabilities. These application models can be pre- or post-processors of the TOUGH2 non-isothermal multiphase flow and transport simulator, or programs that are unrelated to the TOUGH suite of codes. PEST-style template and instruction files are used, respectively, to pass input parameters updated by the iTOUGH2 optimization routines to the model, and to retrieve the model-calculated values that correspond to observable variables. We summarize the iTOUGH2 capabilities and demonstratemore » the flexibility added by the PEST protocol for the solution of a variety of simulation-optimization problems. In particular, the combination of loosely coupled and tightly integrated simulation and optimization routines provides both the flexibility and control needed to solve challenging inversion problems for the analysis of multiphase subsurface flow and transport systems.« less

  2. Error bounds of adaptive dynamic programming algorithms for solving undiscounted optimal control problems.

    PubMed

    Liu, Derong; Li, Hongliang; Wang, Ding

    2015-06-01

    In this paper, we establish error bounds of adaptive dynamic programming algorithms for solving undiscounted infinite-horizon optimal control problems of discrete-time deterministic nonlinear systems. We consider approximation errors in the update equations of both value function and control policy. We utilize a new assumption instead of the contraction assumption in discounted optimal control problems. We establish the error bounds for approximate value iteration based on a new error condition. Furthermore, we also establish the error bounds for approximate policy iteration and approximate optimistic policy iteration algorithms. It is shown that the iterative approximate value function can converge to a finite neighborhood of the optimal value function under some conditions. To implement the developed algorithms, critic and action neural networks are used to approximate the value function and control policy, respectively. Finally, a simulation example is given to demonstrate the effectiveness of the developed algorithms.

  3. Cascaded Optimization for a Persistent Data Ferrying Unmanned Aircraft

    NASA Astrophysics Data System (ADS)

    Carfang, Anthony

    This dissertation develops and assesses a cascaded method for designing optimal periodic trajectories and link schedules for an unmanned aircraft to ferry data between stationary ground nodes. This results in a fast solution method without the need to artificially constrain system dynamics. Focusing on a fundamental ferrying problem that involves one source and one destination, but includes complex vehicle and Radio-Frequency (RF) dynamics, a cascaded structure to the system dynamics is uncovered. This structure is exploited by reformulating the nonlinear optimization problem into one that reduces the independent control to the vehicle's motion, while the link scheduling control is folded into the objective function and implemented as an optimal policy that depends on candidate motion control. This formulation is proven to maintain optimality while reducing computation time in comparison to traditional ferry optimization methods. The discrete link scheduling problem takes the form of a combinatorial optimization problem that is known to be NP-Hard. A derived necessary condition for optimality guides the development of several heuristic algorithms, specifically the Most-Data-First Algorithm and the Knapsack Adaptation. These heuristics are extended to larger ferrying scenarios, and assessed analytically and through Monte Carlo simulation, showing better throughput performance in the same order of magnitude of computation time in comparison to other common link scheduling policies. The cascaded optimization method is implemented with a novel embedded software system on a small, unmanned aircraft to validate the simulation results with field experiments. To address the sensitivity of results on trajectory tracking performance, a system that combines motion and link control with waypoint-based navigation is developed and assessed through field experiments. The data ferrying algorithms are further extended by incorporating a Gaussian process to opportunistically learn

  4. Computing the Feasible Spaces of Optimal Power Flow Problems

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

    Molzahn, Daniel K.

    The solution to an optimal power flow (OPF) problem provides a minimum cost operating point for an electric power system. The performance of OPF solution techniques strongly depends on the problem’s feasible space. This paper presents an algorithm that is guaranteed to compute the entire feasible spaces of small OPF problems to within a specified discretization tolerance. Specifically, the feasible space is computed by discretizing certain of the OPF problem’s inequality constraints to obtain a set of power flow equations. All solutions to the power flow equations at each discretization point are obtained using the Numerical Polynomial Homotopy Continuation (NPHC)more » algorithm. To improve computational tractability, “bound tightening” and “grid pruning” algorithms use convex relaxations to preclude consideration of many discretization points that are infeasible for the OPF problem. Here, the proposed algorithm is used to generate the feasible spaces of two small test cases.« less

  5. Computing the Feasible Spaces of Optimal Power Flow Problems

    DOE PAGES

    Molzahn, Daniel K.

    2017-03-15

    The solution to an optimal power flow (OPF) problem provides a minimum cost operating point for an electric power system. The performance of OPF solution techniques strongly depends on the problem’s feasible space. This paper presents an algorithm that is guaranteed to compute the entire feasible spaces of small OPF problems to within a specified discretization tolerance. Specifically, the feasible space is computed by discretizing certain of the OPF problem’s inequality constraints to obtain a set of power flow equations. All solutions to the power flow equations at each discretization point are obtained using the Numerical Polynomial Homotopy Continuation (NPHC)more » algorithm. To improve computational tractability, “bound tightening” and “grid pruning” algorithms use convex relaxations to preclude consideration of many discretization points that are infeasible for the OPF problem. Here, the proposed algorithm is used to generate the feasible spaces of two small test cases.« less

  6. A mixed analog/digital chaotic neuro-computer system for quadratic assignment problems.

    PubMed

    Horio, Yoshihiko; Ikeguchi, Tohru; Aihara, Kazuyuki

    2005-01-01

    We construct a mixed analog/digital chaotic neuro-computer prototype system for quadratic assignment problems (QAPs). The QAP is one of the difficult NP-hard problems, and includes several real-world applications. Chaotic neural networks have been used to solve combinatorial optimization problems through chaotic search dynamics, which efficiently searches optimal or near optimal solutions. However, preliminary experiments have shown that, although it obtained good feasible solutions, the Hopfield-type chaotic neuro-computer hardware system could not obtain the optimal solution of the QAP. Therefore, in the present study, we improve the system performance by adopting a solution construction method, which constructs a feasible solution using the analog internal state values of the chaotic neurons at each iteration. In order to include the construction method into our hardware, we install a multi-channel analog-to-digital conversion system to observe the internal states of the chaotic neurons. We show experimentally that a great improvement in the system performance over the original Hopfield-type chaotic neuro-computer is obtained. That is, we obtain the optimal solution for the size-10 QAP in less than 1000 iterations. In addition, we propose a guideline for parameter tuning of the chaotic neuro-computer system according to the observation of the internal states of several chaotic neurons in the network.

  7. Optimal matching for prostate brachytherapy seed localization with dimension reduction.

    PubMed

    Lee, Junghoon; Labat, Christian; Jain, Ameet K; Song, Danny Y; Burdette, Everette C; Fichtinger, Gabor; Prince, Jerry L

    2009-01-01

    In prostate brachytherapy, x-ray fluoroscopy has been used for intra-operative dosimetry to provide qualitative assessment of implant quality. More recent developments have made possible 3D localization of the implanted radioactive seeds. This is usually modeled as an assignment problem and solved by resolving the correspondence of seeds. It is, however, NP-hard, and the problem is even harder in practice due to the significant number of hidden seeds. In this paper, we propose an algorithm that can find an optimal solution from multiple projection images with hidden seeds. It solves an equivalent problem with reduced dimensional complexity, thus allowing us to find an optimal solution in polynomial time. Simulation results show the robustness of the algorithm. It was validated on 5 phantom and 18 patient datasets, successfully localizing the seeds with detection rate of > or = 97.6% and reconstruction error of < or = 1.2 mm. This is considered to be clinically excellent performance.

  8. Artificial immune algorithm for multi-depot vehicle scheduling problems

    NASA Astrophysics Data System (ADS)

    Wu, Zhongyi; Wang, Donggen; Xia, Linyuan; Chen, Xiaoling

    2008-10-01

    In the fast-developing logistics and supply chain management fields, one of the key problems in the decision support system is that how to arrange, for a lot of customers and suppliers, the supplier-to-customer assignment and produce a detailed supply schedule under a set of constraints. Solutions to the multi-depot vehicle scheduling problems (MDVRP) help in solving this problem in case of transportation applications. The objective of the MDVSP is to minimize the total distance covered by all vehicles, which can be considered as delivery costs or time consumption. The MDVSP is one of nondeterministic polynomial-time hard (NP-hard) problem which cannot be solved to optimality within polynomial bounded computational time. Many different approaches have been developed to tackle MDVSP, such as exact algorithm (EA), one-stage approach (OSA), two-phase heuristic method (TPHM), tabu search algorithm (TSA), genetic algorithm (GA) and hierarchical multiplex structure (HIMS). Most of the methods mentioned above are time consuming and have high risk to result in local optimum. In this paper, a new search algorithm is proposed to solve MDVSP based on Artificial Immune Systems (AIS), which are inspirited by vertebrate immune systems. The proposed AIS algorithm is tested with 30 customers and 6 vehicles located in 3 depots. Experimental results show that the artificial immune system algorithm is an effective and efficient method for solving MDVSP problems.

  9. The MusIC method: a fast and quasi-optimal solution to the muscle forces estimation problem.

    PubMed

    Muller, A; Pontonnier, C; Dumont, G

    2018-02-01

    The present paper aims at presenting a fast and quasi-optimal method of muscle forces estimation: the MusIC method. It consists in interpolating a first estimation in a database generated offline thanks to a classical optimization problem, and then correcting it to respect the motion dynamics. Three different cost functions - two polynomial criteria and a min/max criterion - were tested on a planar musculoskeletal model. The MusIC method provides a computation frequency approximately 10 times higher compared to a classical optimization problem with a relative mean error of 4% on cost function evaluation.

  10. Substance Abuse: A Hidden Problem within the D/deaf and Hard of Hearing Communities

    ERIC Educational Resources Information Center

    Guthmann, Debra; Graham, Vicki

    2004-01-01

    Current research indicates that D/deaf and hard of hearing clients seeking treatment for substance abuse often encounter obstacles in receiving the help they need. Many of these obstacles are the result of a lack of knowledge and experience with regard to treating D/deaf and hard of hearing people. Programs designed for hearing people that attempt…

  11. Design and implementation of reliability evaluation of SAS hard disk based on RAID card

    NASA Astrophysics Data System (ADS)

    Ren, Shaohua; Han, Sen

    2015-10-01

    Because of the huge advantage of RAID technology in storage, it has been widely used. However, the question associated with this technology is that the hard disk based on the RAID card can not be queried by Operating System. Therefore how to read the self-information and log data of hard disk has been a problem, while this data is necessary for reliability test of hard disk. In traditional way, this information can be read just suitable for SATA hard disk, but not for SAS hard disk. In this paper, we provide a method by using LSI RAID card's Application Program Interface, communicating with RAID card and analyzing the feedback data to solve the problem. Then we will get the necessary information to assess the SAS hard disk.

  12. Self-organization and solution of shortest-path optimization problems with memristive networks

    NASA Astrophysics Data System (ADS)

    Pershin, Yuriy V.; Di Ventra, Massimiliano

    2013-07-01

    We show that memristive networks, namely networks of resistors with memory, can efficiently solve shortest-path optimization problems. Indeed, the presence of memory (time nonlocality) promotes self organization of the network into the shortest possible path(s). We introduce a network entropy function to characterize the self-organized evolution, show the solution of the shortest-path problem and demonstrate the healing property of the solution path. Finally, we provide an algorithm to solve the traveling salesman problem. Similar considerations apply to networks of memcapacitors and meminductors, and networks with memory in various dimensions.

  13. Optimization methods for activities selection problems

    NASA Astrophysics Data System (ADS)

    Mahad, Nor Faradilah; Alias, Suriana; Yaakop, Siti Zulaika; Arshad, Norul Amanina Mohd; Mazni, Elis Sofia

    2017-08-01

    Co-curriculum activities must be joined by every student in Malaysia and these activities bring a lot of benefits to the students. By joining these activities, the students can learn about the time management and they can developing many useful skills. This project focuses on the selection of co-curriculum activities in secondary school using the optimization methods which are the Analytic Hierarchy Process (AHP) and Zero-One Goal Programming (ZOGP). A secondary school in Negeri Sembilan, Malaysia was chosen as a case study. A set of questionnaires were distributed randomly to calculate the weighted for each activity based on the 3 chosen criteria which are soft skills, interesting activities and performances. The weighted was calculated by using AHP and the results showed that the most important criteria is soft skills. Then, the ZOGP model will be analyzed by using LINGO Software version 15.0. There are two priorities to be considered. The first priority which is to minimize the budget for the activities is achieved since the total budget can be reduced by RM233.00. Therefore, the total budget to implement the selected activities is RM11,195.00. The second priority which is to select the co-curriculum activities is also achieved. The results showed that 9 out of 15 activities were selected. Thus, it can concluded that AHP and ZOGP approach can be used as the optimization methods for activities selection problem.

  14. An Integer Programming Model For Solving Heterogeneous Vehicle Routing Problem With Hard Time Window considering Service Choice

    NASA Astrophysics Data System (ADS)

    Susilawati, Enny; Mawengkang, Herman; Efendi, Syahril

    2018-01-01

    Generally a Vehicle Routing Problem with time windows (VRPTW) can be defined as a problem to determine the optimal set of routes used by a fleet of vehicles to serve a given set of customers with service time restrictions; the objective is to minimize the total travel cost (related to the travel times or distances) and operational cost (related to the number of vehicles used). In this paper we address a variant of the VRPTW in which the fleet of vehicle is heterogenic due to the different size of demand from customers. The problem, called Heterogeneous VRP (HVRP) also includes service levels. We use integer programming model to describe the problem. A feasible neighbourhood approach is proposed to solve the model.

  15. A tight upper bound for quadratic knapsack problems in grid-based wind farm layout optimization

    NASA Astrophysics Data System (ADS)

    Quan, Ning; Kim, Harrison M.

    2018-03-01

    The 0-1 quadratic knapsack problem (QKP) in wind farm layout optimization models possible turbine locations as nodes, and power loss due to wake effects between pairs of turbines as edges in a complete graph. The goal is to select up to a certain number of turbine locations such that the sum of selected node and edge coefficients is maximized. Finding the optimal solution to the QKP is difficult in general, but it is possible to obtain a tight upper bound on the QKP's optimal value which facilitates the use of heuristics to solve QKPs by giving a good estimate of the optimality gap of any feasible solution. This article applies an upper bound method that is especially well-suited to QKPs in wind farm layout optimization due to certain features of the formulation that reduce the computational complexity of calculating the upper bound. The usefulness of the upper bound was demonstrated by assessing the performance of the greedy algorithm for solving QKPs in wind farm layout optimization. The results show that the greedy algorithm produces good solutions within 4% of the optimal value for small to medium sized problems considered in this article.

  16. Optimization of Angular-Momentum Biases of Reaction Wheels

    NASA Technical Reports Server (NTRS)

    Lee, Clifford; Lee, Allan

    2008-01-01

    RBOT [RWA Bias Optimization Tool (wherein RWA signifies Reaction Wheel Assembly )] is a computer program designed for computing angular momentum biases for reaction wheels used for providing spacecraft pointing in various directions as required for scientific observations. RBOT is currently deployed to support the Cassini mission to prevent operation of reaction wheels at unsafely high speeds while minimizing time in undesirable low-speed range, where elasto-hydrodynamic lubrication films in bearings become ineffective, leading to premature bearing failure. The problem is formulated as a constrained optimization problem in which maximum wheel speed limit is a hard constraint and a cost functional that increases as speed decreases below a low-speed threshold. The optimization problem is solved using a parametric search routine known as the Nelder-Mead simplex algorithm. To increase computational efficiency for extended operation involving large quantity of data, the algorithm is designed to (1) use large time increments during intervals when spacecraft attitudes or rates of rotation are nearly stationary, (2) use sinusoidal-approximation sampling to model repeated long periods of Earth-point rolling maneuvers to reduce computational loads, and (3) utilize an efficient equation to obtain wheel-rate profiles as functions of initial wheel biases based on conservation of angular momentum (in an inertial frame) using pre-computed terms.

  17. An ant colony optimization heuristic for an integrated production and distribution scheduling problem

    NASA Astrophysics Data System (ADS)

    Chang, Yung-Chia; Li, Vincent C.; Chiang, Chia-Ju

    2014-04-01

    Make-to-order or direct-order business models that require close interaction between production and distribution activities have been adopted by many enterprises in order to be competitive in demanding markets. This article considers an integrated production and distribution scheduling problem in which jobs are first processed by one of the unrelated parallel machines and then distributed to corresponding customers by capacitated vehicles without intermediate inventory. The objective is to find a joint production and distribution schedule so that the weighted sum of total weighted job delivery time and the total distribution cost is minimized. This article presents a mathematical model for describing the problem and designs an algorithm using ant colony optimization. Computational experiments illustrate that the algorithm developed is capable of generating near-optimal solutions. The computational results also demonstrate the value of integrating production and distribution in the model for the studied problem.

  18. Pruning-Based, Energy-Optimal, Deterministic I/O Device Scheduling for Hard Real-Time Systems

    DTIC Science & Technology

    2005-02-01

    However, DPM via I/O device scheduling for hard real - time systems has received relatively little attention. In this paper,we present an offline I/O...polynomial time. We present experimental results to show that EDS and MDO reduce the energy consumption of I/O devices significantly for hard real - time systems .

  19. A Discriminative Sentence Compression Method as Combinatorial Optimization Problem

    NASA Astrophysics Data System (ADS)

    Hirao, Tsutomu; Suzuki, Jun; Isozaki, Hideki

    In the study of automatic summarization, the main research topic was `important sentence extraction' but nowadays `sentence compression' is a hot research topic. Conventional sentence compression methods usually transform a given sentence into a parse tree or a dependency tree, and modify them to get a shorter sentence. However, this method is sometimes too rigid. In this paper, we regard sentence compression as an combinatorial optimization problem that extracts an optimal subsequence of words. Hori et al. also proposed a similar method, but they used only a small number of features and their weights were tuned by hand. We introduce a large number of features such as part-of-speech bigrams and word position in the sentence. Furthermore, we train the system by discriminative learning. According to our experiments, our method obtained better score than other methods with statistical significance.

  20. High hardness in the biocompatible intermetallic compound β-Ti3Au.

    PubMed

    Svanidze, Eteri; Besara, Tiglet; Ozaydin, M Fevsi; Tiwary, Chandra Sekhar; Wang, Jiakui K; Radhakrishnan, Sruthi; Mani, Sendurai; Xin, Yan; Han, Ke; Liang, Hong; Siegrist, Theo; Ajayan, Pulickel M; Morosan, E

    2016-07-01

    The search for new hard materials is often challenging, but strongly motivated by the vast application potential such materials hold. Ti3Au exhibits high hardness values (about four times those of pure Ti and most steel alloys), reduced coefficient of friction and wear rates, and biocompatibility, all of which are optimal traits for orthopedic, dental, and prosthetic applications. In addition, the ability of this compound to adhere to ceramic parts can reduce both the weight and the cost of medical components. The fourfold increase in the hardness of Ti3Au compared to other Ti-Au alloys and compounds can be attributed to the elevated valence electron density, the reduced bond length, and the pseudogap formation. Understanding the origin of hardness in this intermetallic compound provides an avenue toward designing superior biocompatible, hard materials.

  1. Solving the Traveling Salesman's Problem Using the African Buffalo Optimization.

    PubMed

    Odili, Julius Beneoluchi; Mohmad Kahar, Mohd Nizam

    2016-01-01

    This paper proposes the African Buffalo Optimization (ABO) which is a new metaheuristic algorithm that is derived from careful observation of the African buffalos, a species of wild cows, in the African forests and savannahs. This animal displays uncommon intelligence, strategic organizational skills, and exceptional navigational ingenuity in its traversal of the African landscape in search for food. The African Buffalo Optimization builds a mathematical model from the behavior of this animal and uses the model to solve 33 benchmark symmetric Traveling Salesman's Problem and six difficult asymmetric instances from the TSPLIB. This study shows that buffalos are able to ensure excellent exploration and exploitation of the search space through regular communication, cooperation, and good memory of its previous personal exploits as well as tapping from the herd's collective exploits. The results obtained by using the ABO to solve these TSP cases were benchmarked against the results obtained by using other popular algorithms. The results obtained using the African Buffalo Optimization algorithm are very competitive.

  2. Solving the Traveling Salesman's Problem Using the African Buffalo Optimization

    PubMed Central

    Odili, Julius Beneoluchi; Mohmad Kahar, Mohd Nizam

    2016-01-01

    This paper proposes the African Buffalo Optimization (ABO) which is a new metaheuristic algorithm that is derived from careful observation of the African buffalos, a species of wild cows, in the African forests and savannahs. This animal displays uncommon intelligence, strategic organizational skills, and exceptional navigational ingenuity in its traversal of the African landscape in search for food. The African Buffalo Optimization builds a mathematical model from the behavior of this animal and uses the model to solve 33 benchmark symmetric Traveling Salesman's Problem and six difficult asymmetric instances from the TSPLIB. This study shows that buffalos are able to ensure excellent exploration and exploitation of the search space through regular communication, cooperation, and good memory of its previous personal exploits as well as tapping from the herd's collective exploits. The results obtained by using the ABO to solve these TSP cases were benchmarked against the results obtained by using other popular algorithms. The results obtained using the African Buffalo Optimization algorithm are very competitive. PMID:26880872

  3. Fast optimization of binary clusters using a novel dynamic lattice searching method.

    PubMed

    Wu, Xia; Cheng, Wen

    2014-09-28

    Global optimization of binary clusters has been a difficult task despite of much effort and many efficient methods. Directing toward two types of elements (i.e., homotop problem) in binary clusters, two classes of virtual dynamic lattices are constructed and a modified dynamic lattice searching (DLS) method, i.e., binary DLS (BDLS) method, is developed. However, it was found that the BDLS can only be utilized for the optimization of binary clusters with small sizes because homotop problem is hard to be solved without atomic exchange operation. Therefore, the iterated local search (ILS) method is adopted to solve homotop problem and an efficient method based on the BDLS method and ILS, named as BDLS-ILS, is presented for global optimization of binary clusters. In order to assess the efficiency of the proposed method, binary Lennard-Jones clusters with up to 100 atoms are investigated. Results show that the method is proved to be efficient. Furthermore, the BDLS-ILS method is also adopted to study the geometrical structures of (AuPd)79 clusters with DFT-fit parameters of Gupta potential.

  4. 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

  5. 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.

  6. A Guiding Evolutionary Algorithm with Greedy Strategy for Global Optimization Problems.

    PubMed

    Cao, Leilei; Xu, Lihong; Goodman, Erik D

    2016-01-01

    A Guiding Evolutionary Algorithm (GEA) with greedy strategy for global optimization problems is proposed. Inspired by Particle Swarm Optimization, the Genetic Algorithm, and the Bat Algorithm, the GEA was designed to retain some advantages of each method while avoiding some disadvantages. In contrast to the usual Genetic Algorithm, each individual in GEA is crossed with the current global best one instead of a randomly selected individual. The current best individual served as a guide to attract offspring to its region of genotype space. Mutation was added to offspring according to a dynamic mutation probability. To increase the capability of exploitation, a local search mechanism was applied to new individuals according to a dynamic probability of local search. Experimental results show that GEA outperformed the other three typical global optimization algorithms with which it was compared.

  7. A Hybrid Cellular Genetic Algorithm for Multi-objective Crew Scheduling Problem

    NASA Astrophysics Data System (ADS)

    Jolai, Fariborz; Assadipour, Ghazal

    Crew scheduling is one of the important problems of the airline industry. This problem aims to cover a number of flights by crew members, such that all the flights are covered. In a robust scheduling the assignment should be so that the total cost, delays, and unbalanced utilization are minimized. As the problem is NP-hard and the objectives are in conflict with each other, a multi-objective meta-heuristic called CellDE, which is a hybrid cellular genetic algorithm, is implemented as the optimization method. The proposed algorithm provides the decision maker with a set of non-dominated or Pareto-optimal solutions, and enables them to choose the best one according to their preferences. A set of problems of different sizes is generated and solved using the proposed algorithm. Evaluating the performance of the proposed algorithm, three metrics are suggested, and the diversity and the convergence of the achieved Pareto front are appraised. Finally a comparison is made between CellDE and PAES, another meta-heuristic algorithm. The results show the superiority of CellDE.

  8. Combinatorial Algorithms for Portfolio Optimization Problems - Case of Risk Moderate Investor

    NASA Astrophysics Data System (ADS)

    Juarna, A.

    2017-03-01

    Portfolio optimization problem is a problem of finding optimal combination of n stocks from N ≥ n available stocks that gives maximal aggregate return and minimal aggregate risk. In this paper given N = 43 from the IDX (Indonesia Stock Exchange) group of the 45 most-traded stocks, known as the LQ45, with p = 24 data of monthly returns for each stock, spanned over interval 2013-2014. This problem actually is a combinatorial one where its algorithm is constructed based on two considerations: risk moderate type of investor and maximum allowed correlation coefficient between every two eligible stocks. The main outputs resulted from implementation of the algorithms is a multiple curve of three portfolio’s attributes, e.g. the size, the ratio of return to risk, and the percentage of negative correlation coefficient for every two chosen stocks, as function of maximum allowed correlation coefficient between each two stocks. The output curve shows that the portfolio contains three stocks with ratio of return to risk at 14.57 if the maximum allowed correlation coefficient between every two eligible stocks is negative and contains 19 stocks with maximum allowed correlation coefficient 0.17 to get maximum ratio of return to risk at 25.48.

  9. Dynamic Grover search: applications in recommendation systems and optimization problems

    NASA Astrophysics Data System (ADS)

    Chakrabarty, Indranil; Khan, Shahzor; Singh, Vanshdeep

    2017-06-01

    In the recent years, we have seen that Grover search algorithm (Proceedings, 28th annual ACM symposium on the theory of computing, pp. 212-219, 1996) by using quantum parallelism has revolutionized the field of solving huge class of NP problems in comparisons to classical systems. In this work, we explore the idea of extending Grover search algorithm to approximate algorithms. Here we try to analyze the applicability of Grover search to process an unstructured database with a dynamic selection function in contrast to the static selection function used in the original work (Grover in Proceedings, 28th annual ACM symposium on the theory of computing, pp. 212-219, 1996). We show that this alteration facilitates us to extend the application of Grover search to the field of randomized search algorithms. Further, we use the dynamic Grover search algorithm to define the goals for a recommendation system based on which we propose a recommendation algorithm which uses binomial similarity distribution space giving us a quadratic speedup over traditional classical unstructured recommendation systems. Finally, we see how dynamic Grover search can be used to tackle a wide range of optimization problems where we improve complexity over existing optimization algorithms.

  10. A quasi-Newton approach to optimization problems with probability density constraints. [problem solving in mathematical programming

    NASA Technical Reports Server (NTRS)

    Tapia, R. A.; Vanrooy, D. L.

    1976-01-01

    A quasi-Newton method is presented for minimizing a nonlinear function while constraining the variables to be nonnegative and sum to one. The nonnegativity constraints were eliminated by working with the squares of the variables and the resulting problem was solved using Tapia's general theory of quasi-Newton methods for constrained optimization. A user's guide for a computer program implementing this algorithm is provided.

  11. Matrix Interdiction Problem

    NASA Astrophysics Data System (ADS)

    Kasiviswanathan, Shiva Prasad; Pan, Feng

    In the matrix interdiction problem, a real-valued matrix and an integer k is given. The objective is to remove a set of k matrix columns that minimizes in the residual matrix the sum of the row values, where the value of a row is defined to be the largest entry in that row. This combinatorial problem is closely related to bipartite network interdiction problem that can be applied to minimize the probability that an adversary can successfully smuggle weapons. After introducing the matrix interdiction problem, we study the computational complexity of this problem. We show that the matrix interdiction problem is NP-hard and that there exists a constant γ such that it is even NP-hard to approximate this problem within an n γ additive factor. We also present an algorithm for this problem that achieves an (n - k) multiplicative approximation ratio.

  12. Adjoint optimization of natural convection problems: differentially heated cavity

    NASA Astrophysics Data System (ADS)

    Saglietti, Clio; Schlatter, Philipp; Monokrousos, Antonios; Henningson, Dan S.

    2017-12-01

    Optimization of natural convection-driven flows may provide significant improvements to the performance of cooling devices, but a theoretical investigation of such flows has been rarely done. The present paper illustrates an efficient gradient-based optimization method for analyzing such systems. We consider numerically the natural convection-driven flow in a differentially heated cavity with three Prandtl numbers (Pr=0.15{-}7) at super-critical conditions. All results and implementations were done with the spectral element code Nek5000. The flow is analyzed using linear direct and adjoint computations about a nonlinear base flow, extracting in particular optimal initial conditions using power iteration and the solution of the full adjoint direct eigenproblem. The cost function for both temperature and velocity is based on the kinetic energy and the concept of entransy, which yields a quadratic functional. Results are presented as a function of Prandtl number, time horizons and weights between kinetic energy and entransy. In particular, it is shown that the maximum transient growth is achieved at time horizons on the order of 5 time units for all cases, whereas for larger time horizons the adjoint mode is recovered as optimal initial condition. For smaller time horizons, the influence of the weights leads either to a concentric temperature distribution or to an initial condition pattern that opposes the mean shear and grows according to the Orr mechanism. For specific cases, it could also been shown that the computation of optimal initial conditions leads to a degenerate problem, with a potential loss of symmetry. In these situations, it turns out that any initial condition lying in a specific span of the eigenfunctions will yield exactly the same transient amplification. As a consequence, the power iteration converges very slowly and fails to extract all possible optimal initial conditions. According to the authors' knowledge, this behavior is illustrated here for

  13. 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

  14. Existence and discrete approximation for optimization problems governed by fractional differential equations

    NASA Astrophysics Data System (ADS)

    Bai, Yunru; Baleanu, Dumitru; Wu, Guo-Cheng

    2018-06-01

    We investigate a class of generalized differential optimization problems driven by the Caputo derivative. Existence of weak Carathe ´odory solution is proved by using Weierstrass existence theorem, fixed point theorem and Filippov implicit function lemma etc. Then a numerical approximation algorithm is introduced, and a convergence theorem is established. Finally, a nonlinear programming problem constrained by the fractional differential equation is illustrated and the results verify the validity of the algorithm.

  15. The median problems on linear multichromosomal genomes: graph representation and fast exact solutions.

    PubMed

    Xu, Andrew Wei

    2010-09-01

    In genome rearrangement, given a set of genomes G and a distance measure d, the median problem asks for another genome q that minimizes the total distance [Formula: see text]. This is a key problem in genome rearrangement based phylogenetic analysis. Although this problem is known to be NP-hard, we have shown in a previous article, on circular genomes and under the DCJ distance measure, that a family of patterns in the given genomes--represented by adequate subgraphs--allow us to rapidly find exact solutions to the median problem in a decomposition approach. In this article, we extend this result to the case of linear multichromosomal genomes, in order to solve more interesting problems on eukaryotic nuclear genomes. A multi-way capping problem in the linear multichromosomal case imposes an extra computational challenge on top of the difficulty in the circular case, and this difficulty has been underestimated in our previous study and is addressed in this article. We represent the median problem by the capped multiple breakpoint graph, extend the adequate subgraphs into the capped adequate subgraphs, and prove optimality-preserving decomposition theorems, which give us the tools to solve the median problem and the multi-way capping optimization problem together. We also develop an exact algorithm ASMedian-linear, which iteratively detects instances of (capped) adequate subgraphs and decomposes problems into subproblems. Tested on simulated data, ASMedian-linear can rapidly solve most problems with up to several thousand genes, and it also can provide optimal or near-optimal solutions to the median problem under the reversal/HP distance measures. ASMedian-linear is available at http://sites.google.com/site/andrewweixu .

  16. Optimizing Irregular Applications for Energy and Performance on the Tilera Many-core Architecture

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

    Chavarría-Miranda, Daniel; Panyala, Ajay R.; Halappanavar, Mahantesh

    Optimizing applications simultaneously for energy and performance is a complex problem. High performance, parallel, irregular applications are notoriously hard to optimize due to their data-dependent memory accesses, lack of structured locality and complex data structures and code patterns. Irregular kernels are growing in importance in applications such as machine learning, graph analytics and combinatorial scientific computing. Performance- and energy-efficient implementation of these kernels on modern, energy efficient, multicore and many-core platforms is therefore an important and challenging problem. We present results from optimizing two irregular applications { the Louvain method for community detection (Grappolo), and high-performance conjugate gradient (HPCCG) {more » on the Tilera many-core system. We have significantly extended MIT's OpenTuner auto-tuning framework to conduct a detailed study of platform-independent and platform-specific optimizations to improve performance as well as reduce total energy consumption. We explore the optimization design space along three dimensions: memory layout schemes, compiler-based code transformations, and optimization of parallel loop schedules. Using auto-tuning, we demonstrate whole node energy savings of up to 41% relative to a baseline instantiation, and up to 31% relative to manually optimized variants.« less

  17. Dynamic Flow Management Problems in Air Transportation

    NASA Technical Reports Server (NTRS)

    Patterson, Sarah Stock

    1997-01-01

    In 1995, over six hundred thousand licensed pilots flew nearly thirty-five million flights into over eighteen thousand U.S. airports, logging more than 519 billion passenger miles. Since demand for air travel has increased by more than 50% in the last decade while capacity has stagnated, congestion is a problem of undeniable practical significance. In this thesis, we will develop optimization techniques that reduce the impact of congestion on the national airspace. We start by determining the optimal release times for flights into the airspace and the optimal speed adjustment while airborne taking into account the capacitated airspace. This is called the Air Traffic Flow Management Problem (TFMP). We address the complexity, showing that it is NP-hard. We build an integer programming formulation that is quite strong as some of the proposed inequalities are facet defining for the convex hull of solutions. For practical problems, the solutions of the LP relaxation of the TFMP are very often integral. In essence, we reduce the problem to efficiently solving large scale linear programming problems. Thus, the computation times are reasonably small for large scale, practical problems involving thousands of flights. Next, we address the problem of determining how to reroute aircraft in the airspace system when faced with dynamically changing weather conditions. This is called the Air Traffic Flow Management Rerouting Problem (TFMRP) We present an integrated mathematical programming approach for the TFMRP, which utilizes several methodologies, in order to minimize delay costs. In order to address the high dimensionality, we present an aggregate model, in which we formulate the TFMRP as a multicommodity, integer, dynamic network flow problem with certain side constraints. Using Lagrangian relaxation, we generate aggregate flows that are decomposed into a collection of flight paths using a randomized rounding heuristic. This collection of paths is used in a packing integer

  18. Udzawa-type iterative method with parareal preconditioner for a parabolic optimal control problem

    NASA Astrophysics Data System (ADS)

    Lapin, A.; Romanenko, A.

    2016-11-01

    The article deals with the optimal control problem with the parabolic equation as state problem. There are point-wise constraints on the state and control functions. The objective functional involves the observation given in the domain at each moment. The conditions for convergence Udzawa's type iterative method are given. The parareal method to inverse preconditioner is given. The results of calculations are presented.

  19. A Sparse Representation-Based Deployment Method for Optimizing the Observation Quality of Camera Networks

    PubMed Central

    Wang, Chang; Qi, Fei; Shi, Guangming; Wang, Xiaotian

    2013-01-01

    Deployment is a critical issue affecting the quality of service of camera networks. The deployment aims at adopting the least number of cameras to cover the whole scene, which may have obstacles to occlude the line of sight, with expected observation quality. This is generally formulated as a non-convex optimization problem, which is hard to solve in polynomial time. In this paper, we propose an efficient convex solution for deployment optimizing the observation quality based on a novel anisotropic sensing model of cameras, which provides a reliable measurement of the observation quality. The deployment is formulated as the selection of a subset of nodes from a redundant initial deployment with numerous cameras, which is an ℓ0 minimization problem. Then, we relax this non-convex optimization to a convex ℓ1 minimization employing the sparse representation. Therefore, the high quality deployment is efficiently obtained via convex optimization. Simulation results confirm the effectiveness of the proposed camera deployment algorithms. PMID:23989826

  20. Robust optimization with transiently chaotic dynamical systems

    NASA Astrophysics Data System (ADS)

    Sumi, R.; Molnár, B.; Ercsey-Ravasz, M.

    2014-05-01

    Efficiently solving hard optimization problems has been a strong motivation for progress in analog computing. In a recent study we presented a continuous-time dynamical system for solving the NP-complete Boolean satisfiability (SAT) problem, with a one-to-one correspondence between its stable attractors and the SAT solutions. While physical implementations could offer great efficiency, the transiently chaotic dynamics raises the question of operability in the presence of noise, unavoidable on analog devices. Here we show that the probability of finding solutions is robust to noise intensities well above those present on real hardware. We also developed a cellular neural network model realizable with analog circuits, which tolerates even larger noise intensities. These methods represent an opportunity for robust and efficient physical implementations.

  1. Million city traveling salesman problem solution by divide and conquer clustering with adaptive resonance neural networks.

    PubMed

    Mulder, Samuel A; Wunsch, Donald C

    2003-01-01

    The Traveling Salesman Problem (TSP) is a very hard optimization problem in the field of operations research. It has been shown to be NP-complete, and is an often-used benchmark for new optimization techniques. One of the main challenges with this problem is that standard, non-AI heuristic approaches such as the Lin-Kernighan algorithm (LK) and the chained LK variant are currently very effective and in wide use for the common fully connected, Euclidean variant that is considered here. This paper presents an algorithm that uses adaptive resonance theory (ART) in combination with a variation of the Lin-Kernighan local optimization algorithm to solve very large instances of the TSP. The primary advantage of this algorithm over traditional LK and chained-LK approaches is the increased scalability and parallelism allowed by the divide-and-conquer clustering paradigm. Tours obtained by the algorithm are lower quality, but scaling is much better and there is a high potential for increasing performance using parallel hardware.

  2. PID controller tuning using metaheuristic optimization algorithms for benchmark problems

    NASA Astrophysics Data System (ADS)

    Gholap, Vishal; Naik Dessai, Chaitali; Bagyaveereswaran, V.

    2017-11-01

    This paper contributes to find the optimal PID controller parameters using particle swarm optimization (PSO), Genetic Algorithm (GA) and Simulated Annealing (SA) algorithm. The algorithms were developed through simulation of chemical process and electrical system and the PID controller is tuned. Here, two different fitness functions such as Integral Time Absolute Error and Time domain Specifications were chosen and applied on PSO, GA and SA while tuning the controller. The proposed Algorithms are implemented on two benchmark problems of coupled tank system and DC motor. Finally, comparative study has been done with different algorithms based on best cost, number of iterations and different objective functions. The closed loop process response for each set of tuned parameters is plotted for each system with each fitness function.

  3. a Novel Discrete Optimal Transport Method for Bayesian Inverse Problems

    NASA Astrophysics Data System (ADS)

    Bui-Thanh, T.; Myers, A.; Wang, K.; Thiery, A.

    2017-12-01

    We present the Augmented Ensemble Transform (AET) method for generating approximate samples from a high-dimensional posterior distribution as a solution to Bayesian inverse problems. Solving large-scale inverse problems is critical for some of the most relevant and impactful scientific endeavors of our time. Therefore, constructing novel methods for solving the Bayesian inverse problem in more computationally efficient ways can have a profound impact on the science community. This research derives the novel AET method for exploring a posterior by solving a sequence of linear programming problems, resulting in a series of transport maps which map prior samples to posterior samples, allowing for the computation of moments of the posterior. We show both theoretical and numerical results, indicating this method can offer superior computational efficiency when compared to other SMC methods. Most of this efficiency is derived from matrix scaling methods to solve the linear programming problem and derivative-free optimization for particle movement. We use this method to determine inter-well connectivity in a reservoir and the associated uncertainty related to certain parameters. The attached file shows the difference between the true parameter and the AET parameter in an example 3D reservoir problem. The error is within the Morozov discrepancy allowance with lower computational cost than other particle methods.

  4. A frozen Gaussian approximation-based multi-level particle swarm optimization for seismic inversion

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

    Li, Jinglai, E-mail: jinglaili@sjtu.edu.cn; Lin, Guang, E-mail: lin491@purdue.edu; Computational Sciences and Mathematics Division, Pacific Northwest National Laboratory, Richland, WA 99352

    2015-09-01

    In this paper, we propose a frozen Gaussian approximation (FGA)-based multi-level particle swarm optimization (MLPSO) method for seismic inversion of high-frequency wave data. The method addresses two challenges in it: First, the optimization problem is highly non-convex, which makes hard for gradient-based methods to reach global minima. This is tackled by MLPSO which can escape from undesired local minima. Second, the character of high-frequency of seismic waves requires a large number of grid points in direct computational methods, and thus renders an extremely high computational demand on the simulation of each sample in MLPSO. We overcome this difficulty by threemore » steps: First, we use FGA to compute high-frequency wave propagation based on asymptotic analysis on phase plane; Then we design a constrained full waveform inversion problem to prevent the optimization search getting into regions of velocity where FGA is not accurate; Last, we solve the constrained optimization problem by MLPSO that employs FGA solvers with different fidelity. The performance of the proposed method is demonstrated by a two-dimensional full-waveform inversion example of the smoothed Marmousi model.« less

  5. High hardness in the biocompatible intermetallic compound β-Ti3Au

    PubMed Central

    Svanidze, Eteri; Besara, Tiglet; Ozaydin, M. Fevsi; Tiwary, Chandra Sekhar; Wang, Jiakui K.; Radhakrishnan, Sruthi; Mani, Sendurai; Xin, Yan; Han, Ke; Liang, Hong; Siegrist, Theo; Ajayan, Pulickel M.; Morosan, E.

    2016-01-01

    The search for new hard materials is often challenging, but strongly motivated by the vast application potential such materials hold. Ti3Au exhibits high hardness values (about four times those of pure Ti and most steel alloys), reduced coefficient of friction and wear rates, and biocompatibility, all of which are optimal traits for orthopedic, dental, and prosthetic applications. In addition, the ability of this compound to adhere to ceramic parts can reduce both the weight and the cost of medical components. The fourfold increase in the hardness of Ti3Au compared to other Ti–Au alloys and compounds can be attributed to the elevated valence electron density, the reduced bond length, and the pseudogap formation. Understanding the origin of hardness in this intermetallic compound provides an avenue toward designing superior biocompatible, hard materials. PMID:27453942

  6. Programming and Tuning a Quantum Annealing Device to Solve Real World Problems

    NASA Astrophysics Data System (ADS)

    Perdomo-Ortiz, Alejandro; O'Gorman, Bryan; Fluegemann, Joseph; Smelyanskiy, Vadim

    2015-03-01

    Solving real-world applications with quantum algorithms requires overcoming several challenges, ranging from translating the computational problem at hand to the quantum-machine language to tuning parameters of the quantum algorithm that have a significant impact on the performance of the device. In this talk, we discuss these challenges, strategies developed to enhance performance, and also a more efficient implementation of several applications. Although we will focus on applications of interest to NASA's Quantum Artificial Intelligence Laboratory, the methods and concepts presented here apply to a broader family of hard discrete optimization problems, including those that occur in many machine-learning algorithms.

  7. Sorption of water alkalinity and hardness from high-strength wastewater on bifunctional activated carbon: process optimization, kinetics and equilibrium studies.

    PubMed

    Amosa, Mutiu K

    2016-08-01

    Sorption optimization and mechanism of hardness and alkalinity on bifunctional empty fruit bunch-based powdered activation carbon (PAC) were studied. The PAC possessed both high surface area and ion-exchange properties, and it was utilized in the treatment of biotreated palm oil mill effluent. Batch adsorption experiments designed with Design Expert(®) were conducted in correlating the singular and interactive effects of the three adsorption parameters: PAC dosage, agitation speed and contact time. The sorption trends of the two contaminants were sequentially assessed through a full factorial design with three factor interaction models and a central composite design with polynomial models of quadratic order. Analysis of variance revealed the significant factors on each design response with very high R(2) values indicating good agreement between model and experimental values. The optimum operating conditions of the two contaminants differed due to their different regions of operating interests, thus necessitating the utility of desirability factor to get consolidated optimum operation conditions. The equilibrium data for alkalinity and hardness sorption were better represented by the Langmuir isotherm, while the pseudo-second-order kinetic model described the adsorption rates and behavior better. It was concluded that chemisorption contributed majorly to the adsorption process.

  8. Optimal structural design of the midship of a VLCC based on the strategy integrating SVM and GA

    NASA Astrophysics Data System (ADS)

    Sun, Li; Wang, Deyu

    2012-03-01

    In this paper a hybrid process of modeling and optimization, which integrates a support vector machine (SVM) and genetic algorithm (GA), was introduced to reduce the high time cost in structural optimization of ships. SVM, which is rooted in statistical learning theory and an approximate implementation of the method of structural risk minimization, can provide a good generalization performance in metamodeling the input-output relationship of real problems and consequently cuts down on high time cost in the analysis of real problems, such as FEM analysis. The GA, as a powerful optimization technique, possesses remarkable advantages for the problems that can hardly be optimized with common gradient-based optimization methods, which makes it suitable for optimizing models built by SVM. Based on the SVM-GA strategy, optimization of structural scantlings in the midship of a very large crude carrier (VLCC) ship was carried out according to the direct strength assessment method in common structural rules (CSR), which eventually demonstrates the high efficiency of SVM-GA in optimizing the ship structural scantlings under heavy computational complexity. The time cost of this optimization with SVM-GA has been sharply reduced, many more loops have been processed within a small amount of time and the design has been improved remarkably.

  9. Optimization method for an evolutional type inverse heat conduction problem

    NASA Astrophysics Data System (ADS)

    Deng, Zui-Cha; Yu, Jian-Ning; Yang, Liu

    2008-01-01

    This paper deals with the determination of a pair (q, u) in the heat conduction equation u_t-u_{xx}+q(x,t)u=0, with initial and boundary conditions u(x,0)=u_0(x),\\qquad u_x|_{x=0}=u_x|_{x=1}=0, from the overspecified data u(x, t) = g(x, t). By the time semi-discrete scheme, the problem is transformed into a sequence of inverse problems in which the unknown coefficients are purely space dependent. Based on the optimal control framework, the existence, uniqueness and stability of the solution (q, u) are proved. A necessary condition which is a couple system of a parabolic equation and parabolic variational inequality is deduced.

  10. A Guiding Evolutionary Algorithm with Greedy Strategy for Global Optimization Problems

    PubMed Central

    Cao, Leilei; Xu, Lihong; Goodman, Erik D.

    2016-01-01

    A Guiding Evolutionary Algorithm (GEA) with greedy strategy for global optimization problems is proposed. Inspired by Particle Swarm Optimization, the Genetic Algorithm, and the Bat Algorithm, the GEA was designed to retain some advantages of each method while avoiding some disadvantages. In contrast to the usual Genetic Algorithm, each individual in GEA is crossed with the current global best one instead of a randomly selected individual. The current best individual served as a guide to attract offspring to its region of genotype space. Mutation was added to offspring according to a dynamic mutation probability. To increase the capability of exploitation, a local search mechanism was applied to new individuals according to a dynamic probability of local search. Experimental results show that GEA outperformed the other three typical global optimization algorithms with which it was compared. PMID:27293421

  11. A Mixed Integer Efficient Global Optimization Framework: Applied to the Simultaneous Aircraft Design, Airline Allocation and Revenue Management Problem

    NASA Astrophysics Data System (ADS)

    Roy, Satadru

    Traditional approaches to design and optimize a new system, often, use a system-centric objective and do not take into consideration how the operator will use this new system alongside of other existing systems. This "hand-off" between the design of the new system and how the new system operates alongside other systems might lead to a sub-optimal performance with respect to the operator-level objective. In other words, the system that is optimal for its system-level objective might not be best for the system-of-systems level objective of the operator. Among the few available references that describe attempts to address this hand-off, most follow an MDO-motivated subspace decomposition approach of first designing a very good system and then provide this system to the operator who decides the best way to use this new system along with the existing systems. The motivating example in this dissertation presents one such similar problem that includes aircraft design, airline operations and revenue management "subspaces". The research here develops an approach that could simultaneously solve these subspaces posed as a monolithic optimization problem. The monolithic approach makes the problem a Mixed Integer/Discrete Non-Linear Programming (MINLP/MDNLP) problem, which are extremely difficult to solve. The presence of expensive, sophisticated engineering analyses further aggravate the problem. To tackle this challenge problem, the work here presents a new optimization framework that simultaneously solves the subspaces to capture the "synergism" in the problem that the previous decomposition approaches may not have exploited, addresses mixed-integer/discrete type design variables in an efficient manner, and accounts for computationally expensive analysis tools. The framework combines concepts from efficient global optimization, Kriging partial least squares, and gradient-based optimization. This approach then demonstrates its ability to solve an 11 route airline network

  12. Exact and Metaheuristic Approaches for a Bi-Objective School Bus Scheduling Problem.

    PubMed

    Chen, Xiaopan; Kong, Yunfeng; Dang, Lanxue; Hou, Yane; Ye, Xinyue

    2015-01-01

    As a class of hard combinatorial optimization problems, the school bus routing problem has received considerable attention in the last decades. For a multi-school system, given the bus trips for each school, the school bus scheduling problem aims at optimizing bus schedules to serve all the trips within the school time windows. In this paper, we propose two approaches for solving the bi-objective school bus scheduling problem: an exact method of mixed integer programming (MIP) and a metaheuristic method which combines simulated annealing with local search. We develop MIP formulations for homogenous and heterogeneous fleet problems respectively and solve the models by MIP solver CPLEX. The bus type-based formulation for heterogeneous fleet problem reduces the model complexity in terms of the number of decision variables and constraints. The metaheuristic method is a two-stage framework for minimizing the number of buses to be used as well as the total travel distance of buses. We evaluate the proposed MIP and the metaheuristic method on two benchmark datasets, showing that on both instances, our metaheuristic method significantly outperforms the respective state-of-the-art methods.

  13. Exact and Metaheuristic Approaches for a Bi-Objective School Bus Scheduling Problem

    PubMed Central

    Chen, Xiaopan; Kong, Yunfeng; Dang, Lanxue; Hou, Yane; Ye, Xinyue

    2015-01-01

    As a class of hard combinatorial optimization problems, the school bus routing problem has received considerable attention in the last decades. For a multi-school system, given the bus trips for each school, the school bus scheduling problem aims at optimizing bus schedules to serve all the trips within the school time windows. In this paper, we propose two approaches for solving the bi-objective school bus scheduling problem: an exact method of mixed integer programming (MIP) and a metaheuristic method which combines simulated annealing with local search. We develop MIP formulations for homogenous and heterogeneous fleet problems respectively and solve the models by MIP solver CPLEX. The bus type-based formulation for heterogeneous fleet problem reduces the model complexity in terms of the number of decision variables and constraints. The metaheuristic method is a two-stage framework for minimizing the number of buses to be used as well as the total travel distance of buses. We evaluate the proposed MIP and the metaheuristic method on two benchmark datasets, showing that on both instances, our metaheuristic method significantly outperforms the respective state-of-the-art methods. PMID:26176764

  14. Reinforcement learning solution for HJB equation arising in constrained optimal control problem.

    PubMed

    Luo, Biao; Wu, Huai-Ning; Huang, Tingwen; Liu, Derong

    2015-11-01

    The constrained optimal control problem depends on the solution of the complicated Hamilton-Jacobi-Bellman equation (HJBE). In this paper, a data-based off-policy reinforcement learning (RL) method is proposed, which learns the solution of the HJBE and the optimal control policy from real system data. One important feature of the off-policy RL is that its policy evaluation can be realized with data generated by other behavior policies, not necessarily the target policy, which solves the insufficient exploration problem. The convergence of the off-policy RL is proved by demonstrating its equivalence to the successive approximation approach. Its implementation procedure is based on the actor-critic neural networks structure, where the function approximation is conducted with linearly independent basis functions. Subsequently, the convergence of the implementation procedure with function approximation is also proved. Finally, its effectiveness is verified through computer simulations. Copyright © 2015 Elsevier Ltd. All rights reserved.

  15. Hard sphere packings within cylinders.

    PubMed

    Fu, Lin; Steinhardt, William; Zhao, Hao; Socolar, Joshua E S; Charbonneau, Patrick

    2016-03-07

    Arrangements of identical hard spheres confined to a cylinder with hard walls have been used to model experimental systems, such as fullerenes in nanotubes and colloidal wire assembly. Finding the densest configurations, called close packings, of hard spheres of diameter σ in a cylinder of diameter D is a purely geometric problem that grows increasingly complex as D/σ increases, and little is thus known about the regime for D > 2.873σ. In this work, we extend the identification of close packings up to D = 4.00σ by adapting Torquato-Jiao's adaptive-shrinking-cell formulation and sequential-linear-programming (SLP) technique. We identify 17 new structures, almost all of them chiral. Beyond D ≈ 2.85σ, most of the structures consist of an outer shell and an inner core that compete for being close packed. In some cases, the shell adopts its own maximum density configuration, and the stacking of core spheres within it is quasiperiodic. In other cases, an interplay between the two components is observed, which may result in simple periodic structures. In yet other cases, the very distinction between the core and shell vanishes, resulting in more exotic packing geometries, including some that are three-dimensional extensions of structures obtained from packing hard disks in a circle.

  16. A learning approach to the bandwidth multicolouring problem

    NASA Astrophysics Data System (ADS)

    Akbari Torkestani, Javad

    2016-05-01

    In this article, a generalisation of the vertex colouring problem known as bandwidth multicolouring problem (BMCP), in which a set of colours is assigned to each vertex such that the difference between the colours, assigned to each vertex and its neighbours, is by no means less than a predefined threshold, is considered. It is shown that the proposed method can be applied to solve the bandwidth colouring problem (BCP) as well. BMCP is known to be NP-hard in graph theory, and so a large number of approximation solutions, as well as exact algorithms, have been proposed to solve it. In this article, two learning automata-based approximation algorithms are proposed for estimating a near-optimal solution to the BMCP. We show, for the first proposed algorithm, that by choosing a proper learning rate, the algorithm finds the optimal solution with a probability close enough to unity. Moreover, we compute the worst-case time complexity of the first algorithm for finding a 1/(1-ɛ) optimal solution to the given problem. The main advantage of this method is that a trade-off between the running time of algorithm and the colour set size (colouring optimality) can be made, by a proper choice of the learning rate also. Finally, it is shown that the running time of the proposed algorithm is independent of the graph size, and so it is a scalable algorithm for large graphs. The second proposed algorithm is compared with some well-known colouring algorithms and the results show the efficiency of the proposed algorithm in terms of the colour set size and running time of algorithm.

  17. Closed loop problems in biomechanics. Part II--an optimization approach.

    PubMed

    Vaughan, C L; Hay, J G; Andrews, J G

    1982-01-01

    A closed loop problem in biomechanics may be defined as a problem in which there are one or more closed loops formed by the human body in contact with itself or with an external system. Under certain conditions the problem is indeterminate--the unknown forces and torques outnumber the equations. Force transducing devices, which would help solve this problem, have serious drawbacks, and existing methods are inaccurate and non-general. The purposes of the present paper are (1) to develop a general procedure for solving closed loop problems; (2) to illustrate the application of the procedure; and (3) to examine the validity of the procedure. A mathematical optimization approach is applied to the solution of three different closed loop problems--walking up stairs, vertical jumping and cartwheeling. The following conclusions are drawn: (1) the method described is reasonably successful for predicting horizontal and vertical reaction forces at the distal segments although problems exist for predicting the points of application of these forces; (2) the results provide some support for the notion that the human neuromuscular mechanism attempts to minimize the joint torques and thus, to a certain degree, the amount of muscular effort; (3) in the validation procedure it is desirable to have a force device for each of the distal segments in contact with a fixed external system; and (4) the method is sufficiently general to be applied to all classes of closed loop problems.

  18. Robust Dynamic Multi-objective Vehicle Routing Optimization Method.

    PubMed

    Guo, Yi-Nan; Cheng, Jian; Luo, Sha; Gong, Dun-Wei

    2017-03-21

    For dynamic multi-objective vehicle routing problems, the waiting time of vehicle, the number of serving vehicles, the total distance of routes were normally considered as the optimization objectives. Except for above objectives, fuel consumption that leads to the environmental pollution and energy consumption was focused on in this paper. Considering the vehicles' load and the driving distance, corresponding carbon emission model was built and set as an optimization objective. Dynamic multi-objective vehicle routing problems with hard time windows and randomly appeared dynamic customers, subsequently, were modeled. In existing planning methods, when the new service demand came up, global vehicle routing optimization method was triggered to find the optimal routes for non-served customers, which was time-consuming. Therefore, robust dynamic multi-objective vehicle routing method with two-phase is proposed. Three highlights of the novel method are: (i) After finding optimal robust virtual routes for all customers by adopting multi-objective particle swarm optimization in the first phase, static vehicle routes for static customers are formed by removing all dynamic customers from robust virtual routes in next phase. (ii)The dynamically appeared customers append to be served according to their service time and the vehicles' statues. Global vehicle routing optimization is triggered only when no suitable locations can be found for dynamic customers. (iii)A metric measuring the algorithms' robustness is given. The statistical results indicated that the routes obtained by the proposed method have better stability and robustness, but may be sub-optimum. Moreover, time-consuming global vehicle routing optimization is avoided as dynamic customers appear.

  19. Solving fractional optimal control problems within a Chebyshev-Legendre operational technique

    NASA Astrophysics Data System (ADS)

    Bhrawy, A. H.; Ezz-Eldien, S. S.; Doha, E. H.; Abdelkawy, M. A.; Baleanu, D.

    2017-06-01

    In this manuscript, we report a new operational technique for approximating the numerical solution of fractional optimal control (FOC) problems. The operational matrix of the Caputo fractional derivative of the orthonormal Chebyshev polynomial and the Legendre-Gauss quadrature formula are used, and then the Lagrange multiplier scheme is employed for reducing such problems into those consisting of systems of easily solvable algebraic equations. We compare the approximate solutions achieved using our approach with the exact solutions and with those presented in other techniques and we show the accuracy and applicability of the new numerical approach, through two numerical examples.

  20. 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

  1. 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.

  2. Capacitated vehicle-routing problem model for scheduled solid waste collection and route optimization using PSO algorithm.

    PubMed

    Hannan, M A; Akhtar, Mahmuda; Begum, R A; Basri, H; Hussain, A; Scavino, Edgar

    2018-01-01

    Waste collection widely depends on the route optimization problem that involves a large amount of expenditure in terms of capital, labor, and variable operational costs. Thus, the more waste collection route is optimized, the more reduction in different costs and environmental effect will be. This study proposes a modified particle swarm optimization (PSO) algorithm in a capacitated vehicle-routing problem (CVRP) model to determine the best waste collection and route optimization solutions. In this study, threshold waste level (TWL) and scheduling concepts are applied in the PSO-based CVRP model under different datasets. The obtained results from different datasets show that the proposed algorithmic CVRP model provides the best waste collection and route optimization in terms of travel distance, total waste, waste collection efficiency, and tightness at 70-75% of TWL. The obtained results for 1 week scheduling show that 70% of TWL performs better than all node consideration in terms of collected waste, distance, tightness, efficiency, fuel consumption, and cost. The proposed optimized model can serve as a valuable tool for waste collection and route optimization toward reducing socioeconomic and environmental impacts. Copyright © 2017 Elsevier Ltd. All rights reserved.

  3. New Dandelion Algorithm Optimizes Extreme Learning Machine for Biomedical Classification Problems

    PubMed Central

    Li, Xiguang; Zhao, Liang; Gong, Changqing; Liu, Xiaojing

    2017-01-01

    Inspired by the behavior of dandelion sowing, a new novel swarm intelligence algorithm, namely, dandelion algorithm (DA), is proposed for global optimization of complex functions in this paper. In DA, the dandelion population will be divided into two subpopulations, and different subpopulations will undergo different sowing behaviors. Moreover, another sowing method is designed to jump out of local optimum. In order to demonstrate the validation of DA, we compare the proposed algorithm with other existing algorithms, including bat algorithm, particle swarm optimization, and enhanced fireworks algorithm. Simulations show that the proposed algorithm seems much superior to other algorithms. At the same time, the proposed algorithm can be applied to optimize extreme learning machine (ELM) for biomedical classification problems, and the effect is considerable. At last, we use different fusion methods to form different fusion classifiers, and the fusion classifiers can achieve higher accuracy and better stability to some extent. PMID:29085425

  4. Linear quadratic tracking problems in Hilbert space - Application to optimal active noise suppression

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Silcox, R. J.; Keeling, S. L.; Wang, C.

    1989-01-01

    A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.

  5. A Generalized Orienteering Problem for Optimal Search and Interdiction Planning

    DTIC Science & Technology

    2013-09-01

    NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA DISSERTATION A GENERALIZED ORIENTEERING PROBLEM FOR OPTIMAL SEARCH AND INTERDICTION PLANNING by Jesse...provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently...16. SECURITY CLASSIFICATION OF: a . REPORT b. ABSTRACT c. THIS PAGE 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES 19a. NAME OF RESPONSIBLE PERSON 19b

  6. Deaf and hard of hearing students' perspectives on bullying and school climate.

    PubMed

    Weiner, Mary T; Day, Stefanie J; Galvan, Dennis

    2013-01-01

    Student perspectives reflect school climate. The study examined perspectives among deaf and hard of hearing students in residential and large day schools regarding bullying, and compared these perspectives with those of a national database of hearing students. The participants were 812 deaf and hard of hearing students in 11 U.S. schools. Data were derived from the Olweus Bullying Questionnaire (Olweus, 2007b), a standardized self-reported survey with multiple-choice questions focusing on different aspects of bullying problems. Significant bullying problems were found in deaf school programs. It appears that deaf and hard of hearing students experience bullying at rates 2-3 times higher than those reported by hearing students. Deaf and hard of hearing students reported that school personnel intervened less often when bullying occurred than was reported in the hearing sample. Results indicate the need for school climate improvement for all students, regardless of hearing status.

  7. Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1985-01-01

    In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

  8. Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

    NASA Technical Reports Server (NTRS)

    Gibson, J. S.; Rosen, I. G.

    1987-01-01

    In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

  9. The Soda Can Optimization Problem: Getting Close to the Real Thing

    ERIC Educational Resources Information Center

    Premadasa, Kirthi; Martin, Paul; Sprecher, Bryce; Yang, Lai; Dodge, Noah-Helen

    2016-01-01

    Optimizing the dimensions of a soda can is a classic problem that is frequently posed to freshman calculus students. However, if we only minimize the surface area subject to a fixed volume, the result is a can with a square edge-on profile, and this differs significantly from actual cans. By considering a more realistic model for the can that…

  10. 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.

  11. Application of Multi-Objective Human Learning Optimization Method to Solve AC/DC Multi-Objective Optimal Power Flow Problem

    NASA Astrophysics Data System (ADS)

    Cao, Jia; Yan, Zheng; He, Guangyu

    2016-06-01

    This paper introduces an efficient algorithm, multi-objective human learning optimization method (MOHLO), to solve AC/DC multi-objective optimal power flow problem (MOPF). Firstly, the model of AC/DC MOPF including wind farms is constructed, where includes three objective functions, operating cost, power loss, and pollutant emission. Combining the non-dominated sorting technique and the crowding distance index, the MOHLO method can be derived, which involves individual learning operator, social learning operator, random exploration learning operator and adaptive strategies. Both the proposed MOHLO method and non-dominated sorting genetic algorithm II (NSGAII) are tested on an improved IEEE 30-bus AC/DC hybrid system. Simulation results show that MOHLO method has excellent search efficiency and the powerful ability of searching optimal. Above all, MOHLO method can obtain more complete pareto front than that by NSGAII method. However, how to choose the optimal solution from pareto front depends mainly on the decision makers who stand from the economic point of view or from the energy saving and emission reduction point of view.

  12. Macroscopic relationship in primal-dual portfolio optimization problem

    NASA Astrophysics Data System (ADS)

    Shinzato, Takashi

    2018-02-01

    In the present paper, using a replica analysis, we examine the portfolio optimization problem handled in previous work and discuss the minimization of investment risk under constraints of budget and expected return for the case that the distribution of the hyperparameters of the mean and variance of the return rate of each asset are not limited to a specific probability family. Findings derived using our proposed method are compared with those in previous work to verify the effectiveness of our proposed method. Further, we derive a Pythagorean theorem of the Sharpe ratio and macroscopic relations of opportunity loss. Using numerical experiments, the effectiveness of our proposed method is demonstrated for a specific situation.

  13. Discrete bacteria foraging optimization algorithm for graph based problems - a transition from continuous to discrete

    NASA Astrophysics Data System (ADS)

    Sur, Chiranjib; Shukla, Anupam

    2018-03-01

    Bacteria Foraging Optimisation Algorithm is a collective behaviour-based meta-heuristics searching depending on the social influence of the bacteria co-agents in the search space of the problem. The algorithm faces tremendous hindrance in terms of its application for discrete problems and graph-based problems due to biased mathematical modelling and dynamic structure of the algorithm. This had been the key factor to revive and introduce the discrete form called Discrete Bacteria Foraging Optimisation (DBFO) Algorithm for discrete problems which exceeds the number of continuous domain problems represented by mathematical and numerical equations in real life. In this work, we have mainly simulated a graph-based road multi-objective optimisation problem and have discussed the prospect of its utilisation in other similar optimisation problems and graph-based problems. The various solution representations that can be handled by this DBFO has also been discussed. The implications and dynamics of the various parameters used in the DBFO are illustrated from the point view of the problems and has been a combination of both exploration and exploitation. The result of DBFO has been compared with Ant Colony Optimisation and Intelligent Water Drops Algorithms. Important features of DBFO are that the bacteria agents do not depend on the local heuristic information but estimates new exploration schemes depending upon the previous experience and covered path analysis. This makes the algorithm better in combination generation for graph-based problems and combination generation for NP hard problems.

  14. Adaptive Grouping Cloud Model Shuffled Frog Leaping Algorithm for Solving Continuous Optimization Problems

    PubMed Central

    Liu, Haorui; Yi, Fengyan; Yang, Heli

    2016-01-01

    The shuffled frog leaping algorithm (SFLA) easily falls into local optimum when it solves multioptimum function optimization problem, which impacts the accuracy and convergence speed. Therefore this paper presents grouped SFLA for solving continuous optimization problems combined with the excellent characteristics of cloud model transformation between qualitative and quantitative research. The algorithm divides the definition domain into several groups and gives each group a set of frogs. Frogs of each region search in their memeplex, and in the search process the algorithm uses the “elite strategy” to update the location information of existing elite frogs through cloud model algorithm. This method narrows the searching space and it can effectively improve the situation of a local optimum; thus convergence speed and accuracy can be significantly improved. The results of computer simulation confirm this conclusion. PMID:26819584

  15. Near-optimal, asymptotic tracking in control problems involving state-variable inequality constraints

    NASA Technical Reports Server (NTRS)

    Markopoulos, N.; Calise, A. J.

    1993-01-01

    The class of all piecewise time-continuous controllers tracking a given hypersurface in the state space of a dynamical system can be split by the present transformation technique into two disjoint classes; while the first of these contains all controllers which track the hypersurface in finite time, the second contains all controllers that track the hypersurface asymptotically. On this basis, a reformulation is presented for optimal control problems involving state-variable inequality constraints. If the state constraint is regarded as 'soft', there may exist controllers which are asymptotic, two-sided, and able to yield the optimal value of the performance index.

  16. Automation of reverse engineering process in aircraft modeling and related optimization problems

    NASA Technical Reports Server (NTRS)

    Li, W.; Swetits, J.

    1994-01-01

    During the year of 1994, the engineering problems in aircraft modeling were studied. The initial concern was to obtain a surface model with desirable geometric characteristics. Much of the effort during the first half of the year was to find an efficient way of solving a computationally difficult optimization model. Since the smoothing technique in the proposal 'Surface Modeling and Optimization Studies of Aerodynamic Configurations' requires solutions of a sequence of large-scale quadratic programming problems, it is important to design algorithms that can solve each quadratic program in a few interactions. This research led to three papers by Dr. W. Li, which were submitted to SIAM Journal on Optimization and Mathematical Programming. Two of these papers have been accepted for publication. Even though significant progress has been made during this phase of research and computation times was reduced from 30 min. to 2 min. for a sample problem, it was not good enough for on-line processing of digitized data points. After discussion with Dr. Robert E. Smith Jr., it was decided not to enforce shape constraints in order in order to simplify the model. As a consequence, P. Dierckx's nonparametric spline fitting approach was adopted, where one has only one control parameter for the fitting process - the error tolerance. At the same time the surface modeling software developed by Imageware was tested. Research indicated a substantially improved fitting of digitalized data points can be achieved if a proper parameterization of the spline surface is chosen. A winning strategy is to incorporate Dierckx's surface fitting with a natural parameterization for aircraft parts. The report consists of 4 chapters. Chapter 1 provides an overview of reverse engineering related to aircraft modeling and some preliminary findings of the effort in the second half of the year. Chapters 2-4 are the research results by Dr. W. Li on penalty functions and conjugate gradient methods for

  17. Learning automata-based solutions to the nonlinear fractional knapsack problem with applications to optimal resource allocation.

    PubMed

    Granmo, Ole-Christoffer; Oommen, B John; Myrer, Svein Arild; Olsen, Morten Goodwin

    2007-02-01

    This paper considers the nonlinear fractional knapsack problem and demonstrates how its solution can be effectively applied to two resource allocation problems dealing with the World Wide Web. The novel solution involves a "team" of deterministic learning automata (LA). The first real-life problem relates to resource allocation in web monitoring so as to "optimize" information discovery when the polling capacity is constrained. The disadvantages of the currently reported solutions are explained in this paper. The second problem concerns allocating limited sampling resources in a "real-time" manner with the purpose of estimating multiple binomial proportions. This is the scenario encountered when the user has to evaluate multiple web sites by accessing a limited number of web pages, and the proportions of interest are the fraction of each web site that is successfully validated by an HTML validator. Using the general LA paradigm to tackle both of the real-life problems, the proposed scheme improves a current solution in an online manner through a series of informed guesses that move toward the optimal solution. At the heart of the scheme, a team of deterministic LA performs a controlled random walk on a discretized solution space. Comprehensive experimental results demonstrate that the discretization resolution determines the precision of the scheme, and that for a given precision, the current solution (to both problems) is consistently improved until a nearly optimal solution is found--even for switching environments. Thus, the scheme, while being novel to the entire field of LA, also efficiently handles a class of resource allocation problems previously not addressed in the literature.

  18. The Hard-to-Employ--Who Are They? Perspectives on Training the Disadvantaged--The Hard-to-Employ. Personnel Services Review Series 2.

    ERIC Educational Resources Information Center

    Harrison, Don K.; Brown, Dorothy R.

    The hard-to-employ, both urban and rural, share common characteristics of inadequate income, slum housing, inferior education, no medical attention, and lack of real job opportunities. The deficiencies dove-tail, and families are often afflicted with all. The picture may seem bleak, but there is optimism in reclamation of the so-called…

  19. Optimal multi-floor plant layout based on the mathematical programming and particle swarm optimization.

    PubMed

    Lee, Chang Jun

    2015-01-01

    In the fields of researches associated with plant layout optimization, the main goal is to minimize the costs of pipelines and pumping between connecting equipment under various constraints. However, what is the lacking of considerations in previous researches is to transform various heuristics or safety regulations into mathematical equations. For example, proper safety distances between equipments have to be complied for preventing dangerous accidents on a complex plant. Moreover, most researches have handled single-floor plant. However, many multi-floor plants have been constructed for the last decade. Therefore, the proper algorithm handling various regulations and multi-floor plant should be developed. In this study, the Mixed Integer Non-Linear Programming (MINLP) problem including safety distances, maintenance spaces, etc. is suggested based on mathematical equations. The objective function is a summation of pipeline and pumping costs. Also, various safety and maintenance issues are transformed into inequality or equality constraints. However, it is really hard to solve this problem due to complex nonlinear constraints. Thus, it is impossible to use conventional MINLP solvers using derivatives of equations. In this study, the Particle Swarm Optimization (PSO) technique is employed. The ethylene oxide plant is illustrated to verify the efficacy of this study.

  20. Estimates of the absolute error and a scheme for an approximate solution to scheduling problems

    NASA Astrophysics Data System (ADS)

    Lazarev, A. A.

    2009-02-01

    An approach is proposed for estimating absolute errors and finding approximate solutions to classical NP-hard scheduling problems of minimizing the maximum lateness for one or many machines and makespan is minimized. The concept of a metric (distance) between instances of the problem is introduced. The idea behind the approach is, given the problem instance, to construct another instance for which an optimal or approximate solution can be found at the minimum distance from the initial instance in the metric introduced. Instead of solving the original problem (instance), a set of approximating polynomially/pseudopolynomially solvable problems (instances) are considered, an instance at the minimum distance from the given one is chosen, and the resulting schedule is then applied to the original instance.

  1. Peritoneal dialysis catheter implantation: avoiding problems and optimizing outcomes.

    PubMed

    Crabtree, John H

    2015-01-01

    The success of peritoneal dialysis (PD) as renal replacement therapy is dependent upon the patient having a functional long-term peritoneal access. There are a number of identified best practices that must be adhered to during PD catheter placement to achieve a durable and infection-resistant access. The clinical setting, available resources, and the employed catheter insertion method may not always permit complete adherence to these practices; however, an attempt should be made to comply with them as closely as possible. Although omission of any one of the practices can lead to catheter loss, departures from some are committed more frequently, manifesting as commonly occurring clinical problems, such as drain pain, catheter tip migration, omental entrapment, pericatheter leaks and hernias, and poor exit-site location. Understanding the technical pitfalls in PD catheter placement that lead to these problems, enable the provider to modify practice habits to avoid them and optimize outcomes. © 2014 Wiley Periodicals, Inc.

  2. Early identification: Language skills and social functioning in deaf and hard of hearing preschool children.

    PubMed

    Netten, Anouk P; Rieffe, Carolien; Theunissen, Stephanie C P M; Soede, Wim; Dirks, Evelien; Korver, Anna M H; Konings, Saskia; Oudesluys-Murphy, Anne Marie; Dekker, Friedo W; Frijns, Johan H M

    2015-12-01

    Permanent childhood hearing impairment often results in speech and language problems that are already apparent in early childhood. Past studies show a clear link between language skills and the child's social-emotional functioning. The aim of this study was to examine the level of language and communication skills after the introduction of early identification services and their relation with social functioning and behavioral problems in deaf and hard of hearing children. Nationwide cross-sectional observation of a cohort of 85 early identified deaf and hard of hearing preschool children (aged 30-66 months). Parents reported on their child's communicative abilities (MacArthur-Bates Communicative Development Inventory III), social functioning and appearance of behavioral problems (Strengths and Difficulties Questionnaire). Receptive and expressive language skills were measured using the Reynell Developmental Language Scale and the Schlichting Expressive Language Test, derived from the child's medical records. Language and communicative abilities of early identified deaf and hard of hearing children are not on a par with hearing peers. Compared to normative scores from hearing children, parents of deaf and hard of hearing children reported lower social functioning and more behavioral problems. Higher communicative abilities were related to better social functioning and less behavioral problems. No relation was found between the degree of hearing loss, age at amplification, uni- or bilateral amplification, mode of communication and social functioning and behavioral problems. These results suggest that improving the communicative abilities of deaf and hard of hearing children could improve their social-emotional functioning. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

  3. Automatically Generated Algorithms for the Vertex Coloring Problem

    PubMed Central

    Contreras Bolton, Carlos; Gatica, Gustavo; Parada, Víctor

    2013-01-01

    The vertex coloring problem is a classical problem in combinatorial optimization that consists of assigning a color to each vertex of a graph such that no adjacent vertices share the same color, minimizing the number of colors used. Despite the various practical applications that exist for this problem, its NP-hardness still represents a computational challenge. Some of the best computational results obtained for this problem are consequences of hybridizing the various known heuristics. Automatically revising the space constituted by combining these techniques to find the most adequate combination has received less attention. In this paper, we propose exploring the heuristics space for the vertex coloring problem using evolutionary algorithms. We automatically generate three new algorithms by combining elementary heuristics. To evaluate the new algorithms, a computational experiment was performed that allowed comparing them numerically with existing heuristics. The obtained algorithms present an average 29.97% relative error, while four other heuristics selected from the literature present a 59.73% error, considering 29 of the more difficult instances in the DIMACS benchmark. PMID:23516506

  4. Colored Traveling Salesman Problem.

    PubMed

    Li, Jun; Zhou, MengChu; Sun, Qirui; Dai, Xianzhong; Yu, Xiaolong

    2015-11-01

    The multiple traveling salesman problem (MTSP) is an important combinatorial optimization problem. It has been widely and successfully applied to the practical cases in which multiple traveling individuals (salesmen) share the common workspace (city set). However, it cannot represent some application problems where multiple traveling individuals not only have their own exclusive tasks but also share a group of tasks with each other. This work proposes a new MTSP called colored traveling salesman problem (CTSP) for handling such cases. Two types of city groups are defined, i.e., each group of exclusive cities of a single color for a salesman to visit and a group of shared cities of multiple colors allowing all salesmen to visit. Evidences show that CTSP is NP-hard and a multidepot MTSP and multiple single traveling salesman problems are its special cases. We present a genetic algorithm (GA) with dual-chromosome coding for CTSP and analyze the corresponding solution space. Then, GA is improved by incorporating greedy, hill-climbing (HC), and simulated annealing (SA) operations to achieve better performance. By experiments, the limitation of the exact solution method is revealed and the performance of the presented GAs is compared. The results suggest that SAGA can achieve the best quality of solutions and HCGA should be the choice making good tradeoff between the solution quality and computing time.

  5. System identification using Nuclear Norm & Tabu Search optimization

    NASA Astrophysics Data System (ADS)

    Ahmed, Asif A.; Schoen, Marco P.; Bosworth, Ken W.

    2018-01-01

    In recent years, subspace System Identification (SI) algorithms have seen increased research, stemming from advanced minimization methods being applied to the Nuclear Norm (NN) approach in system identification. These minimization algorithms are based on hard computing methodologies. To the authors’ knowledge, as of now, there has been no work reported that utilizes soft computing algorithms to address the minimization problem within the nuclear norm SI framework. A linear, time-invariant, discrete time system is used in this work as the basic model for characterizing a dynamical system to be identified. The main objective is to extract a mathematical model from collected experimental input-output data. Hankel matrices are constructed from experimental data, and the extended observability matrix is employed to define an estimated output of the system. This estimated output and the actual - measured - output are utilized to construct a minimization problem. An embedded rank measure assures minimum state realization outcomes. Current NN-SI algorithms employ hard computing algorithms for minimization. In this work, we propose a simple Tabu Search (TS) algorithm for minimization. TS algorithm based SI is compared with the iterative Alternating Direction Method of Multipliers (ADMM) line search optimization based NN-SI. For comparison, several different benchmark system identification problems are solved by both approaches. Results show improved performance of the proposed SI-TS algorithm compared to the NN-SI ADMM algorithm.

  6. Automated bond order assignment as an optimization problem.

    PubMed

    Dehof, Anna Katharina; Rurainski, Alexander; Bui, Quang Bao Anh; Böcker, Sebastian; Lenhof, Hans-Peter; Hildebrandt, Andreas

    2011-03-01

    Numerous applications in Computational Biology process molecular structures and hence strongly rely not only on correct atomic coordinates but also on correct bond order information. For proteins and nucleic acids, bond orders can be easily deduced but this does not hold for other types of molecules like ligands. For ligands, bond order information is not always provided in molecular databases and thus a variety of approaches tackling this problem have been developed. In this work, we extend an ansatz proposed by Wang et al. that assigns connectivity-based penalty scores and tries to heuristically approximate its optimum. In this work, we present three efficient and exact solvers for the problem replacing the heuristic approximation scheme of the original approach: an A*, an ILP and an fixed-parameter approach (FPT) approach. We implemented and evaluated the original implementation, our A*, ILP and FPT formulation on the MMFF94 validation suite and the KEGG Drug database. We show the benefit of computing exact solutions of the penalty minimization problem and the additional gain when computing all optimal (or even suboptimal) solutions. We close with a detailed comparison of our methods. The A* and ILP solution are integrated into the open-source C++ LGPL library BALL and the molecular visualization and modelling tool BALLView and can be downloaded from our homepage www.ball-project.org. The FPT implementation can be downloaded from http://bio.informatik.uni-jena.de/software/.

  7. Effect of water hardness on the production and microbicidal efficacy of slightly acidic electrolyzed water.

    PubMed

    Forghani, Fereidoun; Park, Joong-Hyun; Oh, Deog-Hwan

    2015-06-01

    Slightly acidic electrolyzed water (SAEW) has been proved as an effective sanitizer against microorganisms attached to foods. However, its physical properties and inactivation efficacy are affected by several factors such as water hardness. Therefore, in this study the effect of water hardness on SAEW properties were studied. Pure cultures of foodborne bacteria were used in vitro and in vivo to evaluate the inactivation efficacy of the SAEWs produced. Results obtained showed water hardness to be an important factor in the production of SAEW. Low water hardness may result in the necessity of further optimization of production process. In this study the addition of 5% HCl and 2 M NaCl at 1.5 mL/min flow rate was found to be the best electrolyte concentration for the optimization of SAEW production from low hardness water (34 ± 2 mg/L). Furthermore, the results showed that pre-heating was a better approach compared to post-production heating of SAEW, resulting in higher ACC values and therefor better sanitization efficacy. Copyright © 2014 Elsevier Ltd. All rights reserved.

  8. Micromagnetic simulations with periodic boundary conditions: Hard-soft nanocomposites

    DOE PAGES

    Wysocki, Aleksander L.; Antropov, Vladimir P.

    2016-12-01

    Here, we developed a micromagnetic method for modeling magnetic systems with periodic boundary conditions along an arbitrary number of dimensions. The main feature is an adaptation of the Ewald summation technique for evaluation of long-range dipolar interactions. The method was applied to investigate the hysteresis process in hard-soft magnetic nanocomposites with various geometries. The dependence of the results on different micromagnetic parameters was studied. We found that for layered structures with an out-of-plane hard phase easy axis the hysteretic properties are very sensitive to the strength of the interlayer exchange coupling, as long as the spontaneous magnetization for the hardmore » phase is significantly smaller than for the soft phase. The origin of this behavior was discussed. Additionally, we investigated the soft phase size optimizing the energy product of hard-soft nanocomposites.« less

  9. Second-order optimality conditions for problems with C1 data

    NASA Astrophysics Data System (ADS)

    Ginchev, Ivan; Ivanov, Vsevolod I.

    2008-04-01

    In this paper we obtain second-order optimality conditions of Karush-Kuhn-Tucker type and Fritz John one for a problem with inequality constraints and a set constraint in nonsmooth settings using second-order directional derivatives. In the necessary conditions we suppose that the objective function and the active constraints are continuously differentiable, but their gradients are not necessarily locally Lipschitz. In the sufficient conditions for a global minimum we assume that the objective function is differentiable at and second-order pseudoconvex at , a notion introduced by the authors [I. Ginchev, V.I. Ivanov, Higher-order pseudoconvex functions, in: I.V. Konnov, D.T. Luc, A.M. Rubinov (Eds.), Generalized Convexity and Related Topics, in: Lecture Notes in Econom. and Math. Systems, vol. 583, Springer, 2007, pp. 247-264], the constraints are both differentiable and quasiconvex at . In the sufficient conditions for an isolated local minimum of order two we suppose that the problem belongs to the class C1,1. We show that they do not hold for C1 problems, which are not C1,1 ones. At last a new notion parabolic local minimum is defined and it is applied to extend the sufficient conditions for an isolated local minimum from problems with C1,1 data to problems with C1 one.

  10. Mongoose: Creation of a Rad-Hard MIPS R3000

    NASA Technical Reports Server (NTRS)

    Lincoln, Dan; Smith, Brian

    1993-01-01

    This paper describes the development of a 32 Bit, full MIPS R3000 code-compatible Rad-Hard CPU, code named Mongoose. Mongoose progressed from contract award, through the design cycle, to operational silicon in 12 months to meet a space mission for NASA. The goal was the creation of a fully static device capable of operation to the maximum Mil-883 derated speed, worst-case post-rad exposure with full operational integrity. This included consideration of features for functional enhancements relating to mission compatibility and removal of commercial practices not supported by Rad-Hard technology. 'Mongoose' developed from an evolution of LSI Logic's MIPS-I embedded processor, LR33000, code named Cobra, to its Rad-Hard 'equivalent', Mongoose. The term 'equivalent' is used to infer that the core of the processor is functionally identical, allowing the same use and optimizations of the MIPS-I Instruction Set software tool suite for compilation, software program trace, etc. This activity was started in September of 1991 under a contract from NASA-Goddard Space Flight Center (GSFC)-Flight Data Systems. The approach affected a teaming of NASA-GSFC for program development, LSI Logic for system and ASIC design coupled with the Rad-Hard process technology, and Harris (GASD) for Rad-Hard microprocessor design expertise. The program culminated with the generation of Rad-Hard Mongoose prototypes one year later.

  11. XY vs X Mixer in Quantum Alternating Operator Ansatz for Optimization Problems with Constraints

    NASA Technical Reports Server (NTRS)

    Wang, Zhihui; Rubin, Nicholas; Rieffel, Eleanor G.

    2018-01-01

    Quantum Approximate Optimization Algorithm, further generalized as Quantum Alternating Operator Ansatz (QAOA), is a family of algorithms for combinatorial optimization problems. It is a leading candidate to run on emerging universal quantum computers to gain insight into quantum heuristics. In constrained optimization, penalties are often introduced so that the ground state of the cost Hamiltonian encodes the solution (a standard practice in quantum annealing). An alternative is to choose a mixing Hamiltonian such that the constraint corresponds to a constant of motion and the quantum evolution stays in the feasible subspace. Better performance of the algorithm is speculated due to a much smaller search space. We consider problems with a constant Hamming weight as the constraint. We also compare different methods of generating the generalized W-state, which serves as a natural initial state for the Hamming-weight constraint. Using graph-coloring as an example, we compare the performance of using XY model as a mixer that preserves the Hamming weight with the performance of adding a penalty term in the cost Hamiltonian.

  12. Optimally Stopped Optimization

    NASA Astrophysics Data System (ADS)

    Vinci, Walter; Lidar, Daniel A.

    2016-11-01

    We combine the fields of heuristic optimization and optimal stopping. We propose a strategy for benchmarking randomized optimization algorithms that minimizes the expected total cost for obtaining a good solution with an optimal number of calls to the solver. To do so, rather than letting the objective function alone define a cost to be minimized, we introduce a further cost-per-call of the algorithm. We show that this problem can be formulated using optimal stopping theory. The expected cost is a flexible figure of merit for benchmarking probabilistic solvers that can be computed when the optimal solution is not known and that avoids the biases and arbitrariness that affect other measures. The optimal stopping formulation of benchmarking directly leads to a real-time optimal-utilization strategy for probabilistic optimizers with practical impact. We apply our formulation to benchmark simulated annealing on a class of maximum-2-satisfiability (MAX2SAT) problems. We also compare the performance of a D-Wave 2X quantum annealer to the Hamze-Freitas-Selby (HFS) solver, a specialized classical heuristic algorithm designed for low-tree-width graphs. On a set of frustrated-loop instances with planted solutions defined on up to N =1098 variables, the D-Wave device is 2 orders of magnitude faster than the HFS solver, and, modulo known caveats related to suboptimal annealing times, exhibits identical scaling with problem size.

  13. A 16-bit Coherent Ising Machine for One-Dimensional Ring and Cubic Graph Problems

    NASA Astrophysics Data System (ADS)

    Takata, Kenta; Marandi, Alireza; Hamerly, Ryan; Haribara, Yoshitaka; Maruo, Daiki; Tamate, Shuhei; Sakaguchi, Hiromasa; Utsunomiya, Shoko; Yamamoto, Yoshihisa

    2016-09-01

    Many tasks in our modern life, such as planning an efficient travel, image processing and optimizing integrated circuit design, are modeled as complex combinatorial optimization problems with binary variables. Such problems can be mapped to finding a ground state of the Ising Hamiltonian, thus various physical systems have been studied to emulate and solve this Ising problem. Recently, networks of mutually injected optical oscillators, called coherent Ising machines, have been developed as promising solvers for the problem, benefiting from programmability, scalability and room temperature operation. Here, we report a 16-bit coherent Ising machine based on a network of time-division-multiplexed femtosecond degenerate optical parametric oscillators. The system experimentally gives more than 99.6% of success rates for one-dimensional Ising ring and nondeterministic polynomial-time (NP) hard instances. The experimental and numerical results indicate that gradual pumping of the network combined with multiple spectral and temporal modes of the femtosecond pulses can improve the computational performance of the Ising machine, offering a new path for tackling larger and more complex instances.

  14. The solution of the optimization problem of small energy complexes using linear programming methods

    NASA Astrophysics Data System (ADS)

    Ivanin, O. A.; Director, L. B.

    2016-11-01

    Linear programming methods were used for solving the optimization problem of schemes and operation modes of distributed generation energy complexes. Applicability conditions of simplex method, applied to energy complexes, including installations of renewable energy (solar, wind), diesel-generators and energy storage, considered. The analysis of decomposition algorithms for various schemes of energy complexes was made. The results of optimization calculations for energy complexes, operated autonomously and as a part of distribution grid, are presented.

  15. A novel non-uniform control vector parameterization approach with time grid refinement for flight level tracking optimal control problems.

    PubMed

    Liu, Ping; Li, Guodong; Liu, Xinggao; Xiao, Long; Wang, Yalin; Yang, Chunhua; Gui, Weihua

    2018-02-01

    High quality control method is essential for the implementation of aircraft autopilot system. An optimal control problem model considering the safe aerodynamic envelop is therefore established to improve the control quality of aircraft flight level tracking. A novel non-uniform control vector parameterization (CVP) method with time grid refinement is then proposed for solving the optimal control problem. By introducing the Hilbert-Huang transform (HHT) analysis, an efficient time grid refinement approach is presented and an adaptive time grid is automatically obtained. With this refinement, the proposed method needs fewer optimization parameters to achieve better control quality when compared with uniform refinement CVP method, whereas the computational cost is lower. Two well-known flight level altitude tracking problems and one minimum time cost problem are tested as illustrations and the uniform refinement control vector parameterization method is adopted as the comparative base. Numerical results show that the proposed method achieves better performances in terms of optimization accuracy and computation cost; meanwhile, the control quality is efficiently improved. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  16. Optimization of Location-Routing Problem for Cold Chain Logistics Considering Carbon Footprint.

    PubMed

    Wang, Songyi; Tao, Fengming; Shi, Yuhe

    2018-01-06

    In order to solve the optimization problem of logistics distribution system for fresh food, this paper provides a low-carbon and environmental protection point of view, based on the characteristics of perishable products, and combines with the overall optimization idea of cold chain logistics distribution network, where the green and low-carbon location-routing problem (LRP) model in cold chain logistics is developed with the minimum total costs as the objective function, which includes carbon emission costs. A hybrid genetic algorithm with heuristic rules is designed to solve the model, and an example is used to verify the effectiveness of the algorithm. Furthermore, the simulation results obtained by a practical numerical example show the applicability of the model while provide green and environmentally friendly location-distribution schemes for the cold chain logistics enterprise. Finally, carbon tax policies are introduced to analyze the impact of carbon tax on the total costs and carbon emissions, which proves that carbon tax policy can effectively reduce carbon dioxide emissions in cold chain logistics network.

  17. Optimization of Location–Routing Problem for Cold Chain Logistics Considering Carbon Footprint

    PubMed Central

    Wang, Songyi; Tao, Fengming; Shi, Yuhe

    2018-01-01

    In order to solve the optimization problem of logistics distribution system for fresh food, this paper provides a low-carbon and environmental protection point of view, based on the characteristics of perishable products, and combines with the overall optimization idea of cold chain logistics distribution network, where the green and low-carbon location–routing problem (LRP) model in cold chain logistics is developed with the minimum total costs as the objective function, which includes carbon emission costs. A hybrid genetic algorithm with heuristic rules is designed to solve the model, and an example is used to verify the effectiveness of the algorithm. Furthermore, the simulation results obtained by a practical numerical example show the applicability of the model while provide green and environmentally friendly location-distribution schemes for the cold chain logistics enterprise. Finally, carbon tax policies are introduced to analyze the impact of carbon tax on the total costs and carbon emissions, which proves that carbon tax policy can effectively reduce carbon dioxide emissions in cold chain logistics network. PMID:29316639

  18. Optimized method for manufacturing large aspheric surfaces

    NASA Astrophysics Data System (ADS)

    Zhou, Xusheng; Li, Shengyi; Dai, Yifan; Xie, Xuhui

    2007-12-01

    Aspheric optics are being used more and more widely in modern optical systems, due to their ability of correcting aberrations, enhancing image quality, enlarging the field of view and extending the range of effect, while reducing the weight and volume of the system. With optical technology development, we have more pressing requirement to large-aperture and high-precision aspheric surfaces. The original computer controlled optical surfacing (CCOS) technique cannot meet the challenge of precision and machining efficiency. This problem has been thought highly of by researchers. Aiming at the problem of original polishing process, an optimized method for manufacturing large aspheric surfaces is put forward. Subsurface damage (SSD), full aperture errors and full band of frequency errors are all in control of this method. Lesser SSD depth can be gained by using little hardness tool and small abrasive grains in grinding process. For full aperture errors control, edge effects can be controlled by using smaller tools and amendment model with material removal function. For full band of frequency errors control, low frequency errors can be corrected with the optimized material removal function, while medium-high frequency errors by using uniform removing principle. With this optimized method, the accuracy of a K9 glass paraboloid mirror can reach rms 0.055 waves (where a wave is 0.6328μm) in a short time. The results show that the optimized method can guide large aspheric surface manufacturing effectively.

  19. Are Individual Differences in Performance on Perceptual and Cognitive Optimization Problems Determined by General Intelligence?

    ERIC Educational Resources Information Center

    Burns, Nicholas R.; Lee, Michael D.; Vickers, Douglas

    2006-01-01

    Studies of human problem solving have traditionally used deterministic tasks that require the execution of a systematic series of steps to reach a rational and optimal solution. Most real-world problems, however, are characterized by uncertainty, the need to consider an enormous number of variables and possible courses of action at each stage in…

  20. Overtaking method based on sand-sifter mechanism: Why do optimistic value functions find optimal solutions in multi-armed bandit problems?

    PubMed

    Ochi, Kento; Kamiura, Moto

    2015-09-01

    A multi-armed bandit problem is a search problem on which a learning agent must select the optimal arm among multiple slot machines generating random rewards. UCB algorithm is one of the most popular methods to solve multi-armed bandit problems. It achieves logarithmic regret performance by coordinating balance between exploration and exploitation. Since UCB algorithms, researchers have empirically known that optimistic value functions exhibit good performance in multi-armed bandit problems. The terms optimistic or optimism might suggest that the value function is sufficiently larger than the sample mean of rewards. The first definition of UCB algorithm is focused on the optimization of regret, and it is not directly based on the optimism of a value function. We need to think the reason why the optimism derives good performance in multi-armed bandit problems. In the present article, we propose a new method, which is called Overtaking method, to solve multi-armed bandit problems. The value function of the proposed method is defined as an upper bound of a confidence interval with respect to an estimator of expected value of reward: the value function asymptotically approaches to the expected value of reward from the upper bound. If the value function is larger than the expected value under the asymptote, then the learning agent is almost sure to be able to obtain the optimal arm. This structure is called sand-sifter mechanism, which has no regrowth of value function of suboptimal arms. It means that the learning agent can play only the current best arm in each time step. Consequently the proposed method achieves high accuracy rate and low regret and some value functions of it can outperform UCB algorithms. This study suggests the advantage of optimism of agents in uncertain environment by one of the simplest frameworks. Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.