INDDGO: Integrated Network Decomposition & Dynamic programming for Graph Optimization

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

Groer, Christopher S; Sullivan, Blair D; Weerapurage, Dinesh P

2012-10-01

It is well-known that dynamic programming algorithms can utilize tree decompositions to provide a way to solve some \\emph{NP}-hard problems on graphs where the complexity is polynomial in the number of nodes and edges in the graph, but exponential in the width of the underlying tree decomposition. However, there has been relatively little computational work done to determine the practical utility of such dynamic programming algorithms. We have developed software to construct tree decompositions using various heuristics and have created a fast, memory-efficient dynamic programming implementation for solving maximum weighted independent set. We describe our software and the algorithms wemore » have implemented, focusing on memory saving techniques for the dynamic programming. We compare the running time and memory usage of our implementation with other techniques for solving maximum weighted independent set, including a commercial integer programming solver and a semi-definite programming solver. Our results indicate that it is possible to solve some instances where the underlying decomposition has width much larger than suggested by the literature. For certain types of problems, our dynamic programming code runs several times faster than these other methods.« less

Determining on-fault earthquake magnitude distributions from integer programming

USGS Publications Warehouse

Geist, Eric L.; Parsons, Thomas E.

2018-01-01

Earthquake magnitude distributions among faults within a fault system are determined from regional seismicity and fault slip rates using binary integer programming. A synthetic earthquake catalog (i.e., list of randomly sampled magnitudes) that spans millennia is first formed, assuming that regional seismicity follows a Gutenberg-Richter relation. Each earthquake in the synthetic catalog can occur on any fault and at any location. The objective is to minimize misfits in the target slip rate for each fault, where slip for each earthquake is scaled from its magnitude. The decision vector consists of binary variables indicating which locations are optimal among all possibilities. Uncertainty estimates in fault slip rates provide explicit upper and lower bounding constraints to the problem. An implicit constraint is that an earthquake can only be located on a fault if it is long enough to contain that earthquake. A general mixed-integer programming solver, consisting of a number of different algorithms, is used to determine the optimal decision vector. A case study is presented for the State of California, where a 4 kyr synthetic earthquake catalog is created and faults with slip ≥3 mm/yr are considered, resulting in >106  variables. The optimal magnitude distributions for each of the faults in the system span a rich diversity of shapes, ranging from characteristic to power-law distributions. 

QSPIN: A High Level Java API for Quantum Computing Experimentation

NASA Technical Reports Server (NTRS)

Barth, Tim

2017-01-01

QSPIN is a high level Java language API for experimentation in QC models used in the calculation of Ising spin glass ground states and related quadratic unconstrained binary optimization (QUBO) problems. The Java API is intended to facilitate research in advanced QC algorithms such as hybrid quantum-classical solvers, automatic selection of constraint and optimization parameters, and techniques for the correction and mitigation of model and solution errors. QSPIN includes high level solver objects tailored to the D-Wave quantum annealing architecture that implement hybrid quantum-classical algorithms [Booth et al.] for solving large problems on small quantum devices, elimination of variables via roof duality, and classical computing optimization methods such as GPU accelerated simulated annealing and tabu search for comparison. A test suite of documented NP-complete applications ranging from graph coloring, covering, and partitioning to integer programming and scheduling are provided to demonstrate current capabilities.

On solving three-dimensional open-dimension rectangular packing problems

NASA Astrophysics Data System (ADS)

Junqueira, Leonardo; Morabito, Reinaldo

2017-05-01

In this article, a recently proposed three-dimensional open-dimension rectangular packing problem is considered, in which the objective is to find a minimal volume rectangular container that packs a set of rectangular boxes. The literature has tackled small-sized instances of this problem by means of optimization solvers, position-free mixed-integer programming (MIP) formulations and piecewise linearization approaches. In this study, the problem is alternatively addressed by means of grid-based position MIP formulations, whereas still considering optimization solvers and the same piecewise linearization techniques. A comparison of the computational performance of both models is then presented, when tested with benchmark problem instances and with new instances, and it is shown that the grid-based position MIP formulation can be competitive, depending on the characteristics of the instances. The grid-based position MIP formulation is also embedded with real-world practical constraints, such as cargo stability, and results are additionally presented.

Job shop scheduling model for non-identic machine with fixed delivery time to minimize tardiness

NASA Astrophysics Data System (ADS)

Kusuma, K. K.; Maruf, A.

2016-02-01

Scheduling non-identic machines problem with low utilization characteristic and fixed delivery time are frequent in manufacture industry. This paper propose a mathematical model to minimize total tardiness for non-identic machines in job shop environment. This model will be categorized as an integer linier programming model and using branch and bound algorithm as the solver method. We will use fixed delivery time as main constraint and different processing time to process a job. The result of this proposed model shows that the utilization of production machines can be increase with minimal tardiness using fixed delivery time as constraint.

An efficient spectral crystal plasticity solver for GPU architectures

NASA Astrophysics Data System (ADS)

Malahe, Michael

2018-03-01

We present a spectral crystal plasticity (CP) solver for graphics processing unit (GPU) architectures that achieves a tenfold increase in efficiency over prior GPU solvers. The approach makes use of a database containing a spectral decomposition of CP simulations performed using a conventional iterative solver over a parameter space of crystal orientations and applied velocity gradients. The key improvements in efficiency come from reducing global memory transactions, exposing more instruction-level parallelism, reducing integer instructions and performing fast range reductions on trigonometric arguments. The scheme also makes more efficient use of memory than prior work, allowing for larger problems to be solved on a single GPU. We illustrate these improvements with a simulation of 390 million crystal grains on a consumer-grade GPU, which executes at a rate of 2.72 s per strain step.

Application specific serial arithmetic arrays

NASA Technical Reports Server (NTRS)

Winters, K.; Mathews, D.; Thompson, T.

1990-01-01

High performance systolic arrays of serial-parallel multiplier elements may be rapidly constructed for specific applications by applying hardware description language techniques to a library of full-custom CMOS building blocks. Single clock pre-charged circuits have been implemented for these arrays at clock rates in excess of 100 Mhz using economical 2-micron (minimum feature size) CMOS processes, which may be quickly configured for a variety of applications. A number of application-specific arrays are presented, including a 2-D convolver for image processing, an integer polynomial solver, and a finite-field polynomial solver.

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

DOE PAGES

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

2017-12-20

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

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

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

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

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

Distributing Earthquakes Among California's Faults: A Binary Integer Programming Approach

NASA Astrophysics Data System (ADS)

Geist, E. L.; Parsons, T.

2016-12-01

Statement of the problem is simple: given regional seismicity specified by a Gutenber-Richter (G-R) relation, how are earthquakes distributed to match observed fault-slip rates? The objective is to determine the magnitude-frequency relation on individual faults. The California statewide G-R b-value and a-value are estimated from historical seismicity, with the a-value accounting for off-fault seismicity. UCERF3 consensus slip rates are used, based on geologic and geodetic data and include estimates of coupling coefficients. The binary integer programming (BIP) problem is set up such that each earthquake from a synthetic catalog spanning millennia can occur at any location along any fault. The decision vector, therefore, consists of binary variables, with values equal to one indicating the location of each earthquake that results in an optimal match of slip rates, in an L1-norm sense. Rupture area and slip associated with each earthquake are determined from a magnitude-area scaling relation. Uncertainty bounds on the UCERF3 slip rates provide explicit minimum and maximum constraints to the BIP model, with the former more important to feasibility of the problem. There is a maximum magnitude limit associated with each fault, based on fault length, providing an implicit constraint. Solution of integer programming problems with a large number of variables (>105 in this study) has been possible only since the late 1990s. In addition to the classic branch-and-bound technique used for these problems, several other algorithms have been recently developed, including pre-solving, sifting, cutting planes, heuristics, and parallelization. An optimal solution is obtained using a state-of-the-art BIP solver for M≥6 earthquakes and California's faults with slip-rates > 1 mm/yr. Preliminary results indicate a surprising diversity of on-fault magnitude-frequency relations throughout the state.

Seismic Retrofit for Electric Power Systems

DOE PAGES

Romero, Natalia; Nozick, Linda K.; Dobson, Ian; ...

2015-05-01

Our paper develops a two-stage stochastic program and solution procedure to optimize the selection of seismic retrofit strategies to increase the resilience of electric power systems against earthquake hazards. The model explicitly considers the range of earthquake events that are possible and, for each, an approximation of the distribution of damage experienced. Furthermore, this is important because electric power systems are spatially distributed and so their performance is driven by the distribution of component damage. We also test this solution procedure against the nonlinear integer solver in LINGO 13 and apply the formulation and solution strategy to the Eastern Interconnection,more » where seismic hazard stems from the New Madrid seismic zone.« less

Pattern-set generation algorithm for the one-dimensional multiple stock sizes cutting stock problem

NASA Astrophysics Data System (ADS)

Cui, Yaodong; Cui, Yi-Ping; Zhao, Zhigang

2015-09-01

A pattern-set generation algorithm (PSG) for the one-dimensional multiple stock sizes cutting stock problem (1DMSSCSP) is presented. The solution process contains two stages. In the first stage, the PSG solves the residual problems repeatedly to generate the patterns in the pattern set, where each residual problem is solved by the column-generation approach, and each pattern is generated by solving a single large object placement problem. In the second stage, the integer linear programming model of the 1DMSSCSP is solved using a commercial solver, where only the patterns in the pattern set are considered. The computational results of benchmark instances indicate that the PSG outperforms existing heuristic algorithms and rivals the exact algorithm in solution quality.

A two-level approach to large mixed-integer programs with application to cogeneration in energy-efficient buildings

DOE PAGES

Lin, Fu; Leyffer, Sven; Munson, Todd

2016-04-12

We study a two-stage mixed-integer linear program (MILP) with more than 1 million binary variables in the second stage. We develop a two-level approach by constructing a semi-coarse model that coarsens with respect to variables and a coarse model that coarsens with respect to both variables and constraints. We coarsen binary variables by selecting a small number of prespecified on/off profiles. We aggregate constraints by partitioning them into groups and taking convex combination over each group. With an appropriate choice of coarsened profiles, the semi-coarse model is guaranteed to find a feasible solution of the original problem and hence providesmore » an upper bound on the optimal solution. We show that solving a sequence of coarse models converges to the same upper bound with proven finite steps. This is achieved by adding violated constraints to coarse models until all constraints in the semi-coarse model are satisfied. We demonstrate the effectiveness of our approach in cogeneration for buildings. Here, the coarsened models allow us to obtain good approximate solutions at a fraction of the time required by solving the original problem. Extensive numerical experiments show that the two-level approach scales to large problems that are beyond the capacity of state-of-the-art commercial MILP solvers.« less

A two-level approach to large mixed-integer programs with application to cogeneration in energy-efficient buildings

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

Lin, Fu; Leyffer, Sven; Munson, Todd

We study a two-stage mixed-integer linear program (MILP) with more than 1 million binary variables in the second stage. We develop a two-level approach by constructing a semi-coarse model that coarsens with respect to variables and a coarse model that coarsens with respect to both variables and constraints. We coarsen binary variables by selecting a small number of prespecified on/off profiles. We aggregate constraints by partitioning them into groups and taking convex combination over each group. With an appropriate choice of coarsened profiles, the semi-coarse model is guaranteed to find a feasible solution of the original problem and hence providesmore » an upper bound on the optimal solution. We show that solving a sequence of coarse models converges to the same upper bound with proven finite steps. This is achieved by adding violated constraints to coarse models until all constraints in the semi-coarse model are satisfied. We demonstrate the effectiveness of our approach in cogeneration for buildings. Here, the coarsened models allow us to obtain good approximate solutions at a fraction of the time required by solving the original problem. Extensive numerical experiments show that the two-level approach scales to large problems that are beyond the capacity of state-of-the-art commercial MILP solvers.« less

Solving Integer Programs from Dependence and Synchronization Problems

DTIC Science & Technology

1993-03-01

DEFF.NSNE Solving Integer Programs from Dependence and Synchronization Problems Jaspal Subhlok March 1993 CMU-CS-93-130 School of Computer ScienceT IC...method Is an exact and efficient way of solving integer programming problems arising in dependence and synchronization analysis of parallel programs...7/;- p Keywords: Exact dependence tesing, integer programming. parallelilzng compilers, parallel program analysis, synchronization analysis Solving

Software For Integer Programming

NASA Technical Reports Server (NTRS)

Fogle, F. R.

1992-01-01

Improved Exploratory Search Technique for Pure Integer Linear Programming Problems (IESIP) program optimizes objective function of variables subject to confining functions or constraints, using discrete optimization or integer programming. Enables rapid solution of problems up to 10 variables in size. Integer programming required for accuracy in modeling systems containing small number of components, distribution of goods, scheduling operations on machine tools, and scheduling production in general. Written in Borland's TURBO Pascal.

Vertical Launch System Loadout Planner

DTIC Science & Technology

2015-03-01

United States Navy USS United States’ Ship VBA Visual Basic for Applications VLP VLS Loadout Planner VLS Vertical Launch System...with 32 gigabytes of random access memory and eight processors, General Algebraic Modeling System (GAMS) CPLEX version 24 (GAMS, 2015) solves this...problem in ten minutes to an integer tolerance of 10%. The GAMS interpreter and CPLEX solver require 75 Megabytes of random access memory for this

Method of Characteristic (MOC) Nozzle Flowfield Solver - User’s Guide and Input Manual

DTIC Science & Technology

2013-01-01

Description: Axi or Planar calculation. Value Description Default 0.0 Planer solution 1.0 Axisymmetric solution * &INPUT: NI Date Type: Integer...angle error !... !... Set Control values !... DELTA = 1.0 !1 axi, 0 planer (Mass flux not working correctly) NI = 81...DELTA = 1.0 !1 axi, 0 planer NI = 71 !NUMBER OF RADIAL POINTS ON INFLOW PLANE (Max 99) NT = 35 !NUMBER OF

Optimal design and dispatch of a system of diesel generators, photovoltaics and batteries for remote locations

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

Scioletti, Michael S.; Newman, Alexandra M.; Goodman, Johanna K.

Renewable energy technologies, specifically, solar photovoltaic cells, combined with battery storage and diesel generators, form a hybrid system capable of independently powering remote locations, i.e., those isolated from larger grids. If sized correctly, hybrid systems reduce fuel consumption compared to diesel generator-only alternatives. We present an optimization model for establishing a hybrid power design and dispatch strategy for remote locations, such as a military forward operating base, that models the acquisition of different power technologies as integer variables and their operation using nonlinear expressions. Our cost-minimizing, nonconvex, mixed-integer, nonlinear program contains a detailed battery model. Due to its complexities, wemore » present linearizations, which include exact and convex under-estimation techniques, and a heuristic, which determines an initial feasible solution to serve as a “warm start” for the solver. We determine, in a few hours at most, solutions within 5% of optimality for a candidate set of technologies; these solutions closely resemble those from the nonlinear model. Lastly, our instances contain real data spanning a yearly horizon at hour fidelity and demonstrate that a hybrid system could reduce fuel consumption by as much as 50% compared to a generator-only solution.« less

Optimal design and dispatch of a system of diesel generators, photovoltaics and batteries for remote locations

DOE PAGES

Scioletti, Michael S.; Newman, Alexandra M.; Goodman, Johanna K.; ...

2017-05-08

Renewable energy technologies, specifically, solar photovoltaic cells, combined with battery storage and diesel generators, form a hybrid system capable of independently powering remote locations, i.e., those isolated from larger grids. If sized correctly, hybrid systems reduce fuel consumption compared to diesel generator-only alternatives. We present an optimization model for establishing a hybrid power design and dispatch strategy for remote locations, such as a military forward operating base, that models the acquisition of different power technologies as integer variables and their operation using nonlinear expressions. Our cost-minimizing, nonconvex, mixed-integer, nonlinear program contains a detailed battery model. Due to its complexities, wemore » present linearizations, which include exact and convex under-estimation techniques, and a heuristic, which determines an initial feasible solution to serve as a “warm start” for the solver. We determine, in a few hours at most, solutions within 5% of optimality for a candidate set of technologies; these solutions closely resemble those from the nonlinear model. Lastly, our instances contain real data spanning a yearly horizon at hour fidelity and demonstrate that a hybrid system could reduce fuel consumption by as much as 50% compared to a generator-only solution.« less

IESIP - AN IMPROVED EXPLORATORY SEARCH TECHNIQUE FOR PURE INTEGER LINEAR PROGRAMMING PROBLEMS

NASA Technical Reports Server (NTRS)

Fogle, F. R.

1994-01-01

IESIP, an Improved Exploratory Search Technique for Pure Integer Linear Programming Problems, addresses the problem of optimizing an objective function of one or more variables subject to a set of confining functions or constraints by a method called discrete optimization or integer programming. Integer programming is based on a specific form of the general linear programming problem in which all variables in the objective function and all variables in the constraints are integers. While more difficult, integer programming is required for accuracy when modeling systems with small numbers of components such as the distribution of goods, machine scheduling, and production scheduling. IESIP establishes a new methodology for solving pure integer programming problems by utilizing a modified version of the univariate exploratory move developed by Robert Hooke and T.A. Jeeves. IESIP also takes some of its technique from the greedy procedure and the idea of unit neighborhoods. A rounding scheme uses the continuous solution found by traditional methods (simplex or other suitable technique) and creates a feasible integer starting point. The Hook and Jeeves exploratory search is modified to accommodate integers and constraints and is then employed to determine an optimal integer solution from the feasible starting solution. The user-friendly IESIP allows for rapid solution of problems up to 10 variables in size (limited by DOS allocation). Sample problems compare IESIP solutions with the traditional branch-and-bound approach. IESIP is written in Borland's TURBO Pascal for IBM PC series computers and compatibles running DOS. Source code and an executable are provided. The main memory requirement for execution is 25K. This program is available on a 5.25 inch 360K MS DOS format diskette. IESIP was developed in 1990. IBM is a trademark of International Business Machines. TURBO Pascal is registered by Borland International.

Local search heuristic for the discrete leader-follower problem with multiple follower objectives

NASA Astrophysics Data System (ADS)

Kochetov, Yury; Alekseeva, Ekaterina; Mezmaz, Mohand

2016-10-01

We study a discrete bilevel problem, called as well as leader-follower problem, with multiple objectives at the lower level. It is assumed that constraints at the upper level can include variables of both levels. For such ill-posed problem we define feasible and optimal solutions for pessimistic case. A central point of this work is a two stage method to get a feasible solution under the pessimistic case, given a leader decision. The target of the first stage is a follower solution that violates the leader constraints. The target of the second stage is a pessimistic feasible solution. Each stage calls a heuristic and a solver for a series of particular mixed integer programs. The method is integrated inside a local search based heuristic that is designed to find near-optimal leader solutions.

Improving Transportation Services for the University of the Thai Chamber of Commerce: A Case Study on Solving the Mixed-Fleet Vehicle Routing Problem with Split Deliveries

NASA Astrophysics Data System (ADS)

Suthikarnnarunai, N.; Olinick, E.

2009-01-01

We present a case study on the application of techniques for solving the Vehicle Routing Problem (VRP) to improve the transportation service provided by the University of The Thai Chamber of Commerce to its staff. The problem is modeled as VRP with time windows, split deliveries, and a mixed fleet. An exact algorithm and a heuristic solution procedure are developed to solve the problem and implemented in the AMPL modeling language and CPLEX Integer Programming solver. Empirical results indicate that the heuristic can find relatively good solutions in a small fraction of the time required by the exact method. We also perform sensitivity analysis and find that a savings in outsourcing cost can be achieved with a small increase in vehicle capacity.

Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

NASA Astrophysics Data System (ADS)

Owolabi, Kolade M.

2018-03-01

In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.

Exploiting Identical Generators in Unit Commitment

DOE PAGES

Knueven, Ben; Ostrowski, Jim; Watson, Jean -Paul

2017-12-14

Here, we present sufficient conditions under which thermal generators can be aggregated in mixed-integer linear programming (MILP) formulations of the unit commitment (UC) problem, while maintaining feasibility and optimality for the original disaggregated problem. Aggregating thermal generators with identical characteristics (e.g., minimum/maximum power output, minimum up/down-time, and cost curves) into a single unit reduces redundancy in the search space induced by both exact symmetry (permutations of generator schedules) and certain classes of mutually non-dominated solutions. We study the impact of aggregation on two large-scale UC instances, one from the academic literature and another based on real-world operator data. Our computationalmore » tests demonstrate that when present, identical generators can negatively affect the performance of modern MILP solvers on UC formulations. Further, we show that our reformation of the UC MILP through aggregation is an effective method for mitigating this source of computational difficulty.« less

Exploiting Identical Generators in Unit Commitment

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

Knueven, Ben; Ostrowski, Jim; Watson, Jean -Paul

Here, we present sufficient conditions under which thermal generators can be aggregated in mixed-integer linear programming (MILP) formulations of the unit commitment (UC) problem, while maintaining feasibility and optimality for the original disaggregated problem. Aggregating thermal generators with identical characteristics (e.g., minimum/maximum power output, minimum up/down-time, and cost curves) into a single unit reduces redundancy in the search space induced by both exact symmetry (permutations of generator schedules) and certain classes of mutually non-dominated solutions. We study the impact of aggregation on two large-scale UC instances, one from the academic literature and another based on real-world operator data. Our computationalmore » tests demonstrate that when present, identical generators can negatively affect the performance of modern MILP solvers on UC formulations. Further, we show that our reformation of the UC MILP through aggregation is an effective method for mitigating this source of computational difficulty.« less

MILP model for integrated balancing and sequencing mixed-model two-sided assembly line with variable launching interval and assignment restrictions

NASA Astrophysics Data System (ADS)

Azmi, N. I. L. Mohd; Ahmad, R.; Zainuddin, Z. M.

2017-09-01

This research explores the Mixed-Model Two-Sided Assembly Line (MMTSAL). There are two interrelated problems in MMTSAL which are line balancing and model sequencing. In previous studies, many researchers considered these problems separately and only few studied them simultaneously for one-sided line. However in this study, these two problems are solved simultaneously to obtain more efficient solution. The Mixed Integer Linear Programming (MILP) model with objectives of minimizing total utility work and idle time is generated by considering variable launching interval and assignment restriction constraint. The problem is analysed using small-size test cases to validate the integrated model. Throughout this paper, numerical experiment was conducted by using General Algebraic Modelling System (GAMS) with the solver CPLEX. Experimental results indicate that integrating the problems of model sequencing and line balancing help to minimise the proposed objectives function.

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

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

Jeff Linderoth

2011-11-06

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

Item Pool Construction Using Mixed Integer Quadratic Programming (MIQP). GMAC® Research Report RR-14-01

ERIC Educational Resources Information Center

Han, Kyung T.; Rudner, Lawrence M.

2014-01-01

This study uses mixed integer quadratic programming (MIQP) to construct multiple highly equivalent item pools simultaneously, and compares the results from mixed integer programming (MIP). Three different MIP/MIQP models were implemented and evaluated using real CAT item pool data with 23 different content areas and a goal of equal information…

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

Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin David.

When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modularmore » In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.« less

Reduced-Size Integer Linear Programming Models for String Selection Problems: Application to the Farthest String Problem.

PubMed

Zörnig, Peter

2015-08-01

We present integer programming models for some variants of the farthest string problem. The number of variables and constraints is substantially less than that of the integer linear programming models known in the literature. Moreover, the solution of the linear programming-relaxation contains only a small proportion of noninteger values, which considerably simplifies the rounding process. Numerical tests have shown excellent results, especially when a small set of long sequences is given.

Optimal Diet Planning for Eczema Patient Using Integer Programming

NASA Astrophysics Data System (ADS)

Zhen Sheng, Low; Sufahani, Suliadi

2018-04-01

Human diet planning is conducted by choosing appropriate food items that fulfill the nutritional requirements into the diet formulation. This paper discusses the application of integer programming to build the mathematical model of diet planning for eczema patients. The model developed is used to solve the diet problem of eczema patients from young age group. The integer programming is a scientific approach to select suitable food items, which seeks to minimize the costs, under conditions of meeting desired nutrient quantities, avoiding food allergens and getting certain foods into the diet that brings relief to the eczema conditions. This paper illustrates that the integer programming approach able to produce the optimal and feasible solution to deal with the diet problem of eczema patient.

Co-optimizing Generation and Transmission Expansion with Wind Power in Large-Scale Power Grids Implementation in the US Eastern Interconnection

DOE PAGES

You, Shutang; Hadley, Stanton W.; Shankar, Mallikarjun; ...

2016-01-12

This paper studies the generation and transmission expansion co-optimization problem with a high wind power penetration rate in the US Eastern Interconnection (EI) power grid. In this paper, the generation and transmission expansion problem for the EI system is modeled as a mixed-integer programming (MIP) problem. Our paper also analyzed a time series generation method to capture the variation and correlation of both load and wind power across regions. The obtained series can be easily introduced into the expansion planning problem and then solved through existing MIP solvers. Simulation results show that the proposed planning model and series generation methodmore » can improve the expansion result significantly through modeling more detailed information of wind and load variation among regions in the US EI system. Moreover, the improved expansion plan that combines generation and transmission will aid system planners and policy makers to maximize the social welfare in large-scale power grids.« less

Performance of a cavity-method-based algorithm for the prize-collecting Steiner tree problem on graphs

NASA Astrophysics Data System (ADS)

Biazzo, Indaco; Braunstein, Alfredo; Zecchina, Riccardo

2012-08-01

We study the behavior of an algorithm derived from the cavity method for the prize-collecting steiner tree (PCST) problem on graphs. The algorithm is based on the zero temperature limit of the cavity equations and as such is formally simple (a fixed point equation resolved by iteration) and distributed (parallelizable). We provide a detailed comparison with state-of-the-art algorithms on a wide range of existing benchmarks, networks, and random graphs. Specifically, we consider an enhanced derivative of the Goemans-Williamson heuristics and the dhea solver, a branch and cut integer linear programming based approach. The comparison shows that the cavity algorithm outperforms the two algorithms in most large instances both in running time and quality of the solution. Finally we prove a few optimality properties of the solutions provided by our algorithm, including optimality under the two postprocessing procedures defined in the Goemans-Williamson derivative and global optimality in some limit cases.

Mathematical model and metaheuristics for simultaneous balancing and sequencing of a robotic mixed-model assembly line

NASA Astrophysics Data System (ADS)

Li, Zixiang; Janardhanan, Mukund Nilakantan; Tang, Qiuhua; Nielsen, Peter

2018-05-01

This article presents the first method to simultaneously balance and sequence robotic mixed-model assembly lines (RMALB/S), which involves three sub-problems: task assignment, model sequencing and robot allocation. A new mixed-integer programming model is developed to minimize makespan and, using CPLEX solver, small-size problems are solved for optimality. Two metaheuristics, the restarted simulated annealing algorithm and co-evolutionary algorithm, are developed and improved to address this NP-hard problem. The restarted simulated annealing method replaces the current temperature with a new temperature to restart the search process. The co-evolutionary method uses a restart mechanism to generate a new population by modifying several vectors simultaneously. The proposed algorithms are tested on a set of benchmark problems and compared with five other high-performing metaheuristics. The proposed algorithms outperform their original editions and the benchmarked methods. The proposed algorithms are able to solve the balancing and sequencing problem of a robotic mixed-model assembly line effectively and efficiently.

Generating subtour elimination constraints for the TSP from pure integer solutions.

PubMed

Pferschy, Ulrich; Staněk, Rostislav

2017-01-01

The traveling salesman problem ( TSP ) is one of the most prominent combinatorial optimization problems. Given a complete graph [Formula: see text] and non-negative distances d for every edge, the TSP asks for a shortest tour through all vertices with respect to the distances d. The method of choice for solving the TSP to optimality is a branch and cut approach . Usually the integrality constraints are relaxed first and all separation processes to identify violated inequalities are done on fractional solutions . In our approach we try to exploit the impressive performance of current ILP-solvers and work only with integer solutions without ever interfering with fractional solutions. We stick to a very simple ILP-model and relax the subtour elimination constraints only. The resulting problem is solved to integer optimality, violated constraints (which are trivial to find) are added and the process is repeated until a feasible solution is found. In order to speed up the algorithm we pursue several attempts to find as many relevant subtours as possible. These attempts are based on the clustering of vertices with additional insights gained from empirical observations and random graph theory. Computational results are performed on test instances taken from the TSPLIB95 and on random Euclidean graphs .

Fuzzy multiobjective models for optimal operation of a hydropower system

NASA Astrophysics Data System (ADS)

Teegavarapu, Ramesh S. V.; Ferreira, André R.; Simonovic, Slobodan P.

2013-06-01

Optimal operation models for a hydropower system using new fuzzy multiobjective mathematical programming models are developed and evaluated in this study. The models use (i) mixed integer nonlinear programming (MINLP) with binary variables and (ii) integrate a new turbine unit commitment formulation along with water quality constraints used for evaluation of reservoir downstream impairment. Reardon method used in solution of genetic algorithm optimization problems forms the basis for development of a new fuzzy multiobjective hydropower system optimization model with creation of Reardon type fuzzy membership functions. The models are applied to a real-life hydropower reservoir system in Brazil. Genetic Algorithms (GAs) are used to (i) solve the optimization formulations to avoid computational intractability and combinatorial problems associated with binary variables in unit commitment, (ii) efficiently address Reardon method formulations, and (iii) deal with local optimal solutions obtained from the use of traditional gradient-based solvers. Decision maker's preferences are incorporated within fuzzy mathematical programming formulations to obtain compromise operating rules for a multiobjective reservoir operation problem dominated by conflicting goals of energy production, water quality and conservation releases. Results provide insight into compromise operation rules obtained using the new Reardon fuzzy multiobjective optimization framework and confirm its applicability to a variety of multiobjective water resources problems.

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.

An Improved Multi-Objective Programming with Augmented ε-Constraint Method for Hazardous Waste Location-Routing Problems

PubMed Central

Yu, Hao; Solvang, Wei Deng

2016-01-01

Hazardous waste location-routing problems are of importance due to the potential risk for nearby residents and the environment. In this paper, an improved mathematical formulation is developed based upon a multi-objective mixed integer programming approach. The model aims at assisting decision makers in selecting locations for different facilities including treatment plants, recycling plants and disposal sites, providing appropriate technologies for hazardous waste treatment, and routing transportation. In the model, two critical factors are taken into account: system operating costs and risk imposed on local residents, and a compensation factor is introduced to the risk objective function in order to account for the fact that the risk level imposed by one type of hazardous waste or treatment technology may significantly vary from that of other types. Besides, the policy instruments for promoting waste recycling are considered, and their influence on the costs and risk of hazardous waste management is also discussed. The model is coded and calculated in Lingo optimization solver, and the augmented ε-constraint method is employed to generate the Pareto optimal curve of the multi-objective optimization problem. The trade-off between different objectives is illustrated in the numerical experiment. PMID:27258293

An Improved Multi-Objective Programming with Augmented ε-Constraint Method for Hazardous Waste Location-Routing Problems.

PubMed

Yu, Hao; Solvang, Wei Deng

2016-05-31

Hazardous waste location-routing problems are of importance due to the potential risk for nearby residents and the environment. In this paper, an improved mathematical formulation is developed based upon a multi-objective mixed integer programming approach. The model aims at assisting decision makers in selecting locations for different facilities including treatment plants, recycling plants and disposal sites, providing appropriate technologies for hazardous waste treatment, and routing transportation. In the model, two critical factors are taken into account: system operating costs and risk imposed on local residents, and a compensation factor is introduced to the risk objective function in order to account for the fact that the risk level imposed by one type of hazardous waste or treatment technology may significantly vary from that of other types. Besides, the policy instruments for promoting waste recycling are considered, and their influence on the costs and risk of hazardous waste management is also discussed. The model is coded and calculated in Lingo optimization solver, and the augmented ε-constraint method is employed to generate the Pareto optimal curve of the multi-objective optimization problem. The trade-off between different objectives is illustrated in the numerical experiment.

The use of integer programming to select bulls across breeding companies with volume price discounts.

PubMed

McConnel, M B; Galligan, D T

2004-10-01

Optimization programs are currently used to aid in the selection of bulls to be used in herd breeding programs. While these programs offer a systematic approach to the problem of semen selection, they ignore the impact of volume discounts. Volume discounts are discounts that vary depending on the number of straws purchased. The dynamic nature of volume discounts means that, in order to be adequately accounted for, they must be considered in the optimization routine. Failing to do this creates a missed economic opportunity because the potential benefits of optimally selecting and combining breeding company discount opportunities are not captured. To address these issues, an integer program was created which used binary decision variables to incorporate the effects of quantity discounts into the optimization program. A consistent set of trait criteria was used to select a group of bulls from 3 sample breeding companies. Three different selection programs were used to select the bulls, 2 traditional methods and the integer method. After the discounts were applied using each method, the integer program resulted in the lowest cost portfolio of bulls. A sensitivity analysis showed that the integer program also resulted in a low cost portfolio when the genetic trait goals were changed to be more or less stringent. In the sample application, a net benefit of the new approach over the traditional approaches was a 12.3 to 20.0% savings in semen cost.

Mathematical programming (MP) model to determine optimal transportation infrastructure for geologic CO2 storage in the Illinois basin

NASA Astrophysics Data System (ADS)

Rehmer, Donald E.

Analysis of results from a mathematical programming model were examined to 1) determine the least cost options for infrastructure development of geologic storage of CO2 in the Illinois Basin, and 2) perform an analysis of a number of CO2 emission tax and oil price scenarios in order to implement development of the least-cost pipeline networks for distribution of CO2. The model, using mixed integer programming, tested the hypothesis of whether viable EOR sequestration sites can serve as nodal points or hubs to expand the CO2 delivery infrastructure to more distal locations from the emissions sources. This is in contrast to previous model results based on a point-to- point model having direct pipeline segments from each CO2 capture site to each storage sink. There is literature on the spoke and hub problem that relates to airline scheduling as well as maritime shipping. A large-scale ship assignment problem that utilized integer linear programming was run on Excel Solver and described by Mourao et al., (2001). Other literature indicates that aircraft assignment in spoke and hub routes can also be achieved using integer linear programming (Daskin and Panayotopoulos, 1989; Hane et al., 1995). The distribution concept is basically the reverse of the "tree and branch" type (Rothfarb et al., 1970) gathering systems for oil and natural gas that industry has been developing for decades. Model results indicate that the inclusion of hubs as variables in the model yields lower transportation costs for geologic carbon dioxide storage over previous models of point-to-point infrastructure geometries. Tabular results and GIS maps of the selected scenarios illustrate that EOR sites can serve as nodal points or hubs for distribution of CO2 to distal oil field locations as well as deeper saline reservoirs. Revenue amounts and capture percentages both show an improvement over solutions when the hubs are not allowed to come into the solution. Other results indicate that geologic storage of CO2 into saline aquifers does not come into solutions selected by the model until the CO 2 emissions tax approaches 50/tonne. CO2 capture and storage begins to occur when the oil price is above 24.42 a barrel based on the constraints of the model. The annual storage capacity of the basin is nearly maximized when the net price of oil is as low as 40 per barrel and the CO2 emission tax is 60/tonne. The results from every subsequent scenario that was examined by this study demonstrate that EOR utilizing anthropogenically captured CO2 will earn net revenue, and thus represents an economically viable option for CO2 storage in the Illinois Basin.

A mixed integer program to model spatial wildfire behavior and suppression placement decisions

Treesearch

Erin J. Belval; Yu Wei; Michael Bevers

2015-01-01

Wildfire suppression combines multiple objectives and dynamic fire behavior to form a complex problem for decision makers. This paper presents a mixed integer program designed to explore integrating spatial fire behavior and suppression placement decisions into a mathematical programming framework. Fire behavior and suppression placement decisions are modeled using...

An Integer Programming Model for Multi-Echelon Supply Chain Decision Problem Considering Inventories

NASA Astrophysics Data System (ADS)

Harahap, Amin; Mawengkang, Herman; Siswadi; Effendi, Syahril

2018-01-01

In this paper we address a problem that is of significance to the industry, namely the optimal decision of a multi-echelon supply chain and the associated inventory systems. By using the guaranteed service approach to model the multi-echelon inventory system, we develop a mixed integer; programming model to simultaneously optimize the transportation, inventory and network structure of a multi-echelon supply chain. To solve the model we develop a direct search approach using a strategy of releasing nonbasic variables from their bounds, combined with the “active constraint” method. This strategy is used to force the appropriate non-integer basic variables to move to their neighbourhood integer points.

An Improved Search Approach for Solving Non-Convex Mixed-Integer Non Linear Programming Problems

NASA Astrophysics Data System (ADS)

Sitopu, Joni Wilson; Mawengkang, Herman; Syafitri Lubis, Riri

2018-01-01

The nonlinear mathematical programming problem addressed in this paper has a structure characterized by a subset of variables restricted to assume discrete values, which are linear and separable from the continuous variables. The strategy of releasing nonbasic variables from their bounds, combined with the “active constraint” method, has been developed. This strategy is used to force the appropriate non-integer basic variables to move to their neighbourhood integer points. Successful implementation of these algorithms was achieved on various test problems.

A Structural Weight Estimation Program (SWEEP) for Aircraft. Volume 11 - Flexible Airloads Stand-Alone Program

DTIC Science & Technology

1974-06-01

stiffness, lb-in. I Integer used to designate wing strip number 2 I Airplanw pitching moment of inertia, slug ft 2 I Airplane yawing moment of inertia...slug ft J Integer used to designated wing-loading distribution, i.e., J-l, loading due to angle of attack J=2> loading due to flap deflection J-3...moment at intersection of load reference line and body interface station (for vertical tail), in.-lb Integer used to designate type of wing airload

Extending ALE3D, an Arbitrarily Connected hexahedral 3D Code, to Very Large Problem Size (U)

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

Nichols, A L

2010-12-15

As the number of compute units increases on the ASC computers, the prospect of running previously unimaginably large problems is becoming a reality. In an arbitrarily connected 3D finite element code, like ALE3D, one must provide a unique identification number for every node, element, face, and edge. This is required for a number of reasons, including defining the global connectivity array required for domain decomposition, identifying appropriate communication patterns after domain decomposition, and determining the appropriate load locations for implicit solvers, for example. In most codes, the unique identification number is defined as a 32-bit integer. Thus the maximum valuemore » available is 231, or roughly 2.1 billion. For a 3D geometry consisting of arbitrarily connected hexahedral elements, there are approximately 3 faces for every element, and 3 edges for every node. Since the nodes and faces need id numbers, using 32-bit integers puts a hard limit on the number of elements in a problem at roughly 700 million. The first solution to this problem would be to replace 32-bit signed integers with 32-bit unsigned integers. This would increase the maximum size of a problem by a factor of 2. This provides some head room, but almost certainly not one that will last long. Another solution would be to replace all 32-bit int declarations with 64-bit long long declarations. (long is either a 32-bit or a 64-bit integer, depending on the OS). The problem with this approach is that there are only a few arrays that actually need to extended size, and thus this would increase the size of the problem unnecessarily. In a future computing environment where CPUs are abundant but memory relatively scarce, this is probably the wrong approach. Based on these considerations, we have chosen to replace only the global identifiers with the appropriate 64-bit integer. The problem with this approach is finding all the places where data that is specified as a 32-bit integer needs to be replaced with the 64-bit integer. that need to be replaced. In the rest of this paper we describe the techniques used to facilitate this transformation, issues raised, and issues still to be addressed. This poster will describe the reasons, methods, issues associated with extending the ALE3D code to run problems larger than 700 million elements.« less

Multiple object tracking using the shortest path faster association algorithm.

PubMed

Xi, Zhenghao; Liu, Heping; Liu, Huaping; Yang, Bin

2014-01-01

To solve the persistently multiple object tracking in cluttered environments, this paper presents a novel tracking association approach based on the shortest path faster algorithm. First, the multiple object tracking is formulated as an integer programming problem of the flow network. Then we relax the integer programming to a standard linear programming problem. Therefore, the global optimum can be quickly obtained using the shortest path faster algorithm. The proposed method avoids the difficulties of integer programming, and it has a lower worst-case complexity than competing methods but better robustness and tracking accuracy in complex environments. Simulation results show that the proposed algorithm takes less time than other state-of-the-art methods and can operate in real time.

Multiple Object Tracking Using the Shortest Path Faster Association Algorithm

PubMed Central

Liu, Heping; Liu, Huaping; Yang, Bin

2014-01-01

To solve the persistently multiple object tracking in cluttered environments, this paper presents a novel tracking association approach based on the shortest path faster algorithm. First, the multiple object tracking is formulated as an integer programming problem of the flow network. Then we relax the integer programming to a standard linear programming problem. Therefore, the global optimum can be quickly obtained using the shortest path faster algorithm. The proposed method avoids the difficulties of integer programming, and it has a lower worst-case complexity than competing methods but better robustness and tracking accuracy in complex environments. Simulation results show that the proposed algorithm takes less time than other state-of-the-art methods and can operate in real time. PMID:25215322

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.

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

Collins, Benjamin S.

The Futility package contains the following: 1) Definition of the size of integers and real numbers; 2) A generic Unit test harness; 3) Definitions for some basic extensions to the Fortran language: arbitrary length strings, a parameter list construct, exception handlers, command line processor, timers; 4) Geometry definitions: point, line, plane, box, cylinder, polyhedron; 5) File wrapper functions: standard Fortran input/output files, Fortran binary files, HDF5 files; 6) Parallel wrapper functions: MPI, and Open MP abstraction layers, partitioning algorithms; 7) Math utilities: BLAS, Matrix and Vector definitions, Linear Solver methods and wrappers for other TPLs (PETSC, MKL, etc), preconditioner classes;more » 8) Misc: random number generator, water saturation properties, sorting algorithms.« less

Dynamic UNITY

DTIC Science & Technology

2002-01-01

UNITY program that implements exactly the same algorithm as Specification 1.1. The correctness of this program is proven in amanner sim- 4 program...chapter, we introduce the Dynamic UNITY formalism, which allows us to reason about algorithms and protocols in which the sets of participating processes...implements Euclid’s algorithm for calculating the greatest common divisor (GCD) of two integers; it repeat- edly reads an integer message from each of its

Stochastic Semidefinite Programming: Applications and Algorithms

DTIC Science & Technology

2012-03-03

doi: 2011/09/07 13:38:21 13 TOTAL: 1 Number of Papers published in non peer-reviewed journals: Baha M. Alzalg and K. A. Ariyawansa, Stochastic...symmetric programming over integers. International Conference on Scientific Computing, Las Vegas, Nevada, July 18--21, 2011. Baha M. Alzalg. On recent...Proceeding publications (other than abstracts): PaperReceived Baha M. Alzalg, K. A. Ariyawansa. Stochastic mixed integer second-order cone programming

A Treatment of Computational Precision, Number Representation, and Large Integers in an Introductory Fortran Course

ERIC Educational Resources Information Center

Richardson, William H., Jr.

2006-01-01

Computational precision is sometimes given short shrift in a first programming course. Treating this topic requires discussing integer and floating-point number representations and inaccuracies that may result from their use. An example of a moderately simple programming problem from elementary statistics was examined. It forced students to…

An Integer Programming Approach to School District Financial Management.

ERIC Educational Resources Information Center

Dembowski, Frederick L.

Because of the nature of school district cash flows, there are opportunities for investing surplus cash and the necessity to borrow cash in deficit periods. The term structure of interest rates makes the manual determination of the optimal financial package impossible. In this research, an integer programming model of this cash management process…

Currency Arbitrage Detection Using a Binary Integer Programming Model

ERIC Educational Resources Information Center

Soon, Wanmei; Ye, Heng-Qing

2011-01-01

In this article, we examine the use of a new binary integer programming (BIP) model to detect arbitrage opportunities in currency exchanges. This model showcases an excellent application of mathematics to the real world. The concepts involved are easily accessible to undergraduate students with basic knowledge in Operations Research. Through this…

Puerto Rico water resources planning model program description

USGS Publications Warehouse

Moody, D.W.; Maddock, Thomas; Karlinger, M.R.; Lloyd, J.J.

1973-01-01

Because the use of the Mathematical Programming System -Extended (MPSX) to solve large linear and mixed integer programs requires the preparation of many input data cards, a matrix generator program to produce the MPSX input data from a much more limited set of data may expedite the use of the mixed integer programming optimization technique. The Model Definition and Control Program (MODCQP) is intended to assist a planner in preparing MPSX input data for the Puerto Rico Water Resources Planning Model. The model utilizes a mixed-integer mathematical program to identify a minimum present cost set of water resources projects (diversions, reservoirs, ground-water fields, desalinization plants, water treatment plants, and inter-basin transfers of water) which will meet a set of future water demands and to determine their sequence of construction. While MODCOP was specifically written to generate MPSX input data for the planning model described in this report, the program can be easily modified to reflect changes in the model's mathematical structure.

An efficient mixed-precision, hybrid CPU-GPU implementation of a nonlinearly implicit one-dimensional particle-in-cell algorithm

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

Chen, Guangye; Chacon, Luis; Barnes, Daniel C

2012-01-01

Recently, a fully implicit, energy- and charge-conserving particle-in-cell method has been developed for multi-scale, full-f kinetic simulations [G. Chen, et al., J. Comput. Phys. 230, 18 (2011)]. The method employs a Jacobian-free Newton-Krylov (JFNK) solver and is capable of using very large timesteps without loss of numerical stability or accuracy. A fundamental feature of the method is the segregation of particle orbit integrations from the field solver, while remaining fully self-consistent. This provides great flexibility, and dramatically improves the solver efficiency by reducing the degrees of freedom of the associated nonlinear system. However, it requires a particle push per nonlinearmore » residual evaluation, which makes the particle push the most time-consuming operation in the algorithm. This paper describes a very efficient mixed-precision, hybrid CPU-GPU implementation of the implicit PIC algorithm. The JFNK solver is kept on the CPU (in double precision), while the inherent data parallelism of the particle mover is exploited by implementing it in single-precision on a graphics processing unit (GPU) using CUDA. Performance-oriented optimizations, with the aid of an analytical performance model, the roofline model, are employed. Despite being highly dynamic, the adaptive, charge-conserving particle mover algorithm achieves up to 300 400 GOp/s (including single-precision floating-point, integer, and logic operations) on a Nvidia GeForce GTX580, corresponding to 20 25% absolute GPU efficiency (against the peak theoretical performance) and 50-70% intrinsic efficiency (against the algorithm s maximum operational throughput, which neglects all latencies). This is about 200-300 times faster than an equivalent serial CPU implementation. When the single-precision GPU particle mover is combined with a double-precision CPU JFNK field solver, overall performance gains 100 vs. the double-precision CPU-only serial version are obtained, with no apparent loss of robustness or accuracy when applied to a challenging long-time scale ion acoustic wave simulation.« less

Dynamic analysis for solid waste management systems: an inexact multistage integer programming approach.

PubMed

Li, Yongping; Huang, Guohe

2009-03-01

In this study, a dynamic analysis approach based on an inexact multistage integer programming (IMIP) model is developed for supporting municipal solid waste (MSW) management under uncertainty. Techniques of interval-parameter programming and multistage stochastic programming are incorporated within an integer-programming framework. The developed IMIP can deal with uncertainties expressed as probability distributions and interval numbers, and can reflect the dynamics in terms of decisions for waste-flow allocation and facility-capacity expansion over a multistage context. Moreover, the IMIP can be used for analyzing various policy scenarios that are associated with different levels of economic consequences. The developed method is applied to a case study of long-term waste-management planning. The results indicate that reasonable solutions have been generated for binary and continuous variables. They can help generate desired decisions of system-capacity expansion and waste-flow allocation with a minimized system cost and maximized system reliability.

Airborne Tactical Crossload Planner

DTIC Science & Technology

2017-12-01

set out in the Airborne Standard Operating Procedure (ASOP). 14. SUBJECT TERMS crossload, airborne, optimization, integer linear programming ...they land to their respective sub-mission locations. In this thesis, we formulate and implement an integer linear program called the Tactical...to meet any desired crossload objectives. xiv We demonstrate TCP with two real-world tactical problems from recent airborne operations: one by the

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.

Logic integer programming models for signaling networks.

PubMed

Haus, Utz-Uwe; Niermann, Kathrin; Truemper, Klaus; Weismantel, Robert

2009-05-01

We propose a static and a dynamic approach to model biological signaling networks, and show how each can be used to answer relevant biological questions. For this, we use the two different mathematical tools of Propositional Logic and Integer Programming. The power of discrete mathematics for handling qualitative as well as quantitative data has so far not been exploited in molecular biology, which is mostly driven by experimental research, relying on first-order or statistical models. The arising logic statements and integer programs are analyzed and can be solved with standard software. For a restricted class of problems the logic models reduce to a polynomial-time solvable satisfiability algorithm. Additionally, a more dynamic model enables enumeration of possible time resolutions in poly-logarithmic time. Computational experiments are included.

A logic-based method for integer programming

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

Hooker, J.; Natraj, N.R.

1994-12-31

We propose a logic-based approach to integer programming that replaces traditional branch-and-cut techniques with logical analogs. Integer variables are regarded as atomic propositions. The constraints give rise to logical formulas that are analogous to separating cuts. No continuous relaxation is used. Rather, the cuts are selected so that they can be easily solved as a discrete relaxation. (In fact, defining a relaxation and generating cuts are best seen as the same problem.) We experiment with relaxations that have a k-tree structure and can be solved by nonserial dynamic programming. We also present logic-based analogs of facet-defining cuts, Chv{acute a}tal rank,more » etc. We conclude with some preliminary computational results.« less

Determination of optimum values for maximizing the profit in bread production: Daily bakery Sdn Bhd

NASA Astrophysics Data System (ADS)

Muda, Nora; Sim, Raymond

2015-02-01

An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. An ILP has many applications in industrial production, including job-shop modelling. A possible objective is to maximize the total production, without exceeding the available resources. In some cases, this can be expressed in terms of a linear program, but variables must be constrained to be integer. It concerned with the optimization of a linear function while satisfying a set of linear equality and inequality constraints and restrictions. It has been used to solve optimization problem in many industries area such as banking, nutrition, agriculture, and bakery and so on. The main purpose of this study is to formulate the best combination of all ingredients in producing different type of bread in Daily Bakery in order to gain maximum profit. This study also focuses on the sensitivity analysis due to changing of the profit and the cost of each ingredient. The optimum result obtained from QM software is RM 65,377.29 per day. This study will be benefited for Daily Bakery and also other similar industries. By formulating a combination of all ingredients make up, they can easily know their total profit in producing bread everyday.

Convex relaxations for gas expansion planning

DOE PAGES

Borraz-Sanchez, Conrado; Bent, Russell Whitford; Backhaus, Scott N.; ...

2016-01-01

Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Here, given the non-convex nature of gas transmission constraints, global optimality and infeasibility guarantees can only be offered by global optimisation approaches. Unfortunately, state-of-the-art global optimisation solvers are unable to scale up to real-world size instances. In this study, we present a convex mixed-integer second-order cone relaxation for the gas expansion planning problem under steady-state conditions. The underlying model offers tight lower bounds with high computational efficiency. In addition, the optimal solution of the relaxation can often be used to derive high-quality solutionsmore » to the original problem, leading to provably tight optimality gaps and, in some cases, global optimal solutions. The convex relaxation is based on a few key ideas, including the introduction of flux direction variables, exact McCormick relaxations, on/off constraints, and integer cuts. Numerical experiments are conducted on the traditional Belgian gas network, as well as other real larger networks. The results demonstrate both the accuracy and computational speed of the relaxation and its ability to produce high-quality solution« less

Computer Corner: Spreadsheets, Power Series, Generating Functions, and Integers.

ERIC Educational Resources Information Center

Snow, Donald R.

1989-01-01

Implements a table algorithm on a spreadsheet program and obtains functions for several number sequences such as the Fibonacci and Catalan numbers. Considers other applications of the table algorithm to integers represented in various number bases. (YP)

Performance Improvements to the Naval Postgraduate School Turbopropulsion Labs Transonic Axially Splittered Rotor

DTIC Science & Technology

2013-12-01

Implementation of current NPS TPL design procedure that uses COTS software (MATLAB, SolidWorks, and ANSYS - CFX ) for the geometric rendering and...procedure that uses commercial-off-the-shelf software (MATLAB, SolidWorks, and ANSYS - CFX ) for the geometric rendering and analysis was modified and... CFX The CFD simulation program in ANSYS Workbench. CFX -Pre CFX boundary conditions and solver settings module. CFX -Solver CFX solver program. CFX

A modified priority list-based MILP method for solving large-scale unit commitment problems

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

Ke, Xinda; Lu, Ning; Wu, Di

This paper studies the typical pattern of unit commitment (UC) results in terms of generator’s cost and capacity. A method is then proposed to combine a modified priority list technique with mixed integer linear programming (MILP) for UC problem. The proposed method consists of two steps. At the first step, a portion of generators are predetermined to be online or offline within a look-ahead period (e.g., a week), based on the demand curve and generator priority order. For the generators whose on/off status is predetermined, at the second step, the corresponding binary variables are removed from the UC MILP problemmore » over the operational planning horizon (e.g., 24 hours). With a number of binary variables removed, the resulted problem can be solved much faster using the off-the-shelf MILP solvers, based on the branch-and-bound algorithm. In the modified priority list method, scale factors are designed to adjust the tradeoff between solution speed and level of optimality. It is found that the proposed method can significantly speed up the UC problem with minor compromise in optimality by selecting appropriate scale factors.« less

Two-MILP models for scheduling elective surgeries within a private healthcare facility.

PubMed

Khlif Hachicha, Hejer; Zeghal Mansour, Farah

2016-11-05

This paper deals with an Integrated Elective Surgery-Scheduling Problem (IESSP) that arises in a privately operated healthcare facility. It aims to optimize the resource utilization of the entire surgery process including pre-operative, per-operative and post-operative activities. Moreover, it addresses a specific feature of private facilities where surgeons are independent service providers and may conduct their surgeries in different private healthcare facilities. Thus, the problem requires the assignment of surgery patients to hospital beds, operating rooms and recovery beds as well as their sequencing over a 1-day period while taking into account surgeons' availability constraints. We present two Mixed Integer Linear Programs (MILP) that model the IESSP as a three-stage hybrid flow-shop scheduling problem with recirculation, resource synchronization, dedicated machines, and blocking constraints. To assess the empirical performance of the proposed models, we conducted experiments on real-world data of a Tunisian private clinic: Clinique Ennasr and on randomly generated instances. Two criteria were minimised: the patients' average length of stay and the number of patients' overnight stays. The computational results show that the proposed models can solve instances with up to 44 surgical cases in a reasonable CPU time using a general-purpose MILP solver.

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

Optimization Routine for Generating Medical Kits for Spaceflight Using the Integrated Medical Model

NASA Technical Reports Server (NTRS)

Graham, Kimberli; Myers, Jerry; Goodenow, Deb

2017-01-01

The Integrated Medical Model (IMM) is a MATLAB model that provides probabilistic assessment of the medical risk associated with human spaceflight missions.Different simulations or profiles can be run in which input conditions regarding both mission characteristics and crew characteristics may vary. For each simulation, the IMM records the total medical events that occur and “treats” each event with resources drawn from import scripts. IMM outputs include Total Medical Events (TME), Crew Health Index (CHI), probability of Evacuation (pEVAC), and probability of Loss of Crew Life (pLOCL).The Crew Health Index is determined by the amount of quality time lost (QTL). Previously, an optimization code was implemented in order to efficiently generate medical kits. The kits were optimized to have the greatest benefit possible, given amass and/or volume constraint. A 6-crew, 14-day lunar mission was chosen for the simulation and run through the IMM for 100,000 trials. A built-in MATLAB solver, mixed-integer linear programming, was used for the optimization routine. Kits were generated in 10% increments ranging from 10%-100% of the benefit constraints. Conditions wheremass alone was minimized, volume alone was minimized, and where mass and volume were minimizedjointly were tested.

An interactive approach based on a discrete differential evolution algorithm for a class of integer bilevel programming problems

NASA Astrophysics Data System (ADS)

Li, Hong; Zhang, Li; Jiao, Yong-Chang

2016-07-01

This paper presents an interactive approach based on a discrete differential evolution algorithm to solve a class of integer bilevel programming problems, in which integer decision variables are controlled by an upper-level decision maker and real-value or continuous decision variables are controlled by a lower-level decision maker. Using the Karush--Kuhn-Tucker optimality conditions in the lower-level programming, the original discrete bilevel formulation can be converted into a discrete single-level nonlinear programming problem with the complementarity constraints, and then the smoothing technique is applied to deal with the complementarity constraints. Finally, a discrete single-level nonlinear programming problem is obtained, and solved by an interactive approach. In each iteration, for each given upper-level discrete variable, a system of nonlinear equations including the lower-level variables and Lagrange multipliers is solved first, and then a discrete nonlinear programming problem only with inequality constraints is handled by using a discrete differential evolution algorithm. Simulation results show the effectiveness of the proposed approach.

Program Package for 3d PIC Model of Plasma Fiber

NASA Astrophysics Data System (ADS)

Kulhánek, Petr; Břeň, David

2007-08-01

A fully three dimensional Particle in Cell model of the plasma fiber had been developed. The code is written in FORTRAN 95, implementation CVF (Compaq Visual Fortran) under Microsoft Visual Studio user interface. Five particle solvers and two field solvers are included in the model. The solvers have relativistic and non-relativistic variants. The model can deal both with periodical and non-periodical boundary conditions. The mechanism of the surface turbulences generation in the plasma fiber was successfully simulated with the PIC program package.

Currency arbitrage detection using a binary integer programming model

NASA Astrophysics Data System (ADS)

Soon, Wanmei; Ye, Heng-Qing

2011-04-01

In this article, we examine the use of a new binary integer programming (BIP) model to detect arbitrage opportunities in currency exchanges. This model showcases an excellent application of mathematics to the real world. The concepts involved are easily accessible to undergraduate students with basic knowledge in Operations Research. Through this work, students can learn to link several types of basic optimization models, namely linear programming, integer programming and network models, and apply the well-known sensitivity analysis procedure to accommodate realistic changes in the exchange rates. Beginning with a BIP model, we discuss how it can be reduced to an equivalent but considerably simpler model, where an efficient algorithm can be applied to find the arbitrages and incorporate the sensitivity analysis procedure. A simple comparison is then made with a different arbitrage detection model. This exercise helps students learn to apply basic Operations Research concepts to a practical real-life example, and provides insights into the processes involved in Operations Research model formulations.

Mixed Integer Programming and Heuristic Scheduling for Space Communication Networks

NASA Technical Reports Server (NTRS)

Cheung, Kar-Ming; Lee, Charles H.

2012-01-01

We developed framework and the mathematical formulation for optimizing communication network using mixed integer programming. The design yields a system that is much smaller, in search space size, when compared to the earlier approach. Our constrained network optimization takes into account the dynamics of link performance within the network along with mission and operation requirements. A unique penalty function is introduced to transform the mixed integer programming into the more manageable problem of searching in a continuous space. The constrained optimization problem was proposed to solve in two stages: first using the heuristic Particle Swarming Optimization algorithm to get a good initial starting point, and then feeding the result into the Sequential Quadratic Programming algorithm to achieve the final optimal schedule. We demonstrate the above planning and scheduling methodology with a scenario of 20 spacecraft and 3 ground stations of a Deep Space Network site. Our approach and framework have been simple and flexible so that problems with larger number of constraints and network can be easily adapted and solved.

An Interactive Artificial Cutting Plane Method for Bicriterion Integer Programming Problems

DTIC Science & Technology

1992-08-01

AUTHOR(S) Diane Breivik Allen, 1st Lt 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER AFIT Student Attending...INTERACTIVE ARTIFICIAL CUTTING PLANE METHOD FOR BICRITERION INTEGER PROGRAMMING PROBLEMS By Diane Breivik Allen A Thesis Submitted to the Faculty of...ITfiSRA&1 DTIC TAB 0 Unannounced 0 Justirication By BY Diane Breivik Allen Distributlon/ Availability CQdes Avail and/or Dist Special Approved: DTI

MACSYMA's symbolic ordinary differential equation solver

NASA Technical Reports Server (NTRS)

Golden, J. P.

1977-01-01

The MACSYMA's symbolic ordinary differential equation solver ODE2 is described. The code for this routine is delineated, which is of interest because it is written in top-level MACSYMA language, and may serve as a good example of programming in that language. Other symbolic ordinary differential equation solvers are mentioned.

Enhanced index tracking modeling in portfolio optimization with mixed-integer programming z approach

NASA Astrophysics Data System (ADS)

Siew, Lam Weng; Jaaman, Saiful Hafizah Hj.; Ismail, Hamizun bin

2014-09-01

Enhanced index tracking is a popular form of portfolio management in stock market investment. Enhanced index tracking aims to construct an optimal portfolio to generate excess return over the return achieved by the stock market index without purchasing all of the stocks that make up the index. The objective of this paper is to construct an optimal portfolio using mixed-integer programming model which adopts regression approach in order to generate higher portfolio mean return than stock market index return. In this study, the data consists of 24 component stocks in Malaysia market index which is FTSE Bursa Malaysia Kuala Lumpur Composite Index from January 2010 until December 2012. The results of this study show that the optimal portfolio of mixed-integer programming model is able to generate higher mean return than FTSE Bursa Malaysia Kuala Lumpur Composite Index return with only selecting 30% out of the total stock market index components.

Smart-Grid Backbone Network Real-Time Delay Reduction via Integer Programming.

PubMed

Pagadrai, Sasikanth; Yilmaz, Muhittin; Valluri, Pratyush

2016-08-01

This research investigates an optimal delay-based virtual topology design using integer linear programming (ILP), which is applied to the current backbone networks such as smart-grid real-time communication systems. A network traffic matrix is applied and the corresponding virtual topology problem is solved using the ILP formulations that include a network delay-dependent objective function and lightpath routing, wavelength assignment, wavelength continuity, flow routing, and traffic loss constraints. The proposed optimization approach provides an efficient deterministic integration of intelligent sensing and decision making, and network learning features for superior smart grid operations by adaptively responding the time-varying network traffic data as well as operational constraints to maintain optimal virtual topologies. A representative optical backbone network has been utilized to demonstrate the proposed optimization framework whose simulation results indicate that superior smart-grid network performance can be achieved using commercial networks and integer programming.

Chromosome structures: reduction of certain problems with unequal gene content and gene paralogs to integer linear programming.

PubMed

Lyubetsky, Vassily; Gershgorin, Roman; Gorbunov, Konstantin

2017-12-06

Chromosome structure is a very limited model of the genome including the information about its chromosomes such as their linear or circular organization, the order of genes on them, and the DNA strand encoding a gene. Gene lengths, nucleotide composition, and intergenic regions are ignored. Although highly incomplete, such structure can be used in many cases, e.g., to reconstruct phylogeny and evolutionary events, to identify gene synteny, regulatory elements and promoters (considering highly conserved elements), etc. Three problems are considered; all assume unequal gene content and the presence of gene paralogs. The distance problem is to determine the minimum number of operations required to transform one chromosome structure into another and the corresponding transformation itself including the identification of paralogs in two structures. We use the DCJ model which is one of the most studied combinatorial rearrangement models. Double-, sesqui-, and single-operations as well as deletion and insertion of a chromosome region are considered in the model; the single ones comprise cut and join. In the reconstruction problem, a phylogenetic tree with chromosome structures in the leaves is given. It is necessary to assign the structures to inner nodes of the tree to minimize the sum of distances between terminal structures of each edge and to identify the mutual paralogs in a fairly large set of structures. A linear algorithm is known for the distance problem without paralogs, while the presence of paralogs makes it NP-hard. If paralogs are allowed but the insertion and deletion operations are missing (and special constraints are imposed), the reduction of the distance problem to integer linear programming is known. Apparently, the reconstruction problem is NP-hard even in the absence of paralogs. The problem of contigs is to find the optimal arrangements for each given set of contigs, which also includes the mutual identification of paralogs. We proved that these problems can be reduced to integer linear programming formulations, which allows an algorithm to redefine the problems to implement a very special case of the integer linear programming tool. The results were tested on synthetic and biological samples. Three well-known problems were reduced to a very special case of integer linear programming, which is a new method of their solutions. Integer linear programming is clearly among the main computational methods and, as generally accepted, is fast on average; in particular, computation systems specifically targeted at it are available. The challenges are to reduce the size of the corresponding integer linear programming formulations and to incorporate a more detailed biological concept in our model of the reconstruction.

Short-term benefits from central unit commitment and dispatch: Application to the Southern African Power Pool

NASA Astrophysics Data System (ADS)

Bowen, Brian Hugh

1998-12-01

Electricity utilities in the Southern African region are conscious that gains could be made from more economically efficient trading but have had no tools with which to analyze the effects of a change in policy. This research is the first to provide transparent quantitative techniques to quantify the impacts of new trading arrangements in this region. The study poses a model of the recently formed Southern African Power Pool, built with the collaboration of the region's national utilities to represent each country's demand and generation/transmission system. The multi-region model includes commitment and dispatch from diverse hydrothermal sources over a vast area. Economic gains are determined by comparing the total costs under free-trade conditions with those from the existing fixed-trade bilateral arrangements. The objective function minimizes production costs needed to meet total demand, subject to each utility's constraints for thermal and hydro generation, transmission, load balance and losses. Linearized thermal cost functions are used along with linearized input output hydropower plant curves and hydrothermal on/off status variables to formulate a mixed-integer programming problem. Results from the modeling show that moving to optimal trading patterns could save between 70 million and 130 million per year. With free-trade policies the quantity of power flow between utilities is doubled and maximum usage is made of the hydropower stations thus reducing costs and fuel use. In electricity exporting countries such as Zambia and Mozambique gains from increased trade are achieved which equal 16% and 18% respectively of the value of their total manufactured exports. A sensitivity analysis is conducted on the possible effects of derating generation, derating transmission and reducing water inflows but gains remain large. Maximum economic gains from optimal trading patterns can be achieved by each country allowing centralized control through the newly founded SAPP coordination center. Using standard mixed integer programming solvers makes the cost of such modeling activity easily affordable to each utility in the Southern African pool. This research provides the utilities with the modeling tools to quantify the gains from increased trade and thereby furthers a move towards greater efficiency, faster economic growth and reduced use of fossil fuels.

Optimized and parallelized implementation of the electronegativity equalization method and the atom-bond electronegativity equalization method.

PubMed

Vareková, R Svobodová; Koca, J

2006-02-01

The most common way to calculate charge distribution in a molecule is ab initio quantum mechanics (QM). Some faster alternatives to QM have also been developed, the so-called "equalization methods" EEM and ABEEM, which are based on DFT. We have implemented and optimized the EEM and ABEEM methods and created the EEM SOLVER and ABEEM SOLVER programs. It has been found that the most time-consuming part of equalization methods is the reduction of the matrix belonging to the equation system generated by the method. Therefore, for both methods this part was replaced by the parallel algorithm WIRS and implemented within the PVM environment. The parallelized versions of the programs EEM SOLVER and ABEEM SOLVER showed promising results, especially on a single computer with several processors (compact PVM). The implemented programs are available through the Web page http://ncbr.chemi.muni.cz/~n19n/eem_abeem.

Applying EXCEL Solver to a watershed management goal-programming problem

Treesearch

J. E. de Steiguer

2000-01-01

This article demonstrates the application of EXCEL® spreadsheet linear programming (LP) solver to a watershed management multiple use goal programming (GP) problem. The data used to demonstrate the application are from a published study for a watershed in northern Colorado. GP has been used by natural resource managers for many years. However, the GP solution by means...

Alternative mathematical programming formulations for FSS synthesis

NASA Technical Reports Server (NTRS)

Reilly, C. H.; Mount-Campbell, C. A.; Gonsalvez, D. J. A.; Levis, C. A.

1986-01-01

A variety of mathematical programming models and two solution strategies are suggested for the problem of allocating orbital positions to (synthesizing) satellites in the Fixed Satellite Service. Mixed integer programming and almost linear programming formulations are presented in detail for each of two objectives: (1) positioning satellites as closely as possible to specified desired locations, and (2) minimizing the total length of the geostationary arc allocated to the satellites whose positions are to be determined. Computational results for mixed integer and almost linear programming models, with the objective of positioning satellites as closely as possible to their desired locations, are reported for three six-administration test problems and a thirteen-administration test problem.

Aerospace Applications of Integer and Combinatorial Optimization

NASA Technical Reports Server (NTRS)

Padula, S. L.; Kincaid, R. K.

1995-01-01

Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in formulating and solving integer and combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem, for example, seeks the optimal locations for vibration-damping devices on an orbiting platform and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.

Aerospace applications on integer and combinatorial optimization

NASA Technical Reports Server (NTRS)

Padula, S. L.; Kincaid, R. K.

1995-01-01

Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in formulating and solving integer and combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem. for example, seeks the optimal locations for vibration-damping devices on an orbiting platform and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.

Integration of progressive hedging and dual decomposition in stochastic integer programs

DOE PAGES

Watson, Jean -Paul; Guo, Ge; Hackebeil, Gabriel; ...

2015-04-07

We present a method for integrating the Progressive Hedging (PH) algorithm and the Dual Decomposition (DD) algorithm of Carøe and Schultz for stochastic mixed-integer programs. Based on the correspondence between lower bounds obtained with PH and DD, a method to transform weights from PH to Lagrange multipliers in DD is found. Fast progress in early iterations of PH speeds up convergence of DD to an exact solution. As a result, we report computational results on server location and unit commitment instances.

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.

Solving the Water Jugs Problem by an Integer Sequence Approach

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2012-01-01

In this article, we present an integer sequence approach to solve the classic water jugs problem. The solution steps can be obtained easily by additions and subtractions only, which is suitable for manual calculation or programming by computer. This approach can be introduced to secondary and undergraduate students, and also to teachers and…

Preconditioned implicit solvers for the Navier-Stokes equations on distributed-memory machines

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Liou, Meng-Sing; Dyson, Rodger W.

1994-01-01

The GMRES method is parallelized, and combined with local preconditioning to construct an implicit parallel solver to obtain steady-state solutions for the Navier-Stokes equations of fluid flow on distributed-memory machines. The new implicit parallel solver is designed to preserve the convergence rate of the equivalent 'serial' solver. A static domain-decomposition is used to partition the computational domain amongst the available processing nodes of the parallel machine. The SPMD (Single-Program Multiple-Data) programming model is combined with message-passing tools to develop the parallel code on a 32-node Intel Hypercube and a 512-node Intel Delta machine. The implicit parallel solver is validated for internal and external flow problems, and is found to compare identically with flow solutions obtained on a Cray Y-MP/8. A peak computational speed of 2300 MFlops/sec has been achieved on 512 nodes of the Intel Delta machine,k for a problem size of 1024 K equations (256 K grid points).

Fast scaffolding with small independent mixed integer programs

PubMed Central

Salmela, Leena; Mäkinen, Veli; Välimäki, Niko; Ylinen, Johannes; Ukkonen, Esko

2011-01-01

Motivation: Assembling genomes from short read data has become increasingly popular, but the problem remains computationally challenging especially for larger genomes. We study the scaffolding phase of sequence assembly where preassembled contigs are ordered based on mate pair data. Results: We present MIP Scaffolder that divides the scaffolding problem into smaller subproblems and solves these with mixed integer programming. The scaffolding problem can be represented as a graph and the biconnected components of this graph can be solved independently. We present a technique for restricting the size of these subproblems so that they can be solved accurately with mixed integer programming. We compare MIP Scaffolder to two state of the art methods, SOPRA and SSPACE. MIP Scaffolder is fast and produces better or as good scaffolds as its competitors on large genomes. Availability: The source code of MIP Scaffolder is freely available at http://www.cs.helsinki.fi/u/lmsalmel/mip-scaffolder/. Contact: leena.salmela@cs.helsinki.fi PMID:21998153

Sequential computation of elementary modes and minimal cut sets in genome-scale metabolic networks using alternate integer linear programming

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

Song, Hyun-Seob; Goldberg, Noam; Mahajan, Ashutosh

Elementary (flux) modes (EMs) have served as a valuable tool for investigating structural and functional properties of metabolic networks. Identification of the full set of EMs in genome-scale networks remains challenging due to combinatorial explosion of EMs in complex networks. It is often, however, that only a small subset of relevant EMs needs to be known, for which optimization-based sequential computation is a useful alternative. Most of the currently available methods along this line are based on the iterative use of mixed integer linear programming (MILP), the effectiveness of which significantly deteriorates as the number of iterations builds up. Tomore » alleviate the computational burden associated with the MILP implementation, we here present a novel optimization algorithm termed alternate integer linear programming (AILP). Results: Our algorithm was designed to iteratively solve a pair of integer programming (IP) and linear programming (LP) to compute EMs in a sequential manner. In each step, the IP identifies a minimal subset of reactions, the deletion of which disables all previously identified EMs. Thus, a subsequent LP solution subject to this reaction deletion constraint becomes a distinct EM. In cases where no feasible LP solution is available, IP-derived reaction deletion sets represent minimal cut sets (MCSs). Despite the additional computation of MCSs, AILP achieved significant time reduction in computing EMs by orders of magnitude. The proposed AILP algorithm not only offers a computational advantage in the EM analysis of genome-scale networks, but also improves the understanding of the linkage between EMs and MCSs.« less

The Computer Bulletin Board.

ERIC Educational Resources Information Center

Batt, Russell H., Ed.

1990-01-01

Described is how spreadsheet and problem solver microcomputer programs may assist students in performing mathematical calculations. Discussed is the application of the equation solver "MathCAD" to various areas in the undergraduate curriculum. (KR)

A two-stage mixed-integer fuzzy programming with interval-valued membership functions approach for flood-diversion planning.

PubMed

Wang, S; Huang, G H

2013-03-15

Flood disasters have been extremely severe in recent decades, and they account for about one third of all natural catastrophes throughout the world. In this study, a two-stage mixed-integer fuzzy programming with interval-valued membership functions (TMFP-IMF) approach is developed for flood-diversion planning under uncertainty. TMFP-IMF integrates the fuzzy flexible programming, two-stage stochastic programming, and integer programming within a general framework. A concept of interval-valued fuzzy membership function is introduced to address complexities of system uncertainties. TMFP-IMF can not only deal with uncertainties expressed as fuzzy sets and probability distributions, but also incorporate pre-regulated water-diversion policies directly into its optimization process. TMFP-IMF is applied to a hypothetical case study of flood-diversion planning for demonstrating its applicability. Results indicate that reasonable solutions can be generated for binary and continuous variables. A variety of flood-diversion and capacity-expansion schemes can be obtained under four scenarios, which enable decision makers (DMs) to identify the most desired one based on their perceptions and attitudes towards the objective-function value and constraints. Copyright © 2013 Elsevier Ltd. All rights reserved.

Exact algorithms for haplotype assembly from whole-genome sequence data.

PubMed

Chen, Zhi-Zhong; Deng, Fei; Wang, Lusheng

2013-08-15

Haplotypes play a crucial role in genetic analysis and have many applications such as gene disease diagnoses, association studies, ancestry inference and so forth. The development of DNA sequencing technologies makes it possible to obtain haplotypes from a set of aligned reads originated from both copies of a chromosome of a single individual. This approach is often known as haplotype assembly. Exact algorithms that can give optimal solutions to the haplotype assembly problem are highly demanded. Unfortunately, previous algorithms for this problem either fail to output optimal solutions or take too long time even executed on a PC cluster. We develop an approach to finding optimal solutions for the haplotype assembly problem under the minimum-error-correction (MEC) model. Most of the previous approaches assume that the columns in the input matrix correspond to (putative) heterozygous sites. This all-heterozygous assumption is correct for most columns, but it may be incorrect for a small number of columns. In this article, we consider the MEC model with or without the all-heterozygous assumption. In our approach, we first use new methods to decompose the input read matrix into small independent blocks and then model the problem for each block as an integer linear programming problem, which is then solved by an integer linear programming solver. We have tested our program on a single PC [a Linux (x64) desktop PC with i7-3960X CPU], using the filtered HuRef and the NA 12878 datasets (after applying some variant calling methods). With the all-heterozygous assumption, our approach can optimally solve the whole HuRef data set within a total time of 31 h (26 h for the most difficult block of the 15th chromosome and only 5 h for the other blocks). To our knowledge, this is the first time that MEC optimal solutions are completely obtained for the filtered HuRef dataset. Moreover, in the general case (without the all-heterozygous assumption), for the HuRef dataset our approach can optimally solve all the chromosomes except the most difficult block in chromosome 15 within a total time of 12 days. For both of the HuRef and NA12878 datasets, the optimal costs in the general case are sometimes much smaller than those in the all-heterozygous case. This implies that some columns in the input matrix (after applying certain variant calling methods) still correspond to false-heterozygous sites. Our program, the optimal solutions found for the HuRef dataset available at http://rnc.r.dendai.ac.jp/hapAssembly.html.

A Comparison of the DISASTER (Trademark) Scheduling Software with a Simultaneous Scheduling Algorithm for Minimizing Maximum Tardiness in Job Shops

DTIC Science & Technology

1993-09-01

goal ( Heizer , Render , and Stair, 1993:94). Integer Prgronmming. Integer programming is a general purpose approach used to optimally solve job shop...Scheduling," Operations Research Journal. 29, No 4: 646-667 (July-August 1981). Heizer , Jay, Barry Render and Ralph M. Stair, Jr. Production and Operations

An integer programming model to optimize resource allocation for wildfire containment.

Treesearch

Geoffrey H. Donovan; Douglas B. Rideout

2003-01-01

Determining the specific mix of fire-fighting resources for a given fire is a necessary condition for identifying the minimum of the Cost Plus Net Value Change (C+NVC) function. Current wildland fire management models may not reliably do so. The problem of identifying the most efficient wildland fire organization is characterized mathematically using integer-...

RSM 1.0 - A RESUPPLY SCHEDULER USING INTEGER OPTIMIZATION

NASA Technical Reports Server (NTRS)

Viterna, L. A.

1994-01-01

RSM, Resupply Scheduling Modeler, is a fully menu-driven program that uses integer programming techniques to determine an optimum schedule for replacing components on or before the end of a fixed replacement period. Although written to analyze the electrical power system on the Space Station Freedom, RSM is quite general and can be used to model the resupply of almost any system subject to user-defined resource constraints. RSM is based on a specific form of the general linear programming problem in which all variables in the objective function and all variables in the constraints are integers. While more computationally intensive, integer programming was required for accuracy when modeling systems with small quantities of components. Input values for component life cane be real numbers, RSM converts them to integers by dividing the lifetime by the period duration, then reducing the result to the next lowest integer. For each component, there is a set of constraints that insure that it is replaced before its lifetime expires. RSM includes user-defined constraints such as transportation mass and volume limits, as well as component life, available repair crew time and assembly sequences. A weighting factor allows the program to minimize factors such as cost. The program then performs an iterative analysis, which is displayed during the processing. A message gives the first period in which resources are being exceeded on each iteration. If the scheduling problem is unfeasible, the final message will also indicate the first period in which resources were exceeded. RSM is written in APL2 for IBM PC series computers and compatibles. A stand-alone executable version of RSM is provided; however, this is a "packed" version of RSM which can only utilize the memory within the 640K DOS limit. This executable requires at least 640K of memory and DOS 3.1 or higher. Source code for an APL2/PC workspace version is also provided. This version of RSM can make full use of any installed extended memory but must be run with the APL2 interpreter; and it requires an 80486 based microcomputer or an 80386 based microcomputer with an 80387 math coprocessor, at least 2Mb of extended memory, and DOS 3.3 or higher. The standard distribution medium for this package is one 5.25 inch 360K MS-DOS format diskette. RSM was developed in 1991. APL2 and IBM PC are registered trademarks of International Business Machines Corporation. MS-DOS is a registered trademark of Microsoft Corporation.

A generalized interval fuzzy mixed integer programming model for a multimodal transportation problem under uncertainty

NASA Astrophysics Data System (ADS)

Tian, Wenli; Cao, Chengxuan

2017-03-01

A generalized interval fuzzy mixed integer programming model is proposed for the multimodal freight transportation problem under uncertainty, in which the optimal mode of transport and the optimal amount of each type of freight transported through each path need to be decided. For practical purposes, three mathematical methods, i.e. the interval ranking method, fuzzy linear programming method and linear weighted summation method, are applied to obtain equivalents of constraints and parameters, and then a fuzzy expected value model is presented. A heuristic algorithm based on a greedy criterion and the linear relaxation algorithm are designed to solve the model.

A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet-Neumann boundary conditions

NASA Astrophysics Data System (ADS)

Reimer, Ashton S.; Cheviakov, Alexei F.

2013-03-01

A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.

A Mixed-Integer Linear Programming Problem which is Efficiently Solvable.

DTIC Science & Technology

1987-10-01

INTEGER LINEAR PROGRAMMING PROBLEM WHICH IS EFFICIENTLY SOLVABLE 12. PERSONAL AUTHOR(S) Leiserson, Charles, and Saxe, James B. 13a. TYPE OF REPORT j13b TIME...ger prongramn rg versions or the problem is not ac’hievable in genieral for sparse inistancves of’ P rolem(r Mi. Th le remrai nder or thris paper is...rClazes c:oIh edge (i,I*) by comlpli urg +- rnirr(z 3, ,x + a,j). A sirnI) le analysis (11 vto Nei [131 indicates why whe Iellinan-Ford algorithm works

Development of a Menu Driven Materials Data Base for Use on Personal Computers

DTIC Science & Technology

1992-07-01

written permission. Copyright Is the responsibility of the Director Publishing and Marketing , AGPS. Enquiries should be directed to the Manager, AGPS...PROGRAM LISTING A-2-1 Program MOB; uses crt; label levell,level2,level3,shutdown,dis;play; var options,code, nlines ,nmeflitemp,i,j4,k :integer; w,chl,ch2,ch3...char; menus :array [I. .1001 of st~ring[801; nline :array [l. .100] of integer; s2 :string[21; control :string[4]; aline :string[801; inm,iflt :text

Numerical System Solver Developed for the National Cycle Program

NASA Technical Reports Server (NTRS)

Binder, Michael P.

1999-01-01

As part of the National Cycle Program (NCP), a powerful new numerical solver has been developed to support the simulation of aeropropulsion systems. This software uses a hierarchical object-oriented design. It can provide steady-state and time-dependent solutions to nonlinear and even discontinuous problems typically encountered when aircraft and spacecraft propulsion systems are simulated. It also can handle constrained solutions, in which one or more factors may limit the behavior of the engine system. Timedependent simulation capabilities include adaptive time-stepping and synchronization with digital control elements. The NCP solver is playing an important role in making the NCP a flexible, powerful, and reliable simulation package.

Stacking-sequence optimization for buckling of laminated plates by integer programming

NASA Technical Reports Server (NTRS)

Haftka, Raphael T.; Walsh, Joanne L.

1991-01-01

Integer-programming formulations for the design of symmetric and balanced laminated plates under biaxial compression are presented. Both maximization of buckling load for a given total thickness and the minimization of total thickness subject to a buckling constraint are formulated. The design variables that define the stacking sequence of the laminate are zero-one integers. It is shown that the formulation results in a linear optimization problem that can be solved on readily available software. This is in contrast to the continuous case, where the design variables are the thicknesses of layers with specified ply orientations, and the optimization problem is nonlinear. Constraints on the stacking sequence such as a limit on the number of contiguous plies of the same orientation and limits on in-plane stiffnesses are easily accommodated. Examples are presented for graphite-epoxy plates under uniaxial and biaxial compression using a commercial software package based on the branch-and-bound algorithm.

Boosting Stochastic Problem Solvers Through Online Self-Analysis of Performance

DTIC Science & Technology

2003-07-21

Boosting Stochastic Problem Solvers Through Online Self-Analysis of Performance Vincent A. Cicirello CMU-RI-TR-03-27 Submitted in partial fulfillment...AND SUBTITLE Boosting Stochastic Problem Solvers Through Online Self-Analysis of Performance 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM...lead to the development of a search control framework, called QD-BEACON that uses online -generated statistical models of search performance to

Distributed mixed-integer fuzzy hierarchical programming for municipal solid waste management. Part I: System identification and methodology development.

PubMed

Cheng, Guanhui; Huang, Guohe; Dong, Cong; Xu, Ye; Chen, Xiujuan; Chen, Jiapei

2017-03-01

Due to the existence of complexities of heterogeneities, hierarchy, discreteness, and interactions in municipal solid waste management (MSWM) systems such as Beijing, China, a series of socio-economic and eco-environmental problems may emerge or worsen and result in irredeemable damages in the following decades. Meanwhile, existing studies, especially ones focusing on MSWM in Beijing, could hardly reflect these complexities in system simulations and provide reliable decision support for management practices. Thus, a framework of distributed mixed-integer fuzzy hierarchical programming (DMIFHP) is developed in this study for MSWM under these complexities. Beijing is selected as a representative case. The Beijing MSWM system is comprehensively analyzed in many aspects such as socio-economic conditions, natural conditions, spatial heterogeneities, treatment facilities, and system complexities, building a solid foundation for system simulation and optimization. Correspondingly, the MSWM system in Beijing is discretized as 235 grids to reflect spatial heterogeneity. A DMIFHP model which is a nonlinear programming problem is constructed to parameterize the Beijing MSWM system. To enable scientific solving of it, a solution algorithm is proposed based on coupling of fuzzy programming and mixed-integer linear programming. Innovations and advantages of the DMIFHP framework are discussed. The optimal MSWM schemes and mechanism revelations will be discussed in another companion paper due to length limitation.

A computational study of the use of an optimization-based method for simulating large multibody systems.

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

Petra, C.; Gavrea, B.; Anitescu, M.

2009-01-01

The present work aims at comparing the performance of several quadratic programming (QP) solvers for simulating large-scale frictional rigid-body systems. Traditional time-stepping schemes for simulation of multibody systems are formulated as linear complementarity problems (LCPs) with copositive matrices. Such LCPs are generally solved by means of Lemke-type algorithms and solvers such as the PATH solver proved to be robust. However, for large systems, the PATH solver or any other pivotal algorithm becomes unpractical from a computational point of view. The convex relaxation proposed by one of the authors allows the formulation of the integration step as a QPD, for whichmore » a wide variety of state-of-the-art solvers are available. In what follows we report the results obtained solving that subproblem when using the QP solvers MOSEK, OOQP, TRON, and BLMVM. OOQP is presented with both the symmetric indefinite solver MA27 and our Cholesky reformulation using the CHOLMOD package. We investigate computational performance and address the correctness of the results from a modeling point of view. We conclude that the OOQP solver, particularly with the CHOLMOD linear algebra solver, has predictable performance and memory use patterns and is far more competitive for these problems than are the other solvers.« less

Split diversity in constrained conservation prioritization using integer linear programming.

PubMed

Chernomor, Olga; Minh, Bui Quang; Forest, Félix; Klaere, Steffen; Ingram, Travis; Henzinger, Monika; von Haeseler, Arndt

2015-01-01

Phylogenetic diversity (PD) is a measure of biodiversity based on the evolutionary history of species. Here, we discuss several optimization problems related to the use of PD, and the more general measure split diversity (SD), in conservation prioritization.Depending on the conservation goal and the information available about species, one can construct optimization routines that incorporate various conservation constraints. We demonstrate how this information can be used to select sets of species for conservation action. Specifically, we discuss the use of species' geographic distributions, the choice of candidates under economic pressure, and the use of predator-prey interactions between the species in a community to define viability constraints.Despite such optimization problems falling into the area of NP hard problems, it is possible to solve them in a reasonable amount of time using integer programming. We apply integer linear programming to a variety of models for conservation prioritization that incorporate the SD measure.We exemplarily show the results for two data sets: the Cape region of South Africa and a Caribbean coral reef community. Finally, we provide user-friendly software at http://www.cibiv.at/software/pda.

Rarity-weighted richness: a simple and reliable alternative to integer programming and heuristic algorithms for minimum set and maximum coverage problems in conservation planning.

PubMed

Albuquerque, Fabio; Beier, Paul

2015-01-01

Here we report that prioritizing sites in order of rarity-weighted richness (RWR) is a simple, reliable way to identify sites that represent all species in the fewest number of sites (minimum set problem) or to identify sites that represent the largest number of species within a given number of sites (maximum coverage problem). We compared the number of species represented in sites prioritized by RWR to numbers of species represented in sites prioritized by the Zonation software package for 11 datasets in which the size of individual planning units (sites) ranged from <1 ha to 2,500 km2. On average, RWR solutions were more efficient than Zonation solutions. Integer programming remains the only guaranteed way find an optimal solution, and heuristic algorithms remain superior for conservation prioritizations that consider compactness and multiple near-optimal solutions in addition to species representation. But because RWR can be implemented easily and quickly in R or a spreadsheet, it is an attractive alternative to integer programming or heuristic algorithms in some conservation prioritization contexts.

Integer programming for improving radiotherapy treatment efficiency.

PubMed

Lv, Ming; Li, Yi; Kou, Bo; Zhou, Zhili

2017-01-01

Patients received by radiotherapy departments are diverse and may be diagnosed with different cancers. Therefore, they need different radiotherapy treatment plans and thus have different needs for medical resources. This research aims to explore the best method of scheduling the admission of patients receiving radiotherapy so as to reduce patient loss and maximize the usage efficiency of service resources. A mix integer programming (MIP) model integrated with special features of radiotherapy is constructed. The data used here is based on the historical data collected and we propose an exact method to solve the MIP model. Compared with the traditional First Come First Served (FCFS) method, the new method has boosted patient admission as well as the usage of linear accelerators (LINAC) and beds. The integer programming model can be used to describe the complex problem of scheduling radio-receiving patients, to identify the bottleneck resources that hinder patient admission, and to obtain the optimal LINAC-bed radio under the current data conditions. Different management strategies can be implemented by adjusting the settings of the MIP model. The computational results can serve as a reference for the policy-makers in decision making.

Mixed Integer Linear Programming model for Crude Palm Oil Supply Chain Planning

NASA Astrophysics Data System (ADS)

Sembiring, Pasukat; Mawengkang, Herman; Sadyadharma, Hendaru; Bu'ulolo, F.; Fajriana

2018-01-01

The production process of crude palm oil (CPO) can be defined as the milling process of raw materials, called fresh fruit bunch (FFB) into end products palm oil. The process usually through a series of steps producing and consuming intermediate products. The CPO milling industry considered in this paper does not have oil palm plantation, therefore the FFB are supplied by several public oil palm plantations. Due to the limited availability of FFB, then it is necessary to choose from which plantations would be appropriate. This paper proposes a mixed integer linear programming model the supply chain integrated problem, which include waste processing. The mathematical programming model is solved using neighborhood search approach.

Reference hypernetted chain theory for ferrofluid bilayer: Distribution functions compared with Monte Carlo

NASA Astrophysics Data System (ADS)

Polyakov, Evgeny A.; Vorontsov-Velyaminov, Pavel N.

2014-08-01

Properties of ferrofluid bilayer (modeled as a system of two planar layers separated by a distance h and each layer carrying a soft sphere dipolar liquid) are calculated in the framework of inhomogeneous Ornstein-Zernike equations with reference hypernetted chain closure (RHNC). The bridge functions are taken from a soft sphere (1/r12) reference system in the pressure-consistent closure approximation. In order to make the RHNC problem tractable, the angular dependence of the correlation functions is expanded into special orthogonal polynomials according to Lado. The resulting equations are solved using the Newton-GRMES algorithm as implemented in the public-domain solver NITSOL. Orientational densities and pair distribution functions of dipoles are compared with Monte Carlo simulation results. A numerical algorithm for the Fourier-Hankel transform of any positive integer order on a uniform grid is presented.

Avoiding Communication in the Lanczos Bidiagonalization Routine and Associated Least Squares QR Solver

DTIC Science & Technology

2015-04-12

Avoiding communication in the Lanczos bidiagonalization routine and associated Least Squares QR solver Erin Carson Electrical Engineering and...Bidiagonalization Routine and Associated Least Squares QR Solver 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d...throughout scienti c codes , are often the bottlenecks in application perfor- mance due to a low computation/communication ratio. In this paper we develop

Using the Gurobi Solvers on the Peregrine System | High-Performance

Science.gov Websites

Peregrine System Gurobi Optimizer is a suite of solvers for mathematical programming. It is licensed for ('GRB_MATLAB_PATH') >> path(path,grb) Gurobi and GAMS GAMS is a high-level modeling system for mathematical

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

DOE PAGES

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

2016-11-27

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

An Integer Programming Model for the Management of a Forest in the North of Portugal

NASA Astrophysics Data System (ADS)

Cerveira, Adelaide; Fonseca, Teresa; Mota, Artur; Martins, Isabel

2011-09-01

This study aims to develop an approach for the management of a forest of maritime pine located in the north region of Portugal. The forest is classified into five public lands, the so-called baldios, extending over 4432 ha. These baldios are co-managed by the Official Forest Services and the local communities mainly for timber production purposes. The forest planning involves non-spatial and spatial constraints. Spatial constraints dictate a maximum clearcut area and an exclusion time. An integer programming model is presented and the computational results are discussed.

Validation of the Chemistry Module for the Euler Solver in Unified Flow Solver

DTIC Science & Technology

2012-03-01

traveling through the atmosphere there are three types of flow regimes that exist; the first is the continuum regime, second is the rarified regime and...The second method has been used in a program called Unified Flow Solver (UFS). UFS is currently being developed under collaborative efforts the Air...thermal non-equilibrium case and finally to a thermo-chemical non- equilibrium case. The data from the simulations will be compared to a second code

Solving the water jugs problem by an integer sequence approach

NASA Astrophysics Data System (ADS)

Man, Yiu-Kwong

2012-01-01

In this article, we present an integer sequence approach to solve the classic water jugs problem. The solution steps can be obtained easily by additions and subtractions only, which is suitable for manual calculation or programming by computer. This approach can be introduced to secondary and undergraduate students, and also to teachers and lecturers involved in teaching mathematical problem solving, recreational mathematics, or elementary number theory.

New Approaches for Very Large-Scale Integer Programming

DTIC Science & Technology

2016-06-24

existing algorithms. This research has been presented at several conferences and has and will appear in archival journals. 15. SUBJECT TERMS integer...This research has been presented at several conferences and has and will appear in archival journals. Distribution Statement This is block 12 on the...pdf Upload a Report Document, if any. The maximum file size for the Report Document is 50MB. Archival Publications (published) during reporting

Decision Engines for Software Analysis Using Satisfiability Modulo Theories Solvers

NASA Technical Reports Server (NTRS)

Bjorner, Nikolaj

2010-01-01

The area of software analysis, testing and verification is now undergoing a revolution thanks to the use of automated and scalable support for logical methods. A well-recognized premise is that at the core of software analysis engines is invariably a component using logical formulas for describing states and transformations between system states. The process of using this information for discovering and checking program properties (including such important properties as safety and security) amounts to automatic theorem proving. In particular, theorem provers that directly support common software constructs offer a compelling basis. Such provers are commonly called satisfiability modulo theories (SMT) solvers. Z3 is a state-of-the-art SMT solver. It is developed at Microsoft Research. It can be used to check the satisfiability of logical formulas over one or more theories such as arithmetic, bit-vectors, lists, records and arrays. The talk describes some of the technology behind modern SMT solvers, including the solver Z3. Z3 is currently mainly targeted at solving problems that arise in software analysis and verification. It has been applied to various contexts, such as systems for dynamic symbolic simulation (Pex, SAGE, Vigilante), for program verification and extended static checking (Spec#/Boggie, VCC, HAVOC), for software model checking (Yogi, SLAM), model-based design (FORMULA), security protocol code (F7), program run-time analysis and invariant generation (VS3). We will describe how it integrates support for a variety of theories that arise naturally in the context of the applications. There are several new promising avenues and the talk will touch on some of these and the challenges related to SMT solvers. Proceedings

Hybrid MPI+OpenMP Programming of an Overset CFD Solver and Performance Investigations

NASA Technical Reports Server (NTRS)

Djomehri, M. Jahed; Jin, Haoqiang H.; Biegel, Bryan (Technical Monitor)

2002-01-01

This report describes a two level parallelization of a Computational Fluid Dynamic (CFD) solver with multi-zone overset structured grids. The approach is based on a hybrid MPI+OpenMP programming model suitable for shared memory and clusters of shared memory machines. The performance investigations of the hybrid application on an SGI Origin2000 (O2K) machine is reported using medium and large scale test problems.

A comparison of SuperLU solvers on the intel MIC architecture

NASA Astrophysics Data System (ADS)

Tuncel, Mehmet; Duran, Ahmet; Celebi, M. Serdar; Akaydin, Bora; Topkaya, Figen O.

2016-10-01

In many science and engineering applications, problems may result in solving a sparse linear system AX=B. For example, SuperLU_MCDT, a linear solver, was used for the large penta-diagonal matrices for 2D problems and hepta-diagonal matrices for 3D problems, coming from the incompressible blood flow simulation (see [1]). It is important to test the status and potential improvements of state-of-the-art solvers on new technologies. In this work, sequential, multithreaded and distributed versions of SuperLU solvers (see [2]) are examined on the Intel Xeon Phi coprocessors using offload programming model at the EURORA cluster of CINECA in Italy. We consider a portfolio of test matrices containing patterned matrices from UFMM ([3]) and randomly located matrices. This architecture can benefit from high parallelism and large vectors. We find that the sequential SuperLU benefited up to 45 % performance improvement from the offload programming depending on the sparse matrix type and the size of transferred and processed data.

Evaluation of out-of-core computer programs for the solution of symmetric banded linear equations. [simultaneous equations

NASA Technical Reports Server (NTRS)

Dunham, R. S.

1976-01-01

FORTRAN coded out-of-core equation solvers that solve using direct methods symmetric banded systems of simultaneous algebraic equations. Banded, frontal and column (skyline) solvers were studied as well as solvers that can partition the working area and thus could fit into any available core. Comparison timings are presented for several typical two dimensional and three dimensional continuum type grids of elements with and without midside nodes. Extensive conclusions are also given.

Fault tolerance in an inner-outer solver: A GVR-enabled case study

DOE PAGES

Zhang, Ziming; Chien, Andrew A.; Teranishi, Keita

2015-04-18

Resilience is a major challenge for large-scale systems. It is particularly important for iterative linear solvers, since they take much of the time of many scientific applications. We show that single bit flip errors in the Flexible GMRES iterative linear solver can lead to high computational overhead or even failure to converge to the right answer. Informed by these results, we design and evaluate several strategies for fault tolerance in both inner and outer solvers appropriate across a range of error rates. We implement them, extending Trilinos’ solver library with the Global View Resilience (GVR) programming model, which provides multi-streammore » snapshots, multi-version data structures with portable and rich error checking/recovery. Lastly, experimental results validate correct execution with low performance overhead under varied error conditions.« less

Integer programming of cement distribution by train

NASA Astrophysics Data System (ADS)

Indarsih

2018-01-01

Cement industry in Central Java distributes cement by train to meet daily demand in Yogyakarta and Central Java area. There are five destination stations. For each destination station, there is a warehouse to load cements. Decision maker of cement industry have a plan to redesign the infrastructure and transportation system. The aim is to determine how many locomotives, train wagons, and containers and how to arrange train schedules with subject to the delivery time. For this purposes, we consider an integer programming to minimize the total of operational cost. Further, we will discuss a case study and the solution the problem can be calculated by LINGO software.

Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

DOE PAGES

Gade, Dinakar; Hackebeil, Gabriel; Ryan, Sarah M.; ...

2016-04-02

We present a method for computing lower bounds in the progressive hedging algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using dual prices that are calculated during execution of the standard PHA. In conclusion, we report computational results on stochastic unit commitment and stochastic server location problem instances, and explore the relationship between key PHA parameters and the quality of the resulting lower bounds.

A User's Manual for ROTTILT Solver: Tiltrotor Fountain Flow Field Prediction

NASA Technical Reports Server (NTRS)

Tadghighi, Hormoz; Rajagopalan, R. Ganesh

1999-01-01

A CFD solver has been developed to provide the time averaged details of the fountain flow typical for tiltrotor aircraft in hover. This Navier-Stokes solver, designated as ROTTILT, assumes the 3-D fountain flowfield to be steady and incompressible. The theoretical background is described in this manual. In order to enable the rotor trim solution in the presence of tiltrotor aircraft components such as wing, nacelle, and fuselage, the solver is coupled with a set of trim routines which are highly efficient in CPU and suitable for CFD analysis. The Cartesian grid technique utilized provides the user with a unique capability for insertion or elimination of any components of the bodies considered for a given tiltrotor aircraft configuration. The flowfield associated with either a semi or full-span configuration can be computed through user options in the ROTTILT input file. Full details associated with the numerical solution implemented in ROTTILT and assumptions are presented. A description of input surface mesh topology is provided in the appendices along with a listing of all preprocessor programs. Input variable definitions and default values are provided for the V22 aircraft. Limited predicted results using the coupled ROTTILT/WOPWOP program for the V22 in hover are made and compared with measurement. To visualize the V22 aircraft and predictions, a preprocessor graphics program GNU-PLOT3D was used. This program is described and example graphic results presented.

Sequential computation of elementary modes and minimal cut sets in genome-scale metabolic networks using alternate integer linear programming.

PubMed

Song, Hyun-Seob; Goldberg, Noam; Mahajan, Ashutosh; Ramkrishna, Doraiswami

2017-08-01

Elementary (flux) modes (EMs) have served as a valuable tool for investigating structural and functional properties of metabolic networks. Identification of the full set of EMs in genome-scale networks remains challenging due to combinatorial explosion of EMs in complex networks. It is often, however, that only a small subset of relevant EMs needs to be known, for which optimization-based sequential computation is a useful alternative. Most of the currently available methods along this line are based on the iterative use of mixed integer linear programming (MILP), the effectiveness of which significantly deteriorates as the number of iterations builds up. To alleviate the computational burden associated with the MILP implementation, we here present a novel optimization algorithm termed alternate integer linear programming (AILP). Our algorithm was designed to iteratively solve a pair of integer programming (IP) and linear programming (LP) to compute EMs in a sequential manner. In each step, the IP identifies a minimal subset of reactions, the deletion of which disables all previously identified EMs. Thus, a subsequent LP solution subject to this reaction deletion constraint becomes a distinct EM. In cases where no feasible LP solution is available, IP-derived reaction deletion sets represent minimal cut sets (MCSs). Despite the additional computation of MCSs, AILP achieved significant time reduction in computing EMs by orders of magnitude. The proposed AILP algorithm not only offers a computational advantage in the EM analysis of genome-scale networks, but also improves the understanding of the linkage between EMs and MCSs. The software is implemented in Matlab, and is provided as supplementary information . hyunseob.song@pnnl.gov. Supplementary data are available at Bioinformatics online. Published by Oxford University Press 2017. This work is written by US Government employees and are in the public domain in the US.

Environment-Aware Production Scheduling for Paint Shops in Automobile Manufacturing: A Multi-Objective Optimization Approach

PubMed Central

Zhang, Rui

2017-01-01

The traditional way of scheduling production processes often focuses on profit-driven goals (such as cycle time or material cost) while tending to overlook the negative impacts of manufacturing activities on the environment in the form of carbon emissions and other undesirable by-products. To bridge the gap, this paper investigates an environment-aware production scheduling problem that arises from a typical paint shop in the automobile manufacturing industry. In the studied problem, an objective function is defined to minimize the emission of chemical pollutants caused by the cleaning of painting devices which must be performed each time before a color change occurs. Meanwhile, minimization of due date violations in the downstream assembly shop is also considered because the two shops are interrelated and connected by a limited-capacity buffer. First, we have developed a mixed-integer programming formulation to describe this bi-objective optimization problem. Then, to solve problems of practical size, we have proposed a novel multi-objective particle swarm optimization (MOPSO) algorithm characterized by problem-specific improvement strategies. A branch-and-bound algorithm is designed for accurately assessing the most promising solutions. Finally, extensive computational experiments have shown that the proposed MOPSO is able to match the solution quality of an exact solver on small instances and outperform two state-of-the-art multi-objective optimizers in literature on large instances with up to 200 cars. PMID:29295603

Environment-Aware Production Schedulingfor Paint Shops in Automobile Manufacturing: A Multi-Objective Optimization Approach.

PubMed

Zhang, Rui

2017-12-25

The traditional way of scheduling production processes often focuses on profit-driven goals (such as cycle time or material cost) while tending to overlook the negative impacts of manufacturing activities on the environment in the form of carbon emissions and other undesirable by-products. To bridge the gap, this paper investigates an environment-aware production scheduling problem that arises from a typical paint shop in the automobile manufacturing industry. In the studied problem, an objective function is defined to minimize the emission of chemical pollutants caused by the cleaning of painting devices which must be performed each time before a color change occurs. Meanwhile, minimization of due date violations in the downstream assembly shop is also considered because the two shops are interrelated and connected by a limited-capacity buffer. First, we have developed a mixed-integer programming formulation to describe this bi-objective optimization problem. Then, to solve problems of practical size, we have proposed a novel multi-objective particle swarm optimization (MOPSO) algorithm characterized by problem-specific improvement strategies. A branch-and-bound algorithm is designed for accurately assessing the most promising solutions. Finally, extensive computational experiments have shown that the proposed MOPSO is able to match the solution quality of an exact solver on small instances and outperform two state-of-the-art multi-objective optimizers in literature on large instances with up to 200 cars.

Short-term bulk energy storage system scheduling for load leveling in unit commitment: modeling, optimization, and sensitivity analysis

PubMed Central

Hemmati, Reza; Saboori, Hedayat

2016-01-01

Energy storage systems (ESSs) have experienced a very rapid growth in recent years and are expected to be a promising tool in order to improving power system reliability and being economically efficient. The ESSs possess many potential benefits in various areas in the electric power systems. One of the main benefits of an ESS, especially a bulk unit, relies on smoothing the load pattern by decreasing on-peak and increasing off-peak loads, known as load leveling. These devices require new methods and tools in order to model and optimize their effects in the power system studies. In this respect, this paper will model bulk ESSs based on the several technical characteristics, introduce the proposed model in the thermal unit commitment (UC) problem, and analyze it with respect to the various sensitive parameters. The technical limitations of the thermal units and transmission network constraints are also considered in the model. The proposed model is a Mixed Integer Linear Programming (MILP) which can be easily solved by strong commercial solvers (for instance CPLEX) and it is appropriate to be used in the practical large scale networks. The results of implementing the proposed model on a test system reveal that proper load leveling through optimum storage scheduling leads to considerable operation cost reduction with respect to the storage system characteristics. PMID:27222741

Prepositioning emergency supplies under uncertainty: a parametric optimization method

NASA Astrophysics Data System (ADS)

Bai, Xuejie; Gao, Jinwu; Liu, Yankui

2018-07-01

Prepositioning of emergency supplies is an effective method for increasing preparedness for disasters and has received much attention in recent years. In this article, the prepositioning problem is studied by a robust parametric optimization method. The transportation cost, supply, demand and capacity are unknown prior to the extraordinary event, which are represented as fuzzy parameters with variable possibility distributions. The variable possibility distributions are obtained through the credibility critical value reduction method for type-2 fuzzy variables. The prepositioning problem is formulated as a fuzzy value-at-risk model to achieve a minimum total cost incurred in the whole process. The key difficulty in solving the proposed optimization model is to evaluate the quantile of the fuzzy function in the objective and the credibility in the constraints. The objective function and constraints can be turned into their equivalent parametric forms through chance constrained programming under the different confidence levels. Taking advantage of the structural characteristics of the equivalent optimization model, a parameter-based domain decomposition method is developed to divide the original optimization problem into six mixed-integer parametric submodels, which can be solved by standard optimization solvers. Finally, to explore the viability of the developed model and the solution approach, some computational experiments are performed on realistic scale case problems. The computational results reported in the numerical example show the credibility and superiority of the proposed parametric optimization method.

Short-term bulk energy storage system scheduling for load leveling in unit commitment: modeling, optimization, and sensitivity analysis.

PubMed

Hemmati, Reza; Saboori, Hedayat

2016-05-01

Energy storage systems (ESSs) have experienced a very rapid growth in recent years and are expected to be a promising tool in order to improving power system reliability and being economically efficient. The ESSs possess many potential benefits in various areas in the electric power systems. One of the main benefits of an ESS, especially a bulk unit, relies on smoothing the load pattern by decreasing on-peak and increasing off-peak loads, known as load leveling. These devices require new methods and tools in order to model and optimize their effects in the power system studies. In this respect, this paper will model bulk ESSs based on the several technical characteristics, introduce the proposed model in the thermal unit commitment (UC) problem, and analyze it with respect to the various sensitive parameters. The technical limitations of the thermal units and transmission network constraints are also considered in the model. The proposed model is a Mixed Integer Linear Programming (MILP) which can be easily solved by strong commercial solvers (for instance CPLEX) and it is appropriate to be used in the practical large scale networks. The results of implementing the proposed model on a test system reveal that proper load leveling through optimum storage scheduling leads to considerable operation cost reduction with respect to the storage system characteristics.

Optimizing communication satellites payload configuration with exact approaches

NASA Astrophysics Data System (ADS)

Stathakis, Apostolos; Danoy, Grégoire; Bouvry, Pascal; Talbi, El-Ghazali; Morelli, Gianluigi

2015-12-01

The satellite communications market is competitive and rapidly evolving. The payload, which is in charge of applying frequency conversion and amplification to the signals received from Earth before their retransmission, is made of various components. These include reconfigurable switches that permit the re-routing of signals based on market demand or because of some hardware failure. In order to meet modern requirements, the size and the complexity of current communication payloads are increasing significantly. Consequently, the optimal payload configuration, which was previously done manually by the engineers with the use of computerized schematics, is now becoming a difficult and time consuming task. Efficient optimization techniques are therefore required to find the optimal set(s) of switch positions to optimize some operational objective(s). In order to tackle this challenging problem for the satellite industry, this work proposes two Integer Linear Programming (ILP) models. The first one is single-objective and focuses on the minimization of the length of the longest channel path, while the second one is bi-objective and additionally aims at minimizing the number of switch changes in the payload switch matrix. Experiments are conducted on a large set of instances of realistic payload sizes using the CPLEX® solver and two well-known exact multi-objective algorithms. Numerical results demonstrate the efficiency and limitations of the ILP approach on this real-world problem.

Combinatorial codon scrambling enables scalable gene synthesis and amplification of repetitive proteins

NASA Astrophysics Data System (ADS)

Tang, Nicholas C.; Chilkoti, Ashutosh

2016-04-01

Most genes are synthesized using seamless assembly methods that rely on the polymerase chain reaction (PCR). However, PCR of genes encoding repetitive proteins either fails or generates nonspecific products. Motivated by the need to efficiently generate new protein polymers through high-throughput gene synthesis, here we report a codon-scrambling algorithm that enables the PCR-based gene synthesis of repetitive proteins by exploiting the codon redundancy of amino acids and finding the least-repetitive synonymous gene sequence. We also show that the codon-scrambling problem is analogous to the well-known travelling salesman problem, and obtain an exact solution to it by using De Bruijn graphs and a modern mixed integer linear programme solver. As experimental proof of the utility of this approach, we use it to optimize the synthetic genes for 19 repetitive proteins, and show that the gene fragments are amenable to PCR-based gene assembly and recombinant expression.

AFMPB: An adaptive fast multipole Poisson-Boltzmann solver for calculating electrostatics in biomolecular systems

NASA Astrophysics Data System (ADS)

Lu, Benzhuo; Cheng, Xiaolin; Huang, Jingfang; McCammon, J. Andrew

2010-06-01

A Fortran program package is introduced for rapid evaluation of the electrostatic potentials and forces in biomolecular systems modeled by the linearized Poisson-Boltzmann equation. The numerical solver utilizes a well-conditioned boundary integral equation (BIE) formulation, a node-patch discretization scheme, a Krylov subspace iterative solver package with reverse communication protocols, and an adaptive new version of fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related libraries and utility tools are available at http://lsec.cc.ac.cn/~lubz/afmpb.html and a mirror site at http://mccammon.ucsd.edu/. This paper is a brief summary of the program: the algorithms, the implementation and the usage. Program summaryProgram title: AFMPB: Adaptive fast multipole Poisson-Boltzmann solver Catalogue identifier: AEGB_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGB_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL 2.0 No. of lines in distributed program, including test data, etc.: 453 649 No. of bytes in distributed program, including test data, etc.: 8 764 754 Distribution format: tar.gz Programming language: Fortran Computer: Any Operating system: Any RAM: Depends on the size of the discretized biomolecular system Classification: 3 External routines: Pre- and post-processing tools are required for generating the boundary elements and for visualization. Users can use MSMS ( http://www.scripps.edu/~sanner/html/msms_home.html) for pre-processing, and VMD ( http://www.ks.uiuc.edu/Research/vmd/) for visualization. Sub-programs included: An iterative Krylov subspace solvers package from SPARSKIT by Yousef Saad ( http://www-users.cs.umn.edu/~saad/software/SPARSKIT/sparskit.html), and the fast multipole methods subroutines from FMMSuite ( http://www.fastmultipole.org/). Nature of problem: Numerical solution of the linearized Poisson-Boltzmann equation that describes electrostatic interactions of molecular systems in ionic solutions. Solution method: A novel node-patch scheme is used to discretize the well-conditioned boundary integral equation formulation of the linearized Poisson-Boltzmann equation. Various Krylov subspace solvers can be subsequently applied to solve the resulting linear system, with a bounded number of iterations independent of the number of discretized unknowns. The matrix-vector multiplication at each iteration is accelerated by the adaptive new versions of fast multipole methods. The AFMPB solver requires other stand-alone pre-processing tools for boundary mesh generation, post-processing tools for data analysis and visualization, and can be conveniently coupled with different time stepping methods for dynamics simulation. Restrictions: Only three or six significant digits options are provided in this version. Unusual features: Most of the codes are in Fortran77 style. Memory allocation functions from Fortran90 and above are used in a few subroutines. Additional comments: The current version of the codes is designed and written for single core/processor desktop machines. Check http://lsec.cc.ac.cn/~lubz/afmpb.html and http://mccammon.ucsd.edu/ for updates and changes. Running time: The running time varies with the number of discretized elements ( N) in the system and their distributions. In most cases, it scales linearly as a function of N.

An Advanced simulation Code for Modeling Inductive Output Tubes

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

Thuc Bui; R. Lawrence Ives

2012-04-27

During the Phase I program, CCR completed several major building blocks for a 3D large signal, inductive output tube (IOT) code using modern computer language and programming techniques. These included a 3D, Helmholtz, time-harmonic, field solver with a fully functional graphical user interface (GUI), automeshing and adaptivity. Other building blocks included the improved electrostatic Poisson solver with temporal boundary conditions to provide temporal fields for the time-stepping particle pusher as well as the self electric field caused by time-varying space charge. The magnetostatic field solver was also updated to solve for the self magnetic field caused by time changing currentmore » density in the output cavity gap. The goal function to optimize an IOT cavity was also formulated, and the optimization methodologies were investigated.« less

Mixed Integer Programming Model and Incremental Optimization for Delivery and Storage Planning Using Truck Terminals

NASA Astrophysics Data System (ADS)

Sakakibara, Kazutoshi; Tian, Yajie; Nishikawa, Ikuko

We discuss the planning of transportation by trucks over a multi-day period. Each truck collects loads from suppliers and delivers them to assembly plants or a truck terminal. By exploiting the truck terminal as a temporal storage, we aim to increase the load ratio of each truck and to minimize the lead time for transportation. In this paper, we show a mixed integer programming model which represents each product explicitly, and discuss the decomposition of the problem into a problem of delivery and storage, and a problem of vehicle routing. Based on this model, we propose a relax-and-fix type heuristic in which decision variables are fixed one by one by mathematical programming techniques such as branch-and-bound methods.

Nearly Interactive Parabolized Navier-Stokes Solver for High Speed Forebody and Inlet Flows

NASA Technical Reports Server (NTRS)

Benson, Thomas J.; Liou, May-Fun; Jones, William H.; Trefny, Charles J.

2009-01-01

A system of computer programs is being developed for the preliminary design of high speed inlets and forebodies. The system comprises four functions: geometry definition, flow grid generation, flow solver, and graphics post-processor. The system runs on a dedicated personal computer using the Windows operating system and is controlled by graphical user interfaces written in MATLAB (The Mathworks, Inc.). The flow solver uses the Parabolized Navier-Stokes equations to compute millions of mesh points in several minutes. Sample two-dimensional and three-dimensional calculations are demonstrated in the paper.

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

PubMed

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

2018-01-01

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

A chance-constrained stochastic approach to intermodal container routing problems

PubMed Central

Zhao, Yi; Zhang, Xi; Whiteing, Anthony

2018-01-01

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

Edit distance for marked point processes revisited: An implementation by binary integer programming

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

Hirata, Yoshito; Aihara, Kazuyuki

2015-12-15

We implement the edit distance for marked point processes [Suzuki et al., Int. J. Bifurcation Chaos 20, 3699–3708 (2010)] as a binary integer program. Compared with the previous implementation using minimum cost perfect matching, the proposed implementation has two advantages: first, by using the proposed implementation, we can apply a wide variety of software and hardware, even spin glasses and coherent ising machines, to calculate the edit distance for marked point processes; second, the proposed implementation runs faster than the previous implementation when the difference between the numbers of events in two time windows for a marked point process ismore » large.« less

SSP: an interval integer linear programming for de novo transcriptome assembly and isoform discovery of RNA-seq reads.

PubMed

Safikhani, Zhaleh; Sadeghi, Mehdi; Pezeshk, Hamid; Eslahchi, Changiz

2013-01-01

Recent advances in the sequencing technologies have provided a handful of RNA-seq datasets for transcriptome analysis. However, reconstruction of full-length isoforms and estimation of the expression level of transcripts with a low cost are challenging tasks. We propose a novel de novo method named SSP that incorporates interval integer linear programming to resolve alternatively spliced isoforms and reconstruct the whole transcriptome from short reads. Experimental results show that SSP is fast and precise in determining different alternatively spliced isoforms along with the estimation of reconstructed transcript abundances. The SSP software package is available at http://www.bioinf.cs.ipm.ir/software/ssp. © 2013.

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.

Integer Linear Programming in Computational Biology

NASA Astrophysics Data System (ADS)

Althaus, Ernst; Klau, Gunnar W.; Kohlbacher, Oliver; Lenhof, Hans-Peter; Reinert, Knut

Computational molecular biology (bioinformatics) is a young research field that is rich in NP-hard optimization problems. The problem instances encountered are often huge and comprise thousands of variables. Since their introduction into the field of bioinformatics in 1997, integer linear programming (ILP) techniques have been successfully applied to many optimization problems. These approaches have added much momentum to development and progress in related areas. In particular, ILP-based approaches have become a standard optimization technique in bioinformatics. In this review, we present applications of ILP-based techniques developed by members and former members of Kurt Mehlhorn’s group. These techniques were introduced to bioinformatics in a series of papers and popularized by demonstration of their effectiveness and potential.

Integer programming applications: Bond trading, mortgage backed security financing, and FASB 115 accounting

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

Nauss, R.

1994-12-31

In this review we describe three integer programming applications involving fixed income securities. A bond trading model is presented that features a number of possible different objectives and collections of constraints including future interest rate scenarios. A mortgage backed security (MBS) financing model that accounts for potential defaults in the MBS is also presented. Finally we describe an approach to allocate collections of bank securities into three categories: hold to maturity, available for sale, or trading. Placement of securities in these categories affects the capital, net income, and liquidity of a bank according to new accounting rules promulgated by themore » Financial Accounting Standards Board.« less

Screening synteny blocks in pairwise genome comparisons through integer programming.

PubMed

Tang, Haibao; Lyons, Eric; Pedersen, Brent; Schnable, James C; Paterson, Andrew H; Freeling, Michael

2011-04-18

It is difficult to accurately interpret chromosomal correspondences such as true orthology and paralogy due to significant divergence of genomes from a common ancestor. Analyses are particularly problematic among lineages that have repeatedly experienced whole genome duplication (WGD) events. To compare multiple "subgenomes" derived from genome duplications, we need to relax the traditional requirements of "one-to-one" syntenic matchings of genomic regions in order to reflect "one-to-many" or more generally "many-to-many" matchings. However this relaxation may result in the identification of synteny blocks that are derived from ancient shared WGDs that are not of interest. For many downstream analyses, we need to eliminate weak, low scoring alignments from pairwise genome comparisons. Our goal is to objectively select subset of synteny blocks whose total scores are maximized while respecting the duplication history of the genomes in comparison. We call this "quota-based" screening of synteny blocks in order to appropriately fill a quota of syntenic relationships within one genome or between two genomes having WGD events. We have formulated the synteny block screening as an optimization problem known as "Binary Integer Programming" (BIP), which is solved using existing linear programming solvers. The computer program QUOTA-ALIGN performs this task by creating a clear objective function that maximizes the compatible set of synteny blocks under given constraints on overlaps and depths (corresponding to the duplication history in respective genomes). Such a procedure is useful for any pairwise synteny alignments, but is most useful in lineages affected by multiple WGDs, like plants or fish lineages. For example, there should be a 1:2 ploidy relationship between genome A and B if genome B had an independent WGD subsequent to the divergence of the two genomes. We show through simulations and real examples using plant genomes in the rosid superorder that the quota-based screening can eliminate ambiguous synteny blocks and focus on specific genomic evolutionary events, like the divergence of lineages (in cross-species comparisons) and the most recent WGD (in self comparisons). The QUOTA-ALIGN algorithm screens a set of synteny blocks to retain only those compatible with a user specified ploidy relationship between two genomes. These blocks, in turn, may be used for additional downstream analyses such as identifying true orthologous regions in interspecific comparisons. There are two major contributions of QUOTA-ALIGN: 1) reducing the block screening task to a BIP problem, which is novel; 2) providing an efficient software pipeline starting from all-against-all BLAST to the screened synteny blocks with dot plot visualizations. Python codes and full documentations are publicly available http://github.com/tanghaibao/quota-alignment. QUOTA-ALIGN program is also integrated as a major component in SynMap http://genomevolution.com/CoGe/SynMap.pl, offering easier access to thousands of genomes for non-programmers. © 2011 Tang et al; licensee BioMed Central Ltd.

Intelligent Tutoring for Programming Tasks: Using Plan Analysis to Generate Better Hints.

DTIC Science & Technology

1982-03-01

construction and execution of a BASIC proqram that assiqns an integer value to a variable and then prints the value of that integer. - ARTICHOKE : assign...the string " ARTICHOKE " to a string variable, assiqn the value of that variable to a second variable, and print the second variable. -SINOP: qet two...the first five tasks: GREENFLAG, ARTICHOKE , SINOP, NINOP, and TWOS. Because the protocols are very lonq, it was necessary to condense them into a

Determining the Surface-to-Air Missile Requirement for Western and Southern Part of the Turkish Air Defense System

DTIC Science & Technology

2008-03-01

been shown to yield success in such applications as well. ( Daskin ,1995). LP optimization, matrix row reduction, a combination of both, or cutting...integer solution (Current, 2002). If the LP relaxation of the SCLP results in a fractional solution, Current, Daskin , and Schilling (2002) recommend...coverage for a given number of SAM sites. The model is formulated as an integer program, and the LINGO 10 software package is used to solve the model

Aerospace applications of integer and combinatorial optimization

NASA Technical Reports Server (NTRS)

Padula, S. L.; Kincaid, R. K.

1995-01-01

Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in solving combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem, for example, seeks the optimal locations for vibration-damping devices on a large space structure and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.

Results of the Clarus Regional Demonstrations : Evaluation of Enhanced Road Weather Forecasting

DOT National Transportation Integrated Search

2012-01-01

The Clarus Initiative is a research effort of the U.S. Department of Transportation Intelligent Transportation Systems Joint Program Office and the Federal Highway Administrations Road Weather Management Program to develop and demonstrate an integ...

Operations research applications in nuclear energy

NASA Astrophysics Data System (ADS)

Johnson, Benjamin Lloyd

This dissertation consists of three papers; the first is published in Annals of Operations Research, the second is nearing submission to INFORMS Journal on Computing, and the third is the predecessor of a paper nearing submission to Progress in Nuclear Energy. We apply operations research techniques to nuclear waste disposal and nuclear safeguards. Although these fields are different, they allow us to showcase some benefits of using operations research techniques to enhance nuclear energy applications. The first paper, "Optimizing High-Level Nuclear Waste Disposal within a Deep Geologic Repository," presents a mixed-integer programming model that determines where to place high-level nuclear waste packages in a deep geologic repository to minimize heat load concentration. We develop a heuristic that increases the size of solvable model instances. The second paper, "Optimally Configuring a Measurement System to Detect Diversions from a Nuclear Fuel Cycle," introduces a simulation-optimization algorithm and an integer-programming model to find the best, or near-best, resource-limited nuclear fuel cycle measurement system with a high degree of confidence. Given location-dependent measurement method precisions, we (i) optimize the configuration of n methods at n locations of a hypothetical nuclear fuel cycle facility, (ii) find the most important location at which to improve method precision, and (iii) determine the effect of measurement frequency on near-optimal configurations and objective values. Our results correspond to existing outcomes but we obtain them at least an order of magnitude faster. The third paper, "Optimizing Nuclear Material Control and Accountability Measurement Systems," extends the integer program from the second paper to locate measurement methods in a larger, hypothetical nuclear fuel cycle scenario given fixed purchase and utilization budgets. This paper also presents two mixed-integer quadratic programming models to increase the precision of existing methods given a fixed improvement budget and to reduce the measurement uncertainty in the system while limiting improvement costs. We quickly obtain similar or better solutions compared to several intuitive analyses that take much longer to perform.

Investigating Integer Restrictions in Linear Programming

ERIC Educational Resources Information Center

Edwards, Thomas G.; Chelst, Kenneth R.; Principato, Angela M.; Wilhelm, Thad L.

2015-01-01

Linear programming (LP) is an application of graphing linear systems that appears in many Algebra 2 textbooks. Although not explicitly mentioned in the Common Core State Standards for Mathematics, linear programming blends seamlessly into modeling with mathematics, the fourth Standard for Mathematical Practice (CCSSI 2010, p. 7). In solving a…

The Retrofit Puzzle Extended: Optimal Fleet Owner Behavior over Multiple Time Periods

DOT National Transportation Integrated Search

2009-08-04

In "The Retrofit Puzzle: Optimal Fleet Owner Behavior in the Context of Diesel Retrofit Incentive Programs" (1) an integer program was developed to model profit-maximizing diesel fleet owner behavior when selecting pollution reduction retrofits. Flee...

System and method for modeling and analyzing complex scenarios

DOEpatents

Shevitz, Daniel Wolf

2013-04-09

An embodiment of the present invention includes a method for analyzing and solving possibility tree. A possibility tree having a plurality of programmable nodes is constructed and solved with a solver module executed by a processor element. The solver module executes the programming of said nodes, and tracks the state of at least a variable through a branch. When a variable of said branch is out of tolerance with a parameter, the solver disables remaining nodes of the branch and marks the branch as an invalid solution. The valid solutions are then aggregated and displayed as valid tree solutions.

Box truss analysis and technology development. Task 1: Mesh analysis and control

NASA Technical Reports Server (NTRS)

Bachtell, E. E.; Bettadapur, S. S.; Coyner, J. V.

1985-01-01

An analytical tool was developed to model, analyze and predict RF performance of box truss antennas with reflective mesh surfaces. The analysis system is unique in that it integrates custom written programs for cord tied mesh surfaces, thereby drastically reducing the cost of analysis. The analysis system is capable of determining the RF performance of antennas under any type of manufacturing or operating environment by integrating together the various disciplines of design, finite element analysis, surface best fit analysis and RF analysis. The Integrated Mesh Analysis System consists of six separate programs: The Mesh Tie System Model Generator, The Loadcase Generator, The Model Optimizer, The Model Solver, The Surface Topography Solver and The RF Performance Solver. Additionally, a study using the mesh analysis system was performed to determine the effect of on orbit calibration, i.e., surface adjustment, on a typical box truss antenna.

CAPRI (Computational Analysis PRogramming Interface): A Solid Modeling Based Infra-Structure for Engineering Analysis and Design Simulations

NASA Technical Reports Server (NTRS)

Haimes, Robert; Follen, Gregory J.

1998-01-01

CAPRI is a CAD-vendor neutral application programming interface designed for the construction of analysis and design systems. By allowing access to the geometry from within all modules (grid generators, solvers and post-processors) such tasks as meshing on the actual surfaces, node enrichment by solvers and defining which mesh faces are boundaries (for the solver and visualization system) become simpler. The overall reliance on file 'standards' is minimized. This 'Geometry Centric' approach makes multi-physics (multi-disciplinary) analysis codes much easier to build. By using the shared (coupled) surface as the foundation, CAPRI provides a single call to interpolate grid-node based data from the surface discretization in one volume to another. Finally, design systems are possible where the results can be brought back into the CAD system (and therefore manufactured) because all geometry construction and modification are performed using the CAD system's geometry kernel.

TADS: A CFD-based turbomachinery and analysis design system with GUI. Volume 2: User's manual

NASA Technical Reports Server (NTRS)

Myers, R. A.; Topp, D. A.; Delaney, R. A.

1995-01-01

The primary objective of this study was the development of a computational fluid dynamics (CFD) based turbomachinery airfoil analysis and design system, controlled by a graphical user interface (GUI). The computer codes resulting from this effort are referred to as the Turbomachinery Analysis and Design System (TADS). This document is intended to serve as a user's manual for the computer programs which comprise the TADS system. TADS couples a throughflow solver (ADPAC) with a quasi-3D blade-to-blade solver (RVCQ3D) in an interactive package. Throughflow analysis capability was developed in ADPAC through the addition of blade force and blockage terms to the governing equations. A GUI was developed to simplify user input and automate the many tasks required to perform turbomachinery analysis and design. The coupling of various programs was done in a way that alternative solvers or grid generators could be easily incorporated into the TADS framework.

NEWTONP - CUMULATIVE BINOMIAL PROGRAMS

NASA Technical Reports Server (NTRS)

Bowerman, P. N.

1994-01-01

The cumulative binomial program, NEWTONP, is one of a set of three programs which calculate cumulative binomial probability distributions for arbitrary inputs. The three programs, NEWTONP, CUMBIN (NPO-17555), and CROSSER (NPO-17557), can be used independently of one another. NEWTONP can be used by statisticians and users of statistical procedures, test planners, designers, and numerical analysts. The program has been used for reliability/availability calculations. NEWTONP calculates the probably p required to yield a given system reliability V for a k-out-of-n system. It can also be used to determine the Clopper-Pearson confidence limits (either one-sided or two-sided) for the parameter p of a Bernoulli distribution. NEWTONP can determine Bayesian probability limits for a proportion (if the beta prior has positive integer parameters). It can determine the percentiles of incomplete beta distributions with positive integer parameters. It can also determine the percentiles of F distributions and the midian plotting positions in probability plotting. NEWTONP is designed to work well with all integer values 0 < k <= n. To run the program, the user simply runs the executable version and inputs the information requested by the program. NEWTONP is not designed to weed out incorrect inputs, so the user must take care to make sure the inputs are correct. Once all input has been entered, the program calculates and lists the result. It also lists the number of iterations of Newton's method required to calculate the answer within the given error. The NEWTONP program is written in C. It was developed on an IBM AT with a numeric co-processor using Microsoft C 5.0. Because the source code is written using standard C structures and functions, it should compile correctly with most C compilers. The program format is interactive. It has been implemented under DOS 3.2 and has a memory requirement of 26K. NEWTONP was developed in 1988.

HAL/S programmer's guide. [space shuttle flight software language

NASA Technical Reports Server (NTRS)

Newbold, P. M.; Hotz, R. L.

1974-01-01

HAL/S is a programming language developed to satisfy the flight software requirements for the space shuttle program. The user's guide explains pertinent language operating procedures and described the various HAL/S facilities for manipulating integer, scalar, vector, and matrix data types.

Are you ready? Managing transportation resources through the Y2K weekend

DOT National Transportation Integrated Search

2011-01-01

The Clarus Initiative, a joint effort of the U.S. Department of Transportation Intelligent Transportation Systems (ITS) Joint Program Office and FHWAs Road Weather Management Program (RWMP), is a six-year effort to develop and demonstrate an integ...

Inexact fuzzy-stochastic mixed-integer programming approach for long-term planning of waste management--Part A: methodology.

PubMed

Guo, P; Huang, G H

2009-01-01

In this study, an inexact fuzzy chance-constrained two-stage mixed-integer linear programming (IFCTIP) approach is proposed for supporting long-term planning of waste-management systems under multiple uncertainties in the City of Regina, Canada. The method improves upon the existing inexact two-stage programming and mixed-integer linear programming techniques by incorporating uncertainties expressed as multiple uncertainties of intervals and dual probability distributions within a general optimization framework. The developed method can provide an effective linkage between the predefined environmental policies and the associated economic implications. Four special characteristics of the proposed method make it unique compared with other optimization techniques that deal with uncertainties. Firstly, it provides a linkage to predefined policies that have to be respected when a modeling effort is undertaken; secondly, it is useful for tackling uncertainties presented as intervals, probabilities, fuzzy sets and their incorporation; thirdly, it facilitates dynamic analysis for decisions of facility-expansion planning and waste-flow allocation within a multi-facility, multi-period, multi-level, and multi-option context; fourthly, the penalties are exercised with recourse against any infeasibility, which permits in-depth analyses of various policy scenarios that are associated with different levels of economic consequences when the promised solid waste-generation rates are violated. In a companion paper, the developed method is applied to a real case for the long-term planning of waste management in the City of Regina, Canada.

An introduction to the COLIN optimization interface.

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

Hart, William Eugene

2003-03-01

We describe COLIN, a Common Optimization Library INterface for C++. COLIN provides C++ template classes that define a generic interface for both optimization problems and optimization solvers. COLIN is specifically designed to facilitate the development of hybrid optimizers, for which one optimizer calls another to solve an optimization subproblem. We illustrate the capabilities of COLIN with an example of a memetic genetic programming solver.

A general multiblock Euler code for propulsion integration. Volume 1: Theory document

NASA Technical Reports Server (NTRS)

Chen, H. C.; Su, T. Y.; Kao, T. J.

1991-01-01

A general multiblock Euler solver was developed for the analysis of flow fields over geometrically complex configurations either in free air or in a wind tunnel. In this approach, the external space around a complex configuration was divided into a number of topologically simple blocks, so that surface-fitted grids and an efficient flow solution algorithm could be easily applied in each block. The computational grid in each block is generated using a combination of algebraic and elliptic methods. A grid generation/flow solver interface program was developed to facilitate the establishment of block-to-block relations and the boundary conditions for each block. The flow solver utilizes a finite volume formulation and an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. The generality of the method was demonstrated through the analysis of two complex configurations at various flow conditions. Results were compared to available test data. Two accompanying volumes, user manuals for the preparation of multi-block grids (vol. 2) and for the Euler flow solver (vol. 3), provide information on input data format and program execution.

Partial ASL extensions for stochastic programming.

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

Gay, David

2010-03-31

partially completed extensions for stochastic programming to the AMPL/solver interface library (ASL).modeling and experimenting with stochastic recourse problems. This software is not primarily for military applications

GLOBAL SOLUTIONS TO FOLDED CONCAVE PENALIZED NONCONVEX LEARNING

PubMed Central

Liu, Hongcheng; Yao, Tao; Li, Runze

2015-01-01

This paper is concerned with solving nonconvex learning problems with folded concave penalty. Despite that their global solutions entail desirable statistical properties, there lack optimization techniques that guarantee global optimality in a general setting. In this paper, we show that a class of nonconvex learning problems are equivalent to general quadratic programs. This equivalence facilitates us in developing mixed integer linear programming reformulations, which admit finite algorithms that find a provably global optimal solution. We refer to this reformulation-based technique as the mixed integer programming-based global optimization (MIPGO). To our knowledge, this is the first global optimization scheme with a theoretical guarantee for folded concave penalized nonconvex learning with the SCAD penalty (Fan and Li, 2001) and the MCP penalty (Zhang, 2010). Numerical results indicate a significant outperformance of MIPGO over the state-of-the-art solution scheme, local linear approximation, and other alternative solution techniques in literature in terms of solution quality. PMID:27141126

RSM 1.0 user's guide: A resupply scheduler using integer optimization

NASA Technical Reports Server (NTRS)

Viterna, Larry A.; Green, Robert D.; Reed, David M.

1991-01-01

The Resupply Scheduling Model (RSM) is a PC based, fully menu-driven computer program. It uses integer programming techniques to determine an optimum schedule to replace components on or before a fixed replacement period, subject to user defined constraints such as transportation mass and volume limits or available repair crew time. Principal input for RSJ includes properties such as mass and volume and an assembly sequence. Resource constraints are entered for each period corresponding to the component properties. Though written to analyze the electrical power system on the Space Station Freedom, RSM is quite general and can be used to model the resupply of almost any system subject to user defined resource constraints. Presented here is a step by step procedure for preparing the input, performing the analysis, and interpreting the results. Instructions for installing the program and information on the algorithms are given.

An integer programming approach to a real-world recyclable waste collection problem in Argentina.

PubMed

Braier, Gustavo; Durán, Guillermo; Marenco, Javier; Wesner, Francisco

2017-05-01

This article reports on the use of mathematical programming techniques to optimise the routes of a recyclable waste collection system servicing Morón, a large municipality outside Buenos Aires, Argentina. The truck routing problem posed by the system is a particular case of the generalised directed open rural postman problem. An integer programming model is developed with a solving procedure built around a subtour-merging algorithm and the addition of subtour elimination constraints. The route solutions generated by the proposed methodology perform significantly better than the previously used, manually designed routes, the main improvement being that coverage of blocks within the municipality with the model solutions is 100% by construction, whereas with the manual routes as much as 16% of the blocks went unserviced. The model-generated routes were adopted by the municipality in 2014 and the national government is planning to introduce the methodology elsewhere in the country.

Mixed integer nonlinear programming model of wireless pricing scheme with QoS attribute of bandwidth and end-to-end delay

NASA Astrophysics Data System (ADS)

Irmeilyana, Puspita, Fitri Maya; Indrawati

2016-02-01

The pricing for wireless networks is developed by considering linearity factors, elasticity price and price factors. Mixed Integer Nonlinear Programming of wireless pricing model is proposed as the nonlinear programming problem that can be solved optimally using LINGO 13.0. The solutions are expected to give some information about the connections between the acceptance factor and the price. Previous model worked on the model that focuses on bandwidth as the QoS attribute. The models attempt to maximize the total price for a connection based on QoS parameter. The QoS attributes used will be the bandwidth and the end to end delay that affect the traffic. The maximum goal to maximum price is achieved when the provider determine the requirement for the increment or decrement of price change due to QoS change and amount of QoS value.

Synchronizable Series Expressions. Part 2. Overview of the Theory and Implementation.

DTIC Science & Technology

1987-11-01

more running time than shown in the table. because time is eventually required in order to collect the garbage it creates. Program Running ’rime Garbage...possible to simply put an enumerator where it is used.) (loop for x integer from I to 4 collect x) - (lotS* ((x (Eup I :to 4))) (declare (type integer x...below. (loop for x from 1 to 4 and for y = 0 then (1- x) collect (list x y)) - (lotS* ((x (Eup 1 :to 4)) (y (Tprevious (1- x) 0))) (Rlist (list x y

Papers on Program Testing,

DTIC Science & Technology

1979-01-01

tractability for scientific analysis. Although much remains to be learned about mutation as a testing tool, there is a considerable body of written material...explicitly address classifications (2) may not have been affected at all! In general, the and (3) in this article , except to point out that even relative...34 ARTICLE B=B’B C IN CACM 1971). C=C*02 INTEGER AiN),N.F D=B+C INTEGER M.NS.R.I.J.W IF (A.NE.D) GOTO 200 MI PRINT 150 NS=N 150 FORMATIIH .RIGHT ANGLED

The Capability Portfolio Analysis Tool (CPAT): A Mixed Integer Linear Programming Formulation for Fleet Modernization Analysis (Version 2.0.2).

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

Waddell, Lucas; Muldoon, Frank; Henry, Stephen Michael

In order to effectively plan the management and modernization of their large and diverse fleets of vehicles, Program Executive Office Ground Combat Systems (PEO GCS) and Program Executive Office Combat Support and Combat Service Support (PEO CS&CSS) commis- sioned the development of a large-scale portfolio planning optimization tool. This software, the Capability Portfolio Analysis Tool (CPAT), creates a detailed schedule that optimally prioritizes the modernization or replacement of vehicles within the fleet - respecting numerous business rules associated with fleet structure, budgets, industrial base, research and testing, etc., while maximizing overall fleet performance through time. This paper contains a thor-more » ough documentation of the terminology, parameters, variables, and constraints that comprise the fleet management mixed integer linear programming (MILP) mathematical formulation. This paper, which is an update to the original CPAT formulation document published in 2015 (SAND2015-3487), covers the formulation of important new CPAT features.« less

An improved exploratory search technique for pure integer linear programming problems

NASA Technical Reports Server (NTRS)

Fogle, F. R.

1990-01-01

The development is documented of a heuristic method for the solution of pure integer linear programming problems. The procedure draws its methodology from the ideas of Hooke and Jeeves type 1 and 2 exploratory searches, greedy procedures, and neighborhood searches. It uses an efficient rounding method to obtain its first feasible integer point from the optimal continuous solution obtained via the simplex method. Since this method is based entirely on simple addition or subtraction of one to each variable of a point in n-space and the subsequent comparison of candidate solutions to a given set of constraints, it facilitates significant complexity improvements over existing techniques. It also obtains the same optimal solution found by the branch-and-bound technique in 44 of 45 small to moderate size test problems. Two example problems are worked in detail to show the inner workings of the method. Furthermore, using an established weighted scheme for comparing computational effort involved in an algorithm, a comparison of this algorithm is made to the more established and rigorous branch-and-bound method. A computer implementation of the procedure, in PC compatible Pascal, is also presented and discussed.

Selection of actuator locations for static shape control of large space structures by heuristic integer programing

NASA Technical Reports Server (NTRS)

Haftka, R. T.; Adelman, H. M.

1984-01-01

Orbiting spacecraft such as large space antennas have to maintain a highly accurate space to operate satisfactorily. Such structures require active and passive controls to mantain an accurate shape under a variety of disturbances. Methods for the optimum placement of control actuators for correcting static deformations are described. In particular, attention is focused on the case were control locations have to be selected from a large set of available sites, so that integer programing methods are called for. The effectiveness of three heuristic techniques for obtaining a near-optimal site selection is compared. In addition, efficient reanalysis techniques for the rapid assessment of control effectiveness are presented. Two examples are used to demonstrate the methods: a simple beam structure and a 55m space-truss-parabolic antenna.

Developing optimal nurses work schedule using integer programming

NASA Astrophysics Data System (ADS)

Shahidin, Ainon Mardhiyah; Said, Mohd Syazwan Md; Said, Noor Hizwan Mohamad; Sazali, Noor Izatie Amaliena

2017-08-01

Time management is the art of arranging, organizing and scheduling one's time for the purpose of generating more effective work and productivity. Scheduling is the process of deciding how to commit resources between varieties of possible tasks. Thus, it is crucial for every organization to have a good work schedule for their staffs. The job of Ward nurses at hospitals runs for 24 hours every day. Therefore, nurses will be working using shift scheduling. This study is aimed to solve the nurse scheduling problem at an emergency ward of a private hospital. A 7-day work schedule for 7 consecutive weeks satisfying all the constraints set by the hospital will be developed using Integer Programming. The work schedule for the nurses obtained gives an optimal solution where all the constraints are being satisfied successfully.

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.

A solution procedure for mixed-integer nonlinear programming formulation of supply chain planning with quantity discounts under demand uncertainty

NASA Astrophysics Data System (ADS)

Yin, Sisi; Nishi, Tatsushi

2014-11-01

Quantity discount policy is decision-making for trade-off prices between suppliers and manufacturers while production is changeable due to demand fluctuations in a real market. In this paper, quantity discount models which consider selection of contract suppliers, production quantity and inventory simultaneously are addressed. The supply chain planning problem with quantity discounts under demand uncertainty is formulated as a mixed-integer nonlinear programming problem (MINLP) with integral terms. We apply an outer-approximation method to solve MINLP problems. In order to improve the efficiency of the proposed method, the problem is reformulated as a stochastic model replacing the integral terms by using a normalisation technique. We present numerical examples to demonstrate the efficiency of the proposed method.

Advances in mixed-integer programming methods for chemical production scheduling.

PubMed

Velez, Sara; Maravelias, Christos T

2014-01-01

The goal of this paper is to critically review advances in the area of chemical production scheduling over the past three decades and then present two recently proposed solution methods that have led to dramatic computational enhancements. First, we present a general framework and problem classification and discuss modeling and solution methods with an emphasis on mixed-integer programming (MIP) techniques. Second, we present two solution methods: (a) a constraint propagation algorithm that allows us to compute parameters that are then used to tighten MIP scheduling models and (b) a reformulation that introduces new variables, thus leading to effective branching. We also present computational results and an example illustrating how these methods are implemented, as well as the resulting enhancements. We close with a discussion of open research challenges and future research directions.

Engineering the Implementation of Pumped Hydro Energy Storage in the Arizona Power Grid

NASA Astrophysics Data System (ADS)

Dixon, William Jesse J.

This thesis addresses the issue of making an economic case for bulk energy storage in the Arizona bulk power system. Pumped hydro energy storage (PHES) is used in this study. Bulk energy storage has often been suggested for large scale electric power systems in order to levelize load (store energy when it is inexpensive [energy demand is low] and discharge energy when it is expensive [energy demand is high]). It also has the potential to provide opportunities to avoid transmission and generation expansion, and provide for generation reserve margins. As the level of renewable energy resources increases, the uncertainty and variability of wind and solar resources may be improved by bulk energy storage technologies. For this study, the MATLab software platform is used, a mathematical based modeling language, optimization solvers (specifically Gurobi), and a power flow solver (PowerWorld) are used to simulate an economic dispatch problem that includes energy storage and transmission losses. A program is created which utilizes quadratic programming to analyze various cases using a 2010 summer peak load from the Arizona portion of the Western Electricity Coordinating Council (WECC) system. Actual data from industry are used in this test bed. In this thesis, the full capabilities of Gurobi are not utilized (e.g., integer variables, binary variables). However, the formulation shown here does create a platform such that future, more sophisticated modeling may readily be incorporated. The developed software is used to assess the Arizona test bed with a low level of energy storage to study how the storage power limit effects several optimization outputs such as the system wide operating costs. Large levels of energy storage are then added to see how high level energy storage affects peak shaving, load factor, and other system applications. Finally, various constraint relaxations are made to analyze why the applications tested eventually approach a constant value. This research illustrates the use of energy storage which helps minimize the system wide generator operating cost by "shaving" energy off of the peak demand. The thesis builds on the work of another recent researcher with the objectives of strengthening the assumptions used, checking the solutions obtained, utilizing higher level simulation languages to affirm results, and expanding the results and conclusions. One important point not fully discussed in the present thesis is the impact of efficiency in the pumped hydro cycle. The efficiency of the cycle for modern units is estimated at higher than 90%. Inclusion of pumped hydro losses is relegated to future work.

Recent advances in the modeling of plasmas with the Particle-In-Cell methods

NASA Astrophysics Data System (ADS)

Vay, Jean-Luc; Lehe, Remi; Vincenti, Henri; Godfrey, Brendan; Lee, Patrick; Haber, Irv

2015-11-01

The Particle-In-Cell (PIC) approach is the method of choice for self-consistent simulations of plasmas from first principles. The fundamentals of the PIC method were established decades ago but improvements or variations are continuously being proposed. We report on several recent advances in PIC related algorithms, including: (a) detailed analysis of the numerical Cherenkov instability and its remediation, (b) analytic pseudo-spectral electromagnetic solvers in Cartesian and cylindrical (with azimuthal modes decomposition) geometries, (c) arbitrary-order finite-difference and generalized pseudo-spectral Maxwell solvers, (d) novel analysis of Maxwell's solvers' stencil variation and truncation, in application to domain decomposition strategies and implementation of Perfectly Matched Layers in high-order and pseudo-spectral solvers. Work supported by US-DOE Contracts DE-AC02-05CH11231 and the US-DOE SciDAC program ComPASS. Used resources of NERSC, supported by US-DOE Contract DE-AC02-05CH11231.

A divide-and-conquer approach to determine the Pareto frontier for optimization of protein engineering experiments.

PubMed

He, Lu; Friedman, Alan M; Bailey-Kellogg, Chris

2012-03-01

In developing improved protein variants by site-directed mutagenesis or recombination, there are often competing objectives that must be considered in designing an experiment (selecting mutations or breakpoints): stability versus novelty, affinity versus specificity, activity versus immunogenicity, and so forth. Pareto optimal experimental designs make the best trade-offs between competing objectives. Such designs are not "dominated"; that is, no other design is better than a Pareto optimal design for one objective without being worse for another objective. Our goal is to produce all the Pareto optimal designs (the Pareto frontier), to characterize the trade-offs and suggest designs most worth considering, but to avoid explicitly considering the large number of dominated designs. To do so, we develop a divide-and-conquer algorithm, Protein Engineering Pareto FRontier (PEPFR), that hierarchically subdivides the objective space, using appropriate dynamic programming or integer programming methods to optimize designs in different regions. This divide-and-conquer approach is efficient in that the number of divisions (and thus calls to the optimizer) is directly proportional to the number of Pareto optimal designs. We demonstrate PEPFR with three protein engineering case studies: site-directed recombination for stability and diversity via dynamic programming, site-directed mutagenesis of interacting proteins for affinity and specificity via integer programming, and site-directed mutagenesis of a therapeutic protein for activity and immunogenicity via integer programming. We show that PEPFR is able to effectively produce all the Pareto optimal designs, discovering many more designs than previous methods. The characterization of the Pareto frontier provides additional insights into the local stability of design choices as well as global trends leading to trade-offs between competing criteria. Copyright © 2011 Wiley Periodicals, Inc.

The Cybernetic Writing Program.

ERIC Educational Resources Information Center

Lowe, Kelly Fisher

This paper looks at the role of a Writing Program Administrator, and applies the idea of a cybernetic system to the administration of the program. In this cybernetic model, the Writing Program Administrator (WPA) works as both a problem solver and problem causer, with the responsibility of keeping the program in proper balance. A cybernetic…

PBEQ-Solver for online visualization of electrostatic potential of biomolecules.

PubMed

Jo, Sunhwan; Vargyas, Miklos; Vasko-Szedlar, Judit; Roux, Benoît; Im, Wonpil

2008-07-01

PBEQ-Solver provides a web-based graphical user interface to read biomolecular structures, solve the Poisson-Boltzmann (PB) equations and interactively visualize the electrostatic potential. PBEQ-Solver calculates (i) electrostatic potential and solvation free energy, (ii) protein-protein (DNA or RNA) electrostatic interaction energy and (iii) pKa of a selected titratable residue. All the calculations can be performed in both aqueous solvent and membrane environments (with a cylindrical pore in the case of membrane). PBEQ-Solver uses the PBEQ module in the biomolecular simulation program CHARMM to solve the finite-difference PB equation of molecules specified by users. Users can interactively inspect the calculated electrostatic potential on the solvent-accessible surface as well as iso-electrostatic potential contours using a novel online visualization tool based on MarvinSpace molecular visualization software, a Java applet integrated within CHARMM-GUI (http://www.charmm-gui.org). To reduce the computational time on the server, and to increase the efficiency in visualization, all the PB calculations are performed with coarse grid spacing (1.5 A before and 1 A after focusing). PBEQ-Solver suggests various physical parameters for PB calculations and users can modify them if necessary. PBEQ-Solver is available at http://www.charmm-gui.org/input/pbeqsolver.

A CFD Heterogeneous Parallel Solver Based on Collaborating CPU and GPU

NASA Astrophysics Data System (ADS)

Lai, Jianqi; Tian, Zhengyu; Li, Hua; Pan, Sha

2018-03-01

Since Graphic Processing Unit (GPU) has a strong ability of floating-point computation and memory bandwidth for data parallelism, it has been widely used in the areas of common computing such as molecular dynamics (MD), computational fluid dynamics (CFD) and so on. The emergence of compute unified device architecture (CUDA), which reduces the complexity of compiling program, brings the great opportunities to CFD. There are three different modes for parallel solution of NS equations: parallel solver based on CPU, parallel solver based on GPU and heterogeneous parallel solver based on collaborating CPU and GPU. As we can see, GPUs are relatively rich in compute capacity but poor in memory capacity and the CPUs do the opposite. We need to make full use of the GPUs and CPUs, so a CFD heterogeneous parallel solver based on collaborating CPU and GPU has been established. Three cases are presented to analyse the solver’s computational accuracy and heterogeneous parallel efficiency. The numerical results agree well with experiment results, which demonstrate that the heterogeneous parallel solver has high computational precision. The speedup on a single GPU is more than 40 for laminar flow, it decreases for turbulent flow, but it still can reach more than 20. What’s more, the speedup increases as the grid size becomes larger.

Integer Optimization Model for a Logistic System based on Location-Routing Considering Distance and Chosen Route

NASA Astrophysics Data System (ADS)

Mulyasari, Joni; Mawengkang, Herman; Efendi, Syahril

2018-02-01

In a distribution network it is important to decide the locations of facilities that impacts not only the profitability of an organization but the ability to serve customers.Generally the location-routing problem is to minimize the overall cost by simultaneously selecting a subset of candidate facilities and constructing a set of delivery routes that satisfy some restrictions. In this paper we impose restriction on the route that should be passed for delivery. We use integer programming model to describe the problem. A feasible neighbourhood search is proposed to solve the result model.

A new Fortran 90 program to compute regular and irregular associated Legendre functions (new version announcement)

NASA Astrophysics Data System (ADS)

Schneider, Barry I.; Segura, Javier; Gil, Amparo; Guan, Xiaoxu; Bartschat, Klaus

2018-04-01

This is a revised and updated version of a modern Fortran 90 code to compute the regular Plm (x) and irregular Qlm (x) associated Legendre functions for all x ∈(- 1 , + 1) (on the cut) and | x | > 1 and integer degree (l) and order (m). The necessity to revise the code comes as a consequence of some comments of Prof. James Bremer of the UC//Davis Mathematics Department, who discovered that there were errors in the code for large integer degree and order for the normalized regular Legendre functions on the cut.

Modeling an integrated hospital management planning problem using integer optimization approach

NASA Astrophysics Data System (ADS)

Sitepu, Suryati; Mawengkang, Herman; Irvan

2017-09-01

Hospital is a very important institution to provide health care for people. It is not surprising that nowadays the people’s demands for hospital is increasing. However, due to the rising cost of healthcare services, hospitals need to consider efficiencies in order to overcome these two problems. This paper deals with an integrated strategy of staff capacity management and bed allocation planning to tackle these problems. Mathematically, the strategy can be modeled as an integer linear programming problem. We solve the model using a direct neighborhood search approach, based on the notion of superbasic variables.

Least-Squares Spectral Element Solutions to the CAA Workshop Benchmark Problems

NASA Technical Reports Server (NTRS)

Lin, Wen H.; Chan, Daniel C.

1997-01-01

This paper presents computed results for some of the CAA benchmark problems via the acoustic solver developed at Rocketdyne CFD Technology Center under the corporate agreement between Boeing North American, Inc. and NASA for the Aerospace Industry Technology Program. The calculations are considered as benchmark testing of the functionality, accuracy, and performance of the solver. Results of these computations demonstrate that the solver is capable of solving the propagation of aeroacoustic signals. Testing of sound generation and on more realistic problems is now pursued for the industrial applications of this solver. Numerical calculations were performed for the second problem of Category 1 of the current workshop problems for an acoustic pulse scattered from a rigid circular cylinder, and for two of the first CAA workshop problems, i. e., the first problem of Category 1 for the propagation of a linear wave and the first problem of Category 4 for an acoustic pulse reflected from a rigid wall in a uniform flow of Mach 0.5. The aim for including the last two problems in this workshop is to test the effectiveness of some boundary conditions set up in the solver. Numerical results of the last two benchmark problems have been compared with their corresponding exact solutions and the comparisons are excellent. This demonstrates the high fidelity of the solver in handling wave propagation problems. This feature lends the method quite attractive in developing a computational acoustic solver for calculating the aero/hydrodynamic noise in a violent flow environment.

Recent research in network problems with applications

NASA Technical Reports Server (NTRS)

Thompson, G. L.

1980-01-01

The capabilities of network codes and their extensions are surveyed in regard to specially structured integer programming problems which are solved by using the solutions of a series of ordinary network problems.

Integer programming model for optimizing bus timetable using genetic algorithm

NASA Astrophysics Data System (ADS)

Wihartiko, F. D.; Buono, A.; Silalahi, B. P.

2017-01-01

Bus timetable gave an information for passengers to ensure the availability of bus services. Timetable optimal condition happened when bus trips frequency could adapt and suit with passenger demand. In the peak time, the number of bus trips would be larger than the off-peak time. If the number of bus trips were more frequent than the optimal condition, it would make a high operating cost for bus operator. Conversely, if the number of trip was less than optimal condition, it would make a bad quality service for passengers. In this paper, the bus timetabling problem would be solved by integer programming model with modified genetic algorithm. Modification was placed in the chromosomes design, initial population recovery technique, chromosomes reconstruction and chromosomes extermination on specific generation. The result of this model gave the optimal solution with accuracy 99.1%.

Reconstructing cerebrovascular networks under local physiological constraints by integer programming

DOE PAGES

Rempfler, Markus; Schneider, Matthias; Ielacqua, Giovanna D.; ...

2015-04-23

We introduce a probabilistic approach to vessel network extraction that enforces physiological constraints on the vessel structure. The method accounts for both image evidence and geometric relationships between vessels by solving an integer program, which is shown to yield the maximum a posteriori (MAP) estimate to the probabilistic model. Starting from an over-connected network, it is pruning vessel stumps and spurious connections by evaluating the local geometry and the global connectivity of the graph. We utilize a high-resolution micro computed tomography (µCT) dataset of a cerebrovascular corrosion cast to obtain a reference network and learn the prior distributions of ourmore » probabilistic model. As a result, we perform experiments on micro magnetic resonance angiography (µMRA) images of mouse brains and discuss properties of the networks obtained under different tracking and pruning approaches.« less

FPGA Implementation of Optimal 3D-Integer DCT Structure for Video Compression

PubMed Central

2015-01-01

A novel optimal structure for implementing 3D-integer discrete cosine transform (DCT) is presented by analyzing various integer approximation methods. The integer set with reduced mean squared error (MSE) and high coding efficiency are considered for implementation in FPGA. The proposed method proves that the least resources are utilized for the integer set that has shorter bit values. Optimal 3D-integer DCT structure is determined by analyzing the MSE, power dissipation, coding efficiency, and hardware complexity of different integer sets. The experimental results reveal that direct method of computing the 3D-integer DCT using the integer set [10, 9, 6, 2, 3, 1, 1] performs better when compared to other integer sets in terms of resource utilization and power dissipation. PMID:26601120

Software Reviews.

ERIC Educational Resources Information Center

Science Software Quarterly, 1984

1984-01-01

Provides extensive reviews of computer software, examining documentation, ease of use, performance, error handling, special features, and system requirements. Includes statistics, problem-solving (TK Solver), label printing, database management, experimental psychology, Encyclopedia Britannica biology, and DNA-sequencing programs. A program for…

Automated Simultaneous Assembly of Multistage Testlets for a High-Stakes Licensing Examination

ERIC Educational Resources Information Center

Breithaupt, Krista; Hare, Donovan R.

2007-01-01

Many challenges exist for high-stakes testing programs offering continuous computerized administration. The automated assembly of test questions to exactly meet content and other requirements, provide uniformity, and control item exposure can be modeled and solved by mixed-integer programming (MIP) methods. A case study of the computerized…

THREE-PEE SAMPLING THEORY and program 'THRP' for computer generation of selection criteria

Treesearch

L. R. Grosenbaugh

1965-01-01

Theory necessary for sampling with probability proportional to prediction ('three-pee,' or '3P,' sampling) is first developed and then exemplified by numerical comparisons of several estimators. Program 'T RP' for computer generation of appropriate 3P-sample-selection criteria is described, and convenient random integer dispensers are...

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

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments.

PubMed

Fisicaro, G; Genovese, L; Andreussi, O; Marzari, N; Goedecker, S

2016-01-07

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

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

Fisicaro, G., E-mail: giuseppe.fisicaro@unibas.ch; Goedecker, S.; Genovese, L.

2016-01-07

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and themore » linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.« less

Incorporation of Fixed Installation Costs into Optimization of Groundwater Remediation with a New Efficient Surrogate Nonlinear Mixed Integer Optimization Algorithm

NASA Astrophysics Data System (ADS)

Shoemaker, Christine; Wan, Ying

2016-04-01

Optimization of nonlinear water resources management issues which have a mixture of fixed (e.g. construction cost for a well) and variable (e.g. cost per gallon of water pumped) costs has been not well addressed because prior algorithms for the resulting nonlinear mixed integer problems have required many groundwater simulations (with different configurations of decision variable), especially when the solution space is multimodal. In particular heuristic methods like genetic algorithms have often been used in the water resources area, but they require so many groundwater simulations that only small systems have been solved. Hence there is a need to have a method that reduces the number of expensive groundwater simulations. A recently published algorithm for nonlinear mixed integer programming using surrogates was shown in this study to greatly reduce the computational effort for obtaining accurate answers to problems involving fixed costs for well construction as well as variable costs for pumping because of a substantial reduction in the number of groundwater simulations required to obtain an accurate answer. Results are presented for a US EPA hazardous waste site. The nonlinear mixed integer surrogate algorithm is general and can be used on other problems arising in hydrology with open source codes in Matlab and python ("pySOT" in Bitbucket).

Conjunctive management of multi-reservoir network system and groundwater system

NASA Astrophysics Data System (ADS)

Mani, A.; Tsai, F. T. C.

2015-12-01

This study develops a successive mixed-integer linear fractional programming (successive MILFP) method to conjunctively manage water resources provided by a multi-reservoir network system and a groundwater system. The conjunctive management objectives are to maximize groundwater withdrawals and maximize reservoir storages while satisfying water demands and raising groundwater level to a target level. The decision variables in the management problem are reservoir releases and spills, network flows and groundwater pumping rates. Using the fractional programming approach, the objective function is defined as a ratio of total groundwater withdraws to total reservoir storage deficits from the maximum storages. Maximizing this ratio function tends to maximizing groundwater use and minimizing surface water use. This study introduces a conditional constraint on groundwater head in order to sustain aquifers from overpumping: if current groundwater level is less than a target level, groundwater head at the next time period has to be raised; otherwise, it is allowed to decrease up to a certain extent. This conditional constraint is formulated into a set of mixed binary nonlinear constraints and results in a mixed-integer nonlinear fractional programming (MINLFP) problem. To solve the MINLFP problem, we first use the response matrix approach to linearize groundwater head with respect to pumping rate and reduce the problem to an MILFP problem. Using the Charnes-Cooper transformation, the MILFP is transformed to an equivalent mixed-integer linear programming (MILP). The solution of the MILP is successively updated by updating the response matrix in every iteration. The study uses IBM CPLEX to solve the MILP problem. The methodology is applied to water resources management in northern Louisiana. This conjunctive management approach aims to recover the declining groundwater level of the stressed Sparta aquifer by using surface water from a network of four reservoirs as an alternative source of supply.

Calculating the Mean Amplitude of Glycemic Excursions from Continuous Glucose Data Using an Open-Code Programmable Algorithm Based on the Integer Nonlinear Method.

PubMed

Yu, Xuefei; Lin, Liangzhuo; Shen, Jie; Chen, Zhi; Jian, Jun; Li, Bin; Xin, Sherman Xuegang

2018-01-01

The mean amplitude of glycemic excursions (MAGE) is an essential index for glycemic variability assessment, which is treated as a key reference for blood glucose controlling at clinic. However, the traditional "ruler and pencil" manual method for the calculation of MAGE is time-consuming and prone to error due to the huge data size, making the development of robust computer-aided program an urgent requirement. Although several software products are available instead of manual calculation, poor agreement among them is reported. Therefore, more studies are required in this field. In this paper, we developed a mathematical algorithm based on integer nonlinear programming. Following the proposed mathematical method, an open-code computer program named MAGECAA v1.0 was developed and validated. The results of the statistical analysis indicated that the developed program was robust compared to the manual method. The agreement among the developed program and currently available popular software is satisfied, indicating that the worry about the disagreement among different software products is not necessary. The open-code programmable algorithm is an extra resource for those peers who are interested in the related study on methodology in the future.

Solving a discrete model of the lac operon using Z3

NASA Astrophysics Data System (ADS)

Gutierrez, Natalia A.

2014-05-01

A discrete model for the Lcac Operon is solved using the SMT-solver Z3. Traditionally the Lac Operon is formulated in a continuous math model. This model is a system of ordinary differential equations. Here, it was considerated as a discrete model, based on a Boolean red. The biological problem of Lac Operon is enunciated as a problem of Boolean satisfiability, and it is solved using an STM-solver named Z3. Z3 is a powerful solver that allows understanding the basic dynamic of the Lac Operon in an easier and more efficient way. The multi-stability of the Lac Operon can be easily computed with Z3. The code that solves the Boolean red can be written in Python language or SMT-Lib language. Both languages were used in local version of the program as online version of Z3. For future investigations it is proposed to solve the Boolean red of Lac Operon using others SMT-solvers as cvc4, alt-ergo, mathsat and yices.

Multi-task feature selection in microarray data by binary integer programming.

PubMed

Lan, Liang; Vucetic, Slobodan

2013-12-20

A major challenge in microarray classification is that the number of features is typically orders of magnitude larger than the number of examples. In this paper, we propose a novel feature filter algorithm to select the feature subset with maximal discriminative power and minimal redundancy by solving a quadratic objective function with binary integer constraints. To improve the computational efficiency, the binary integer constraints are relaxed and a low-rank approximation to the quadratic term is applied. The proposed feature selection algorithm was extended to solve multi-task microarray classification problems. We compared the single-task version of the proposed feature selection algorithm with 9 existing feature selection methods on 4 benchmark microarray data sets. The empirical results show that the proposed method achieved the most accurate predictions overall. We also evaluated the multi-task version of the proposed algorithm on 8 multi-task microarray datasets. The multi-task feature selection algorithm resulted in significantly higher accuracy than when using the single-task feature selection methods.

Cpu/gpu Computing for AN Implicit Multi-Block Compressible Navier-Stokes Solver on Heterogeneous Platform

NASA Astrophysics Data System (ADS)

Deng, Liang; Bai, Hanli; Wang, Fang; Xu, Qingxin

2016-06-01

CPU/GPU computing allows scientists to tremendously accelerate their numerical codes. In this paper, we port and optimize a double precision alternating direction implicit (ADI) solver for three-dimensional compressible Navier-Stokes equations from our in-house Computational Fluid Dynamics (CFD) software on heterogeneous platform. First, we implement a full GPU version of the ADI solver to remove a lot of redundant data transfers between CPU and GPU, and then design two fine-grain schemes, namely “one-thread-one-point” and “one-thread-one-line”, to maximize the performance. Second, we present a dual-level parallelization scheme using the CPU/GPU collaborative model to exploit the computational resources of both multi-core CPUs and many-core GPUs within the heterogeneous platform. Finally, considering the fact that memory on a single node becomes inadequate when the simulation size grows, we present a tri-level hybrid programming pattern MPI-OpenMP-CUDA that merges fine-grain parallelism using OpenMP and CUDA threads with coarse-grain parallelism using MPI for inter-node communication. We also propose a strategy to overlap the computation with communication using the advanced features of CUDA and MPI programming. We obtain speedups of 6.0 for the ADI solver on one Tesla M2050 GPU in contrast to two Xeon X5670 CPUs. Scalability tests show that our implementation can offer significant performance improvement on heterogeneous platform.

Teachers as Thinking Coaches: Creating Strategic Learners and Problem Solvers.

ERIC Educational Resources Information Center

Gaskins, Irene W.

1989-01-01

An across-the-curriculum program was developed to teach learning, thinking, and problem-solving skills to bright middle-school underachievers. This article describes the pilot program's theoretical basis, axioms of program development, guidelines for teaching metacognitive strategies, and a framework for strategy implementation. (Author/JDD)

Improvements to the Unstructured Mesh Generator MESH3D

NASA Technical Reports Server (NTRS)

Thomas, Scott D.; Baker, Timothy J.; Cliff, Susan E.

1999-01-01

The AIRPLANE process starts with an aircraft geometry stored in a CAD system. The surface is modeled with a mesh of triangles and then the flow solver produces pressures at surface points which may be integrated to find forces and moments. The biggest advantage is that the grid generation bottleneck of the CFD process is eliminated when an unstructured tetrahedral mesh is used. MESH3D is the key to turning around the first analysis of a CAD geometry in days instead of weeks. The flow solver part of AIRPLANE has proven to be robust and accurate over a decade of use at NASA. It has been extensively validated with experimental data and compares well with other Euler flow solvers. AIRPLANE has been applied to all the HSR geometries treated at Ames over the course of the HSR program in order to verify the accuracy of other flow solvers. The unstructured approach makes handling complete and complex geometries very simple because only the surface of the aircraft needs to be discretized, i.e. covered with triangles. The volume mesh is created automatically by MESH3D. AIRPLANE runs well on multiple platforms. Vectorization on the Cray Y-MP is reasonable for a code that uses indirect addressing. Massively parallel computers such as the IBM SP2, SGI Origin 2000, and the Cray T3E have been used with an MPI version of the flow solver and the code scales very well on these systems. AIRPLANE can run on a desktop computer as well. AIRPLANE has a future. The unstructured technologies developed as part of the HSR program are now targeting high Reynolds number viscous flow simulation. The pacing item in this effort is Navier-Stokes mesh generation.

Comparison of penalty functions on a penalty approach to mixed-integer optimization

NASA Astrophysics Data System (ADS)

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

2016-06-01

In this paper, we present a comparative study involving several penalty functions that can be used in a penalty approach for globally solving bound mixed-integer nonlinear programming (bMIMLP) problems. The penalty approach relies on a continuous reformulation of the bMINLP problem by adding a particular penalty term to the objective function. A penalty function based on the `erf' function is proposed. The continuous nonlinear optimization problems are sequentially solved by the population-based firefly algorithm. Preliminary numerical experiments are carried out in order to analyze the quality of the produced solutions, when compared with other penalty functions available in the literature.

Finite pure integer programming algorithms employing only hyperspherically deduced cuts

NASA Technical Reports Server (NTRS)

Young, R. D.

1971-01-01

Three algorithms are developed that may be based exclusively on hyperspherically deduced cuts. The algorithms only apply, therefore, to problems structured so that these cuts are valid. The algorithms are shown to be finite.

Speedy Alchemy.

ERIC Educational Resources Information Center

Deininger, Rolf A.; Berger, Carl F., Jr.

1983-01-01

Provides instructions for interfacing a pH meter directly to an Apple II microcomputer without an analog-to-digital converter. Includes program listing (with enough remark statements to make it self-documenting) in Integer Basic to display the pH readings. (Author/JN)

Solving large-scale fixed cost integer linear programming models for grid-based location problems with heuristic techniques

NASA Astrophysics Data System (ADS)

Noor-E-Alam, Md.; Doucette, John

2015-08-01

Grid-based location problems (GBLPs) can be used to solve location problems in business, engineering, resource exploitation, and even in the field of medical sciences. To solve these decision problems, an integer linear programming (ILP) model is designed and developed to provide the optimal solution for GBLPs considering fixed cost criteria. Preliminary results show that the ILP model is efficient in solving small to moderate-sized problems. However, this ILP model becomes intractable in solving large-scale instances. Therefore, a decomposition heuristic is proposed to solve these large-scale GBLPs, which demonstrates significant reduction of solution runtimes. To benchmark the proposed heuristic, results are compared with the exact solution via ILP. The experimental results show that the proposed method significantly outperforms the exact method in runtime with minimal (and in most cases, no) loss of optimality.

A Generalized National Planning Approach for Admission Capacity in Higher Education: A Nonlinear Integer Goal Programming Model with a Novel Differential Evolution Algorithm

PubMed Central

El-Qulity, Said Ali; Mohamed, Ali Wagdy

2016-01-01

This paper proposes a nonlinear integer goal programming model (NIGPM) for solving the general problem of admission capacity planning in a country as a whole. The work aims to satisfy most of the required key objectives of a country related to the enrollment problem for higher education. The system general outlines are developed along with the solution methodology for application to the time horizon in a given plan. The up-to-date data for Saudi Arabia is used as a case study and a novel evolutionary algorithm based on modified differential evolution (DE) algorithm is used to solve the complexity of the NIGPM generated for different goal priorities. The experimental results presented in this paper show their effectiveness in solving the admission capacity for higher education in terms of final solution quality and robustness. PMID:26819583

A Generalized National Planning Approach for Admission Capacity in Higher Education: A Nonlinear Integer Goal Programming Model with a Novel Differential Evolution Algorithm.

PubMed

El-Qulity, Said Ali; Mohamed, Ali Wagdy

2016-01-01

This paper proposes a nonlinear integer goal programming model (NIGPM) for solving the general problem of admission capacity planning in a country as a whole. The work aims to satisfy most of the required key objectives of a country related to the enrollment problem for higher education. The system general outlines are developed along with the solution methodology for application to the time horizon in a given plan. The up-to-date data for Saudi Arabia is used as a case study and a novel evolutionary algorithm based on modified differential evolution (DE) algorithm is used to solve the complexity of the NIGPM generated for different goal priorities. The experimental results presented in this paper show their effectiveness in solving the admission capacity for higher education in terms of final solution quality and robustness.

Combinatorial optimization games

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

Deng, X.; Ibaraki, Toshihide; Nagamochi, Hiroshi

1997-06-01

We introduce a general integer programming formulation for a class of combinatorial optimization games, which immediately allows us to improve the algorithmic result for finding amputations in the core (an important solution concept in cooperative game theory) of the network flow game on simple networks by Kalai and Zemel. An interesting result is a general theorem that the core for this class of games is nonempty if and only if a related linear program has an integer optimal solution. We study the properties for this mathematical condition to hold for several interesting problems, and apply them to resolve algorithmic andmore » complexity issues for their cores along the line as put forward in: decide whether the core is empty; if the core is empty, find an imputation in the core; given an imputation x, test whether x is in the core. We also explore the properties of totally balanced games in this succinct formulation of cooperative games.« less

Extension of the Time-Spectral Approach to Overset Solvers for Arbitrary Motion

NASA Technical Reports Server (NTRS)

Leffell, Joshua Isaac; Murman, Scott M.; Pulliam, Thomas H.

2012-01-01

Forced periodic flows arise in a broad range of aerodynamic applications such as rotorcraft, turbomachinery, and flapping wing configurations. Standard practice involves solving the unsteady flow equations forward in time until the initial transient exits the domain and a statistically stationary flow is achieved. It is often required to simulate through several periods to remove the initial transient making unsteady design optimization prohibitively expensive for most realistic problems. An effort to reduce the computational cost of these calculations led to the development of the Harmonic Balance method [1, 2] which capitalizes on the periodic nature of the solution. The approach exploits the fact that forced temporally periodic flow, while varying in the time domain, is invariant in the frequency domain. Expanding the temporal variation at each spatial node into a Fourier series transforms the unsteady governing equations into a steady set of equations in integer harmonics that can be tackled with the acceleration techniques afforded to steady-state flow solvers. Other similar approaches, such as the Nonlinear Frequency Domain [3,4,5], Reduced Frequency [6] and Time-Spectral [7, 8, 9] methods, were developed shortly thereafter. Additionally, adjoint-based optimization techniques can be applied [10, 11] as well as frequency-adaptive methods [12, 13, 14] to provide even more flexibility to the method. The Fourier temporal basis functions imply spectral convergence as the number of harmonic modes, and correspondingly number of time samples, N, is increased. Some elect to solve the equations in the frequency domain directly, while others choose to transform the equations back into the time domain to simplify the process of adding this capability to existing solvers, but each harnesses the underlying steady solution in the frequency domain. These temporal projection methods will herein be collectively referred to as Time-Spectral methods. Time-Spectral methods have demonstrated marked success in reducing the computational costs associated with simulating periodic forced flows, but have yet to be fully applied to overset or Cartesian solvers for arbitrary motion with dynamic hole-cutting. Overset and Cartesian grid methodologies are versatile techniques capable of handling complex geometry configurations in practical engineering applications, and the combination of the Time-Spectral approach with this general capability potentially provides an enabling new design and analysis tool. In an arbitrary moving-body scenario for these approaches, a Lagrangian body moves through a fixed Eulerian mesh and mesh points in the Eulerian mesh interior to the solid body are removed (cut or blanked), leaving a hole in the Eulerian mesh. During the dynamic motion some gridpoints in the domain are blanked and do not have a complete set of time-samples preventing a direct implementation of the Time-Spectral method. Murman[6] demonstrated the Time-Spectral approach for a Cartesian solver with a rigid domain motion, wherein the hole cutting remains constant. Similarly, Custer et al. [15, 16] used the NASA overset OVERFLOW solver and limited the amount of relative motion to ensure static hole-cutting and interpolation. Recently, Mavriplis and Mundis[17] demonstrated a qualitative method for applying the Time-Spectral approach to an unstructured overset solver for arbitrary motion. The goal of the current work is to develop a robust and general method for handling arbitrary motion with the Time-Spectral approach within an overset or Cartesian mesh method, while still approaching the spectral convergence rate of the original Time-Spectral approach. The viscous OVERFLOW solver will be augmented with the new Time-Spectral algorithm and the capability of the method for benchmark problems in rotorcraft and turbomachinery will be demonstrated. This abstract begins with a brief synopsis of the Time-Spectral approach for overset grids and provides details of e current approach to allow for arbitrary motion. Model problem results in one and two dimensions are included to demonstrate the viability of the method and the convergence properties. Section IV briefly outlines the implementation into the OVERFLOW solver, and the abstract closes with a description of the benchmark test cases which will be included in the final paper.

Radar Resource Management in a Dense Target Environment

DTIC Science & Technology

2014-03-01

problem faced by networked MFRs . While relaxing our assumptions concerning information gain presents numerous challenges worth exploring, future research...linear programming MFR multifunction phased array radar MILP mixed integer linear programming NATO North Atlantic Treaty Organization PDF probability...1: INTRODUCTION Multifunction phased array radars ( MFRs ) are capable of performing various tasks in rapid succession. The performance of target search

The Multiplier Effect: The Case for Multi-School, Global Education Programs

ERIC Educational Resources Information Center

Dugan, Rik; Nink, Matt

2010-01-01

Multi-school and multi-country programs greatly enhance leadership development and global awareness in students and teachers, while creating better problem solvers, stronger relationships, and wider community impact than any single-school program. That's why Global Youth Leadership Institute (GYLI) and National Association of Independent Schools…

A statistical mechanical approach to restricted integer partition functions

NASA Astrophysics Data System (ADS)

Zhou, Chi-Chun; Dai, Wu-Sheng

2018-05-01

The main aim of this paper is twofold: (1) suggesting a statistical mechanical approach to the calculation of the generating function of restricted integer partition functions which count the number of partitions—a way of writing an integer as a sum of other integers under certain restrictions. In this approach, the generating function of restricted integer partition functions is constructed from the canonical partition functions of various quantum gases. (2) Introducing a new type of restricted integer partition functions corresponding to general statistics which is a generalization of Gentile statistics in statistical mechanics; many kinds of restricted integer partition functions are special cases of this restricted integer partition function. Moreover, with statistical mechanics as a bridge, we reveal a mathematical fact: the generating function of restricted integer partition function is just the symmetric function which is a class of functions being invariant under the action of permutation groups. Using this approach, we provide some expressions of restricted integer partition functions as examples.

Stochastic Dynamic Mixed-Integer Programming (SD-MIP)

DTIC Science & Technology

2015-05-05

stochastic linear programming ( SLP ) problems. By using a combination of ideas from cutting plane theory of deterministic MIP (especially disjunctive...developed to date. b) As part of this project, we have also developed tools for very large scale Stochastic Linear Programming ( SLP ). There are...several reasons for this. First, SLP models continue to challenge many of the fastest computers to date, and many applications within the DoD (e.g

Mixed-Integer Nonconvex Quadratic Optimization Relaxations and Performance Analysis

DTIC Science & Technology

2016-10-11

Analysis of Interior Point Algorithms for Non-Lipschitz and Nonconvex Minimization,” (W. Bian, X. Chen, and Ye), Math Programming, 149 (2015) 301-327...Chen, Ge, Wang, Ye), Math Programming, 143 (1-2) (2014) 371-383. This paper resolved an important open question in cardinality constrained...Statistical Performance, and Algorithmic Theory for Local Solutions,” (H. Liu, T. Yao, R. Li, Y. Ye) manuscript, 2nd revision in Math Programming

Materiel Acquisition Management of U.S. Army Attack Helicopters

DTIC Science & Technology

1989-06-02

used to evaluate the existing helicopter program periodically in order to determine utility in reference to all evaluation criteria. Defintion of... mixed integer linear programming model, the Phoenix model has demonstrated the potential to assist in the analysis of strategic and operational issues in...Fleet Max i of Aircraft per Fleet Programmed Buys .. -- Technology Unit Production mix Retirement Start-up ROTIE Flying Hour Aviation Overheadl I Aviation

Computerised curve deconvolution of TL/OSL curves using a popular spreadsheet program.

PubMed

Afouxenidis, D; Polymeris, G S; Tsirliganis, N C; Kitis, G

2012-05-01

This paper exploits the possibility of using commercial software for thermoluminescence and optically stimulated luminescence curve deconvolution analysis. The widely used software package Microsoft Excel, with the Solver utility has been used to perform deconvolution analysis to both experimental and reference glow curves resulted from the GLOw Curve ANalysis INtercomparison project. The simple interface of this programme combined with the powerful Solver utility, allows the analysis of complex stimulated luminescence curves into their components and the evaluation of the associated luminescence parameters.

Automated Discovery of Simulation Between Programs

DTIC Science & Technology

2014-10-18

relation. These relations enable the refinement-step of SimAbs. We have implemented SimAbs using UFO framework and Z3 SMT-solver and applied it to...step of SimAbs. We implemented SimAbs and AE-VAL on the top of the UFO framework [1, 15] and an SMT-solver Z3 [8], respectively. We have evaluated SimAbs...ut 6 Evaluation We have implemented SimAbs in the UFO framework, and evaluated it on the Software Verification Competition (SVCOMP’14) benchmarks and

Modelling of a Solar Thermal Power Plant for Benchmarking Blackbox Optimization Solvers

NASA Astrophysics Data System (ADS)

Lemyre Garneau, Mathieu

A new family of problems is provided to serve as a benchmark for blackbox optimization solvers. The problems are single or bi-objective and vary in complexity in terms of the number of variables used (from 5 to 29), the type of variables (integer, real, category), the number of constraints (from 5 to 17) and their types (binary or continuous). In order to provide problems exhibiting dynamics that reflect real engineering challenges, they are extracted from an original numerical model of a concentrated solar power (CSP) power plant with molten salt thermal storage. The model simulates the performance of the power plant by using a high level modeling of each of its main components, namely, an heliostats field, a central cavity receiver, a molten salt heat storage, a steam generator and an idealized powerblock. The heliostats field layout is determined through a simple automatic strategy that finds the best individual positions on the field by considering their respective cosine efficiency, atmospheric scattering and spillage losses as a function of the design parameters. A Monte-Carlo integral method is used to evaluate the heliostats field's optical performance throughout the day so that shadowing effects between heliostats are considered, and the results of this evaluation provide the inputs to simulate the levels and temperatures of the thermal storage. The molten salt storage inventory is used to transfer thermal energy to the powerblock, which simulates a simple Rankine cycle with a single steam turbine. Auxiliary models are used to provide additional optimization constraints on the investment cost, parasitic losses or components failure. The results of preliminary optimizations performed with the NOMAD software using default settings are provided to show the validity of the problems.

Integer programming methods for reserve selection and design

Treesearch

Robert G. Haight; Stephanie A. Snyder

2009-01-01

How many nature reserves should there be? Where should they be located? Which places have highest priority for protection? Conservation biologists, economists, and operations researchers have been developing quantitative methods to address these questions since the 1980s.

Optimal traffic resource allocation and management.

DOT National Transportation Integrated Search

2010-05-01

"In this paper, we address the problem of determining the patrol routes of state troopers for maximum coverage of : highway spots with high frequencies of crashes (hot spots). We develop a mixed integer linear programming model : for this problem und...

Efficient Remainder Rule

ERIC Educational Resources Information Center

Firozzaman, Firoz; Firoz, Fahim

2017-01-01

Understanding the solution of a problem may require the reader to have background knowledge on the subject. For instance, finding an integer which, when divided by a nonzero integer leaves a remainder; but when divided by another nonzero integer may leave a different remainder. To find a smallest positive integer or a set of integers following the…

Hybrid Nested Partitions and Math Programming Framework for Large-scale Combinatorial Optimization

DTIC Science & Technology

2010-03-31

optimization problems: 1) exact algorithms and 2) metaheuristic algorithms . This project will integrate concepts from these two technologies to develop...optimal solutions within an acceptable amount of computation time, and 2) metaheuristic algorithms such as genetic algorithms , tabu search, and the...integer programming decomposition approaches, such as Dantzig Wolfe decomposition and Lagrangian relaxation, and metaheuristics such as the Nested

Automated Test Assembly Using lp_Solve Version 5.5 in R

ERIC Educational Resources Information Center

Diao, Qi; van der Linden, Wim J.

2011-01-01

This article reviews the use of the software program lp_solve version 5.5 for solving mixed-integer automated test assembly (ATA) problems. The program is freely available under Lesser General Public License 2 (LGPL2). It can be called from the statistical language R using the lpSolveAPI interface. Three empirical problems are presented to…

Fixed-speed and Variable-speed Pumped Storage Dispatch Model in Power Systems with High Renewable Penetration

NASA Astrophysics Data System (ADS)

Yuan, Bo; Zong, Jin; Xu, Zhicheng

2018-06-01

According to different operating characteristics of pumped storage fixed speed unit and variable speed unit, a joint dispatching model of pumped storage unit and other types of units based on mixed integer linear optimization is constructed. The model takes into account the operating conditions, reservoir capacity, cycle type and other pumped storage unit constraints, but also consider the frequent start and stop and the stability of the operation of the unit caused by the loss. Using the Cplex solver to solve the model, the empirical example of the provincial power grid shows that the model can effectively arrange the pumping storage speed and the dispatching operation of the variable speed unit under the precondition of economic life of the unit, and give full play to the function of peak shaving and accommodating new energy. Because of its more flexible regulation characteristics of power generation and pumping conditions, the variable speed unit can better improve the operating conditions of other units in the system and promote the new energy dissipation.

47 CFR 1.2202 - Competitive bidding design options.

Code of Federal Regulations, 2014 CFR

2014-10-01

... Section 1.2202 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Grants...) Procedures that utilize mathematical computer optimization software, such as integer programming, to evaluate... evaluating bids using a ranking based on specified factors. (B) Procedures that combine computer optimization...

SPECIES RICHNESS AND BIODIVERSITY CONSERVATION PRIORITIES IN BRITISH COLUMBIA

EPA Science Inventory

Patterns in the geographic distribution of seven species groups were used to identify important areas for conservation in British Columbia, Canada. Potential priority sites for conservation were determined using an integer programming algorithm that maximized the number of speci...

Implementation of a fully-balanced periodic tridiagonal solver on a parallel distributed memory architecture

NASA Technical Reports Server (NTRS)

Eidson, T. M.; Erlebacher, G.

1994-01-01

While parallel computers offer significant computational performance, it is generally necessary to evaluate several programming strategies. Two programming strategies for a fairly common problem - a periodic tridiagonal solver - are developed and evaluated. Simple model calculations as well as timing results are presented to evaluate the various strategies. The particular tridiagonal solver evaluated is used in many computational fluid dynamic simulation codes. The feature that makes this algorithm unique is that these simulation codes usually require simultaneous solutions for multiple right-hand-sides (RHS) of the system of equations. Each RHS solutions is independent and thus can be computed in parallel. Thus a Gaussian elimination type algorithm can be used in a parallel computation and the more complicated approaches such as cyclic reduction are not required. The two strategies are a transpose strategy and a distributed solver strategy. For the transpose strategy, the data is moved so that a subset of all the RHS problems is solved on each of the several processors. This usually requires significant data movement between processor memories across a network. The second strategy attempts to have the algorithm allow the data across processor boundaries in a chained manner. This usually requires significantly less data movement. An approach to accomplish this second strategy in a near-perfect load-balanced manner is developed. In addition, an algorithm will be shown to directly transform a sequential Gaussian elimination type algorithm into the parallel chained, load-balanced algorithm.

Selective Optimization

DTIC Science & Technology

2015-07-06

NUMBER 5b. GRANT NUMBER AFOSR FA9550-12-1-0154 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Shabbir Ahmed and Santanu S. Dey 5d. PROJECT NUMBER 5e. TASK...standard mixed-integer programming (MIP) formulations of selective optimization problems. While such formulations can be attacked by commercial...F33615-86-C-5169. 5b. GRANT NUMBER. Enter all grant numbers as they appear in the report, e.g. AFOSR-82-1234. 5c. PROGRAM ELEMENT NUMBER. Enter

SU-F-T-540: Comprehensive Fluence Delivery Optimization with Multileaf Collimation

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

Weppler, S; Villarreal-Barajas, J; Department of Medical Physics, Tom Baker Cancer Center, Calgary, Alberta

2016-06-15

Purpose: Multileaf collimator (MLC) leaf sequencing is performed via commercial black-box implementations, on which a user has limited to no access. We have developed an explicit, generic MLC sequencing model to serve as a tool for future investigations of fluence map optimization, fluence delivery optimization, and rotational collimator delivery methods. Methods: We have developed a novel, comprehensive model to effectively account for a variety of transmission and penumbra effects previously treated on an ad hoc basis in the literature. As the model is capable of quantifying a variety of effects, we utilize the asymmetric leakage intensity across each leaf tomore » deliver fluence maps with pixel size smaller than the narrowest leaf width. Developed using linear programming and mixed integer programming formulations, the model is implemented using state of the art open-source solvers. To demonstrate the versatility of the algorithm, a graphical user interface (GUI) was developed in MATLAB capable of accepting custom leaf specifications and transmission parameters. As a preliminary proof-ofconcept, we have sequenced the leaves of a Varian 120 Leaf Millennium MLC for five prostate cancer patient fields and one head and neck field. Predetermined fluence maps have been processed by data smoothing methods to obtain pixel sizes of 2.5 cm{sup 2}. The quality of output was analyzed using computer simulations. Results: For the prostate fields, an average root mean squared error (RMSE) of 0.82 and gamma (0.5mm/0.5%) of 91.4% were observed compared to RMSE and gamma (0.5mm/0.5%) values of 7.04 and 34.0% when the leakage considerations were omitted. Similar results were observed for the head and neck case. Conclusion: A model to sequence MLC leaves to optimality has been proposed. Future work will involve extensive testing and evaluation of the method on clinical MLCs and comparison with black-box leaf sequencing algorithms currently used by commercial treatment planning systems.« less

Cumulative Poisson Distribution Program

NASA Technical Reports Server (NTRS)

Bowerman, Paul N.; Scheuer, Ernest M.; Nolty, Robert

1990-01-01

Overflow and underflow in sums prevented. Cumulative Poisson Distribution Program, CUMPOIS, one of two computer programs that make calculations involving cumulative Poisson distributions. Both programs, CUMPOIS (NPO-17714) and NEWTPOIS (NPO-17715), used independently of one another. CUMPOIS determines cumulative Poisson distribution, used to evaluate cumulative distribution function (cdf) for gamma distributions with integer shape parameters and cdf for X (sup2) distributions with even degrees of freedom. Used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. Written in C.

An installed nacelle design code using a multiblock Euler solver. Volume 1: Theory document

NASA Technical Reports Server (NTRS)

Chen, H. C.

1992-01-01

An efficient multiblock Euler design code was developed for designing a nacelle installed on geometrically complex airplane configurations. This approach employed a design driver based on a direct iterative surface curvature method developed at LaRC. A general multiblock Euler flow solver was used for computing flow around complex geometries. The flow solver used a finite-volume formulation with explicit time-stepping to solve the Euler Equations. It used a multiblock version of the multigrid method to accelerate the convergence of the calculations. The design driver successively updated the surface geometry to reduce the difference between the computed and target pressure distributions. In the flow solver, the change in surface geometry was simulated by applying surface transpiration boundary conditions to avoid repeated grid generation during design iterations. Smoothness of the designed surface was ensured by alternate application of streamwise and circumferential smoothings. The capability and efficiency of the code was demonstrated through the design of both an isolated nacelle and an installed nacelle at various flow conditions. Information on the execution of the computer program is provided in volume 2.

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

Huang, Kuo -Ling; Mehrotra, Sanjay

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadraticmore » programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).« less

''A Parallel Adaptive Simulation Tool for Two Phase Steady State Reacting Flows in Industrial Boilers and Furnaces''

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

Michael J. Bockelie

2002-01-04

This DOE SBIR Phase II final report summarizes research that has been performed to develop a parallel adaptive tool for modeling steady, two phase turbulent reacting flow. The target applications for the new tool are full scale, fossil-fuel fired boilers and furnaces such as those used in the electric utility industry, chemical process industry and mineral/metal process industry. The type of analyses to be performed on these systems are engineering calculations to evaluate the impact on overall furnace performance due to operational, process or equipment changes. To develop a Computational Fluid Dynamics (CFD) model of an industrial scale furnace requiresmore » a carefully designed grid that will capture all of the large and small scale features of the flowfield. Industrial systems are quite large, usually measured in tens of feet, but contain numerous burners, air injection ports, flames and localized behavior with dimensions that are measured in inches or fractions of inches. To create an accurate computational model of such systems requires capturing length scales within the flow field that span several orders of magnitude. In addition, to create an industrially useful model, the grid can not contain too many grid points - the model must be able to execute on an inexpensive desktop PC in a matter of days. An adaptive mesh provides a convenient means to create a grid that can capture both fine flow field detail within a very large domain with a ''reasonable'' number of grid points. However, the use of an adaptive mesh requires the development of a new flow solver. To create the new simulation tool, we have combined existing reacting CFD modeling software with new software based on emerging block structured Adaptive Mesh Refinement (AMR) technologies developed at Lawrence Berkeley National Laboratory (LBNL). Specifically, we combined: -physical models, modeling expertise, and software from existing combustion simulation codes used by Reaction Engineering International; -mesh adaption, data management, and parallelization software and technology being developed by users of the BoxLib library at LBNL; and -solution methods for problems formulated on block structured grids that were being developed in collaboration with technical staff members at the University of Utah Center for High Performance Computing (CHPC) and at LBNL. The combustion modeling software used by Reaction Engineering International represents an investment of over fifty man-years of development, conducted over a period of twenty years. Thus, it was impractical to achieve our objective by starting from scratch. The research program resulted in an adaptive grid, reacting CFD flow solver that can be used only on limited problems. In current form the code is appropriate for use on academic problems with simplified geometries. The new solver is not sufficiently robust or sufficiently general to be used in a ''production mode'' for industrial applications. The principle difficulty lies with the multi-level solver technology. The use of multi-level solvers on adaptive grids with embedded boundaries is not yet a mature field and there are many issues that remain to be resolved. From the lessons learned in this SBIR program, we have started work on a new flow solver with an AMR capability. The new code is based on a conventional cell-by-cell mesh refinement strategy used in unstructured grid solvers that employ hexahedral cells. The new solver employs several of the concepts and solution strategies developed within this research program. The formulation of the composite grid problem for the new solver has been designed to avoid the embedded boundary complications encountered in this SBIR project. This follow-on effort will result in a reacting flow CFD solver with localized mesh capability that can be used to perform engineering calculations on industrial problems in a production mode.« less

Solution of monotone complementarity and general convex programming problems using a modified potential reduction interior point method

DOE PAGES

Huang, Kuo -Ling; Mehrotra, Sanjay

2016-11-08

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadraticmore » programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).« less

A package for 3-D unstructured grid generation, finite-element flow solution and flow field visualization

NASA Technical Reports Server (NTRS)

Parikh, Paresh; Pirzadeh, Shahyar; Loehner, Rainald

1990-01-01

A set of computer programs for 3-D unstructured grid generation, fluid flow calculations, and flow field visualization was developed. The grid generation program, called VGRID3D, generates grids over complex configurations using the advancing front method. In this method, the point and element generation is accomplished simultaneously, VPLOT3D is an interactive, menudriven pre- and post-processor graphics program for interpolation and display of unstructured grid data. The flow solver, VFLOW3D, is an Euler equation solver based on an explicit, two-step, Taylor-Galerkin algorithm which uses the Flux Corrected Transport (FCT) concept for a wriggle-free solution. Using these programs, increasingly complex 3-D configurations of interest to aerospace community were gridded including a complete Space Transportation System comprised of the space-shuttle orbitor, the solid-rocket boosters, and the external tank. Flow solutions were obtained on various configurations in subsonic, transonic, and supersonic flow regimes.

Visualization and Tracking of Parallel CFD Simulations

NASA Technical Reports Server (NTRS)

Vaziri, Arsi; Kremenetsky, Mark

1995-01-01

We describe a system for interactive visualization and tracking of a 3-D unsteady computational fluid dynamics (CFD) simulation on a parallel computer. CM/AVS, a distributed, parallel implementation of a visualization environment (AVS) runs on the CM-5 parallel supercomputer. A CFD solver is run as a CM/AVS module on the CM-5. Data communication between the solver, other parallel visualization modules, and a graphics workstation, which is running AVS, are handled by CM/AVS. Partitioning of the visualization task, between CM-5 and the workstation, can be done interactively in the visual programming environment provided by AVS. Flow solver parameters can also be altered by programmable interactive widgets. This system partially removes the requirement of storing large solution files at frequent time steps, a characteristic of the traditional 'simulate (yields) store (yields) visualize' post-processing approach.

Exact calculation of distributions on integers, with application to sequence alignment.

PubMed

Newberg, Lee A; Lawrence, Charles E

2009-01-01

Computational biology is replete with high-dimensional discrete prediction and inference problems. Dynamic programming recursions can be applied to several of the most important of these, including sequence alignment, RNA secondary-structure prediction, phylogenetic inference, and motif finding. In these problems, attention is frequently focused on some scalar quantity of interest, a score, such as an alignment score or the free energy of an RNA secondary structure. In many cases, score is naturally defined on integers, such as a count of the number of pairing differences between two sequence alignments, or else an integer score has been adopted for computational reasons, such as in the test of significance of motif scores. The probability distribution of the score under an appropriate probabilistic model is of interest, such as in tests of significance of motif scores, or in calculation of Bayesian confidence limits around an alignment. Here we present three algorithms for calculating the exact distribution of a score of this type; then, in the context of pairwise local sequence alignments, we apply the approach so as to find the alignment score distribution and Bayesian confidence limits.

Center for Parallel Optimization

DTIC Science & Technology

1993-09-30

BOLLING AFB DC 20332-0001 _ii _ 11. SUPPLEMENTARY NOTES 12a. DISTRIBUTION/ AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE APPROVED FOR PUBLIC RELEASE...Machines Corporation, March 16-19, 1993 , A Branch- and-Bound Method for Mixed Integer Programming on the CM-.5 "* Dr. Roberto Musmanno, University of

Topics

ERIC Educational Resources Information Center

Mathematics Teaching, 1973

1973-01-01

This column includes the description of a game involving addition and subtraction of integers represented by colored bricks, a general formula for an enlargement in the Cartesian plane, an analysis of the possibilities for certain games of board Solitaire, and a BASIC program for a recreational mathematics problem. (DT)

Numerical simulation of the hydrodynamic instabilities of Richtmyer-Meshkov and Rayleigh-Taylor

NASA Astrophysics Data System (ADS)

Fortova, S. V.; Shepelev, V. V.; Troshkin, O. V.; Kozlov, S. A.

2017-09-01

The paper presents the results of numerical simulation of the development of hydrodynamic instabilities of Richtmyer-Meshkov and Rayleigh-Taylor encountered in experiments [1-3]. For the numerical solution used the TPS software package (Turbulence Problem Solver) that implements a generalized approach to constructing computer programs for a wide range of problems of hydrodynamics, described by the system of equations of hyperbolic type. As numerical methods are used the method of large particles and ENO-scheme of the second order with Roe solver for the approximate solution of the Riemann problem.

Albany/FELIX: A parallel, scalable and robust, finite element, first-order Stokes approximation ice sheet solver built for advanced analysis

DOE PAGES

Tezaur, I. K.; Perego, M.; Salinger, A. G.; ...

2015-04-27

This paper describes a new parallel, scalable and robust finite element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX, is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and template-based generic programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, alongmore » with their implementation. The results of several verification studies of the model accuracy are presented using (1) new test cases for simplified two-dimensional (2-D) versions of the governing equations derived using the method of manufactured solutions, and (2) canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution are then studied on problems involving a realistic Greenland ice sheet geometry discretized using hexahedral and tetrahedral meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic multilevel preconditioner, constructed based on the idea of semi-coarsening.« less

Generalised Assignment Matrix Methodology in Linear Programming

ERIC Educational Resources Information Center

Jerome, Lawrence

2012-01-01

Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same…

QuTiP 2: A Python framework for the dynamics of open quantum systems

NASA Astrophysics Data System (ADS)

Johansson, J. R.; Nation, P. D.; Nori, Franco

2013-04-01

We present version 2 of QuTiP, the Quantum Toolbox in Python. Compared to the preceding version [J.R. Johansson, P.D. Nation, F. Nori, Comput. Phys. Commun. 183 (2012) 1760.], we have introduced numerous new features, enhanced performance, and made changes in the Application Programming Interface (API) for improved functionality and consistency within the package, as well as increased compatibility with existing conventions used in other scientific software packages for Python. The most significant new features include efficient solvers for arbitrary time-dependent Hamiltonians and collapse operators, support for the Floquet formalism, and new solvers for Bloch-Redfield and Floquet-Markov master equations. Here we introduce these new features, demonstrate their use, and give a summary of the important backward-incompatible API changes introduced in this version. Catalog identifier: AEMB_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMB_v2_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 33625 No. of bytes in distributed program, including test data, etc.: 410064 Distribution format: tar.gz Programming language: Python. Computer: i386, x86-64. Operating system: Linux, Mac OSX. RAM: 2+ Gigabytes Classification: 7. External routines: NumPy, SciPy, Matplotlib, Cython Catalog identifier of previous version: AEMB_v1_0 Journal reference of previous version: Comput. Phys. Comm. 183 (2012) 1760 Does the new version supercede the previous version?: Yes Nature of problem: Dynamics of open quantum systems Solution method: Numerical solutions to Lindblad, Floquet-Markov, and Bloch-Redfield master equations, as well as the Monte Carlo wave function method. Reasons for new version: Compared to the preceding version we have introduced numerous new features, enhanced performance, and made changes in the Application Programming Interface (API) for improved functionality and consistency within the package, as well as increased compatibility with existing conventions used in other scientific software packages for Python. The most significant new features include efficient solvers for arbitrary time-dependent Hamiltonians and collapse operators, support for the Floquet formalism, and new solvers for Bloch-Redfield and Floquet-Markov master equations. Restrictions: Problems must meet the criteria for using the master equation in Lindblad, Floquet-Markov, or Bloch-Redfield form. Running time: A few seconds up to several tens of hours, depending on size of the underlying Hilbert space.

Newton/Poisson-Distribution Program

NASA Technical Reports Server (NTRS)

Bowerman, Paul N.; Scheuer, Ernest M.

1990-01-01

NEWTPOIS, one of two computer programs making calculations involving cumulative Poisson distributions. NEWTPOIS (NPO-17715) and CUMPOIS (NPO-17714) used independently of one another. NEWTPOIS determines Poisson parameter for given cumulative probability, from which one obtains percentiles for gamma distributions with integer shape parameters and percentiles for X(sup2) distributions with even degrees of freedom. Used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. Program written in C.

Integers as Transformations.

ERIC Educational Resources Information Center

Thompson, Patrick W.; Dreyfus, Tommy

1988-01-01

Investigates whether elementary school students can construct operations of thought for integers and integer addition crucial for understanding elementary algebra. Two sixth graders were taught using a computer. Results included both students being able to construct mental operations for negating arbitrary integers and determining sign and…

SU-E-T-22: A Deterministic Solver of the Boltzmann-Fokker-Planck Equation for Dose Calculation

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

Hong, X; Gao, H; Paganetti, H

2015-06-15

Purpose: The Boltzmann-Fokker-Planck equation (BFPE) accurately models the migration of photons/charged particles in tissues. While the Monte Carlo (MC) method is popular for solving BFPE in a statistical manner, we aim to develop a deterministic BFPE solver based on various state-of-art numerical acceleration techniques for rapid and accurate dose calculation. Methods: Our BFPE solver is based on the structured grid that is maximally parallelizable, with the discretization in energy, angle and space, and its cross section coefficients are derived or directly imported from the Geant4 database. The physical processes that are taken into account are Compton scattering, photoelectric effect, pairmore » production for photons, and elastic scattering, ionization and bremsstrahlung for charged particles.While the spatial discretization is based on the diamond scheme, the angular discretization synergizes finite element method (FEM) and spherical harmonics (SH). Thus, SH is used to globally expand the scattering kernel and FFM is used to locally discretize the angular sphere. As a Result, this hybrid method (FEM-SH) is both accurate in dealing with forward-peaking scattering via FEM, and efficient for multi-energy-group computation via SH. In addition, FEM-SH enables the analytical integration in energy variable of delta scattering kernel for elastic scattering with reduced truncation error from the numerical integration based on the classic SH-based multi-energy-group method. Results: The accuracy of the proposed BFPE solver was benchmarked against Geant4 for photon dose calculation. In particular, FEM-SH had improved accuracy compared to FEM, while both were within 2% of the results obtained with Geant4. Conclusion: A deterministic solver of the Boltzmann-Fokker-Planck equation is developed for dose calculation, and benchmarked against Geant4. Xiang Hong and Hao Gao were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang Talent Program (#14PJ1404500)« less

A Flexible CUDA LU-based Solver for Small, Batched Linear Systems

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

Tumeo, Antonino; Gawande, Nitin A.; Villa, Oreste

This chapter presents the implementation of a batched CUDA solver based on LU factorization for small linear systems. This solver may be used in applications such as reactive flow transport models, which apply the Newton-Raphson technique to linearize and iteratively solve the sets of non linear equations that represent the reactions for ten of thousands to millions of physical locations. The implementation exploits somewhat counterintuitive GPGPU programming techniques: it assigns the solution of a matrix (representing a system) to a single CUDA thread, does not exploit shared memory and employs dynamic memory allocation on the GPUs. These techniques enable ourmore » implementation to simultaneously solve sets of systems with over 100 equations and to employ LU decomposition with complete pivoting, providing the higher numerical accuracy required by certain applications. Other currently available solutions for batched linear solvers are limited by size and only support partial pivoting, although they may result faster in certain conditions. We discuss the code of our implementation and present a comparison with the other implementations, discussing the various tradeoffs in terms of performance and flexibility. This work will enable developers that need batched linear solvers to choose whichever implementation is more appropriate to the features and the requirements of their applications, and even to implement dynamic switching approaches that can choose the best implementation depending on the input data.« less

Implementing High-Performance Geometric Multigrid Solver with Naturally Grained Messages

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

Shan, Hongzhang; Williams, Samuel; Zheng, Yili

2015-10-26

Structured-grid linear solvers often require manually packing and unpacking of communication data to achieve high performance.Orchestrating this process efficiently is challenging, labor-intensive, and potentially error-prone.In this paper, we explore an alternative approach that communicates the data with naturally grained messagesizes without manual packing and unpacking. This approach is the distributed analogue of shared-memory programming, taking advantage of the global addressspace in PGAS languages to provide substantial programming ease. However, its performance may suffer from the large number of small messages. We investigate theruntime support required in the UPC ++ library for this naturally grained version to close the performance gapmore » between the two approaches and attain comparable performance at scale using the High-Performance Geometric Multgrid (HPGMG-FV) benchmark as a driver.« less

Classifying the Progression of Ductal Carcinoma from Single-Cell Sampled Data via Integer Linear Programming: A Case Study

PubMed Central

Catanzaro, Daniele; Schäffer, Alejandro A.; Schwartz, Russell

2016-01-01

Ductal Carcinoma In Situ (DCIS) is a precursor lesion of Invasive Ductal Carcinoma (IDC) of the breast. Investigating its temporal progression could provide fundamental new insights for the development of better diagnostic tools to predict which cases of DCIS will progress to IDC. We investigate the problem of reconstructing a plausible progression from single-cell sampled data of an individual with Synchronous DCIS and IDC. Specifically, by using a number of assumptions derived from the observation of cellular atypia occurring in IDC, we design a possible predictive model using integer linear programming (ILP). Computational experiments carried out on a preexisting data set of 13 patients with simultaneous DCIS and IDC show that the corresponding predicted progression models are classifiable into categories having specific evolutionary characteristics. The approach provides new insights into mechanisms of clonal progression in breast cancers and helps illustrate the power of the ILP approach for similar problems in reconstructing tumor evolution scenarios under complex sets of constraints. PMID:26353381

A mathematical model for municipal solid waste management - A case study in Hong Kong.

PubMed

Lee, C K M; Yeung, C L; Xiong, Z R; Chung, S H

2016-12-01

With the booming economy and increasing population, the accumulation of waste has become an increasingly arduous issue and has aroused the attention from all sectors of society. Hong Kong which has a relative high daily per capita domestic waste generation rate in Asia has not yet established a comprehensive waste management system. This paper conducts a review of waste management approaches and models. Researchers highlight that mathematical models provide useful information for decision-makers to select appropriate choices and save cost. It is suggested to consider municipal solid waste management in a holistic view and improve the utilization of waste management infrastructures. A mathematical model which adopts integer linear programming and mixed integer programming has been developed for Hong Kong municipal solid waste management. A sensitivity analysis was carried out to simulate different scenarios which provide decision-makers important information for establishing Hong Kong waste management system. Copyright © 2016 Elsevier Ltd. All rights reserved.

A new mathematical modeling for pure parsimony haplotyping problem.

PubMed

Feizabadi, R; Bagherian, M; Vaziri, H R; Salahi, M

2016-11-01

Pure parsimony haplotyping (PPH) problem is important in bioinformatics because rational haplotyping inference plays important roles in analysis of genetic data, mapping complex genetic diseases such as Alzheimer's disease, heart disorders and etc. Haplotypes and genotypes are m-length sequences. Although several integer programing models have already been presented for PPH problem, its NP-hardness characteristic resulted in ineffectiveness of those models facing the real instances especially instances with many heterozygous sites. In this paper, we assign a corresponding number to each haplotype and genotype and based on those numbers, we set a mixed integer programing model. Using numbers, instead of sequences, would lead to less complexity of the new model in comparison with previous models in a way that there are neither constraints nor variables corresponding to heterozygous nucleotide sites in it. Experimental results approve the efficiency of the new model in producing better solution in comparison to two state-of-the art haplotyping approaches. Copyright © 2016 Elsevier Inc. All rights reserved.

Discovering Link Communities in Complex Networks by an Integer Programming Model and a Genetic Algorithm

PubMed Central

Li, Zhenping; Zhang, Xiang-Sun; Wang, Rui-Sheng; Liu, Hongwei; Zhang, Shihua

2013-01-01

Identification of communities in complex networks is an important topic and issue in many fields such as sociology, biology, and computer science. Communities are often defined as groups of related nodes or links that correspond to functional subunits in the corresponding complex systems. While most conventional approaches have focused on discovering communities of nodes, some recent studies start partitioning links to find overlapping communities straightforwardly. In this paper, we propose a new quantity function for link community identification in complex networks. Based on this quantity function we formulate the link community partition problem into an integer programming model which allows us to partition a complex network into overlapping communities. We further propose a genetic algorithm for link community detection which can partition a network into overlapping communities without knowing the number of communities. We test our model and algorithm on both artificial networks and real-world networks. The results demonstrate that the model and algorithm are efficient in detecting overlapping community structure in complex networks. PMID:24386268

Integer Linear Programming for Constrained Multi-Aspect Committee Review Assignment

PubMed Central

Karimzadehgan, Maryam; Zhai, ChengXiang

2011-01-01

Automatic review assignment can significantly improve the productivity of many people such as conference organizers, journal editors and grant administrators. A general setup of the review assignment problem involves assigning a set of reviewers on a committee to a set of documents to be reviewed under the constraint of review quota so that the reviewers assigned to a document can collectively cover multiple topic aspects of the document. No previous work has addressed such a setup of committee review assignments while also considering matching multiple aspects of topics and expertise. In this paper, we tackle the problem of committee review assignment with multi-aspect expertise matching by casting it as an integer linear programming problem. The proposed algorithm can naturally accommodate any probabilistic or deterministic method for modeling multiple aspects to automate committee review assignments. Evaluation using a multi-aspect review assignment test set constructed using ACM SIGIR publications shows that the proposed algorithm is effective and efficient for committee review assignments based on multi-aspect expertise matching. PMID:22711970

Fish Processed Production Planning Using Integer Stochastic Programming Model

NASA Astrophysics Data System (ADS)

Firmansyah, Mawengkang, Herman

2011-06-01

Fish and its processed products are the most affordable source of animal protein in the diet of most people in Indonesia. The goal in production planning is to meet customer demand over a fixed time horizon divided into planning periods by optimizing the trade-off between economic objectives such as production cost and customer satisfaction level. The major decisions are production and inventory levels for each product and the number of workforce in each planning period. In this paper we consider the management of small scale traditional business at North Sumatera Province which performs processing fish into several local seafood products. The inherent uncertainty of data (e.g. demand, fish availability), together with the sequential evolution of data over time leads the production planning problem to a nonlinear mixed-integer stochastic programming model. We use scenario generation based approach and feasible neighborhood search for solving the model. The results which show the amount of each fish processed product and the number of workforce needed in each horizon planning are presented.

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

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

Classifying the Progression of Ductal Carcinoma from Single-Cell Sampled Data via Integer Linear Programming: A Case Study.

PubMed

Catanzaro, Daniele; Shackney, Stanley E; Schaffer, Alejandro A; Schwartz, Russell

2016-01-01

Ductal Carcinoma In Situ (DCIS) is a precursor lesion of Invasive Ductal Carcinoma (IDC) of the breast. Investigating its temporal progression could provide fundamental new insights for the development of better diagnostic tools to predict which cases of DCIS will progress to IDC. We investigate the problem of reconstructing a plausible progression from single-cell sampled data of an individual with synchronous DCIS and IDC. Specifically, by using a number of assumptions derived from the observation of cellular atypia occurring in IDC, we design a possible predictive model using integer linear programming (ILP). Computational experiments carried out on a preexisting data set of 13 patients with simultaneous DCIS and IDC show that the corresponding predicted progression models are classifiable into categories having specific evolutionary characteristics. The approach provides new insights into mechanisms of clonal progression in breast cancers and helps illustrate the power of the ILP approach for similar problems in reconstructing tumor evolution scenarios under complex sets of constraints.

A supplier selection and order allocation problem with stochastic demands

NASA Astrophysics Data System (ADS)

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

2011-08-01

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

Answer Set Programming and Other Computing Paradigms

ERIC Educational Resources Information Center

Meng, Yunsong

2013-01-01

Answer Set Programming (ASP) is one of the most prominent and successful knowledge representation paradigms. The success of ASP is due to its expressive non-monotonic modeling language and its efficient computational methods originating from building propositional satisfiability solvers. The wide adoption of ASP has motivated several extensions to…

Non-integer viscoelastic constitutive law to model soft biological tissues to in-vivo indentation.

PubMed

Demirci, Nagehan; Tönük, Ergin

2014-01-01

During the last decades, derivatives and integrals of non-integer orders are being more commonly used for the description of constitutive behavior of various viscoelastic materials including soft biological tissues. Compared to integer order constitutive relations, non-integer order viscoelastic material models of soft biological tissues are capable of capturing a wider range of viscoelastic behavior obtained from experiments. Although integer order models may yield comparably accurate results, non-integer order material models have less number of parameters to be identified in addition to description of an intermediate material that can monotonically and continuously be adjusted in between an ideal elastic solid and an ideal viscous fluid. In this work, starting with some preliminaries on non-integer (fractional) calculus, the "spring-pot", (intermediate mechanical element between a solid and a fluid), non-integer order three element (Zener) solid model, finally a user-defined large strain non-integer order viscoelastic constitutive model was constructed to be used in finite element simulations. Using the constitutive equation developed, by utilizing inverse finite element method and in vivo indentation experiments, soft tissue material identification was performed. The results indicate that material coefficients obtained from relaxation experiments, when optimized with creep experimental data could simulate relaxation, creep and cyclic loading and unloading experiments accurately. Non-integer calculus viscoelastic constitutive models, having physical interpretation and modeling experimental data accurately is a good alternative to classical phenomenological viscoelastic constitutive equations.

Proceedings of the Second NASA Formal Methods Symposium

NASA Technical Reports Server (NTRS)

Munoz, Cesar (Editor)

2010-01-01

This publication contains the proceedings of the Second NASA Formal Methods Symposium sponsored by the National Aeronautics and Space Administration and held in Washington D.C. April 13-15, 2010. Topics covered include: Decision Engines for Software Analysis using Satisfiability Modulo Theories Solvers; Verification and Validation of Flight-Critical Systems; Formal Methods at Intel -- An Overview; Automatic Review of Abstract State Machines by Meta Property Verification; Hardware-independent Proofs of Numerical Programs; Slice-based Formal Specification Measures -- Mapping Coupling and Cohesion Measures to Formal Z; How Formal Methods Impels Discovery: A Short History of an Air Traffic Management Project; A Machine-Checked Proof of A State-Space Construction Algorithm; Automated Assume-Guarantee Reasoning for Omega-Regular Systems and Specifications; Modeling Regular Replacement for String Constraint Solving; Using Integer Clocks to Verify the Timing-Sync Sensor Network Protocol; Can Regulatory Bodies Expect Efficient Help from Formal Methods?; Synthesis of Greedy Algorithms Using Dominance Relations; A New Method for Incremental Testing of Finite State Machines; Verification of Faulty Message Passing Systems with Continuous State Space in PVS; Phase Two Feasibility Study for Software Safety Requirements Analysis Using Model Checking; A Prototype Embedding of Bluespec System Verilog in the PVS Theorem Prover; SimCheck: An Expressive Type System for Simulink; Coverage Metrics for Requirements-Based Testing: Evaluation of Effectiveness; Software Model Checking of ARINC-653 Flight Code with MCP; Evaluation of a Guideline by Formal Modelling of Cruise Control System in Event-B; Formal Verification of Large Software Systems; Symbolic Computation of Strongly Connected Components Using Saturation; Towards the Formal Verification of a Distributed Real-Time Automotive System; Slicing AADL Specifications for Model Checking; Model Checking with Edge-valued Decision Diagrams; and Data-flow based Model Analysis.

Parallel Computation of the Jacobian Matrix for Nonlinear Equation Solvers Using MATLAB

NASA Technical Reports Server (NTRS)

Rose, Geoffrey K.; Nguyen, Duc T.; Newman, Brett A.

2017-01-01

Demonstrating speedup for parallel code on a multicore shared memory PC can be challenging in MATLAB due to underlying parallel operations that are often opaque to the user. This can limit potential for improvement of serial code even for the so-called embarrassingly parallel applications. One such application is the computation of the Jacobian matrix inherent to most nonlinear equation solvers. Computation of this matrix represents the primary bottleneck in nonlinear solver speed such that commercial finite element (FE) and multi-body-dynamic (MBD) codes attempt to minimize computations. A timing study using MATLAB's Parallel Computing Toolbox was performed for numerical computation of the Jacobian. Several approaches for implementing parallel code were investigated while only the single program multiple data (spmd) method using composite objects provided positive results. Parallel code speedup is demonstrated but the goal of linear speedup through the addition of processors was not achieved due to PC architecture.

GENASIS Mathematics : Object-oriented manifolds, operations, and solvers for large-scale physics simulations

NASA Astrophysics Data System (ADS)

Cardall, Christian Y.; Budiardja, Reuben D.

2018-01-01

The large-scale computer simulation of a system of physical fields governed by partial differential equations requires some means of approximating the mathematical limit of continuity. For example, conservation laws are often treated with a 'finite-volume' approach in which space is partitioned into a large number of small 'cells,' with fluxes through cell faces providing an intuitive discretization modeled on the mathematical definition of the divergence operator. Here we describe and make available Fortran 2003 classes furnishing extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon, along with individual 'unit test' programs and larger example problems demonstrating their use. These classes inaugurate the Mathematics division of our developing astrophysics simulation code GENASIS (Gen eral A strophysical Si mulation S ystem), which will be expanded over time to include additional meshing options, mathematical operations, solver types, and solver variations appropriate for many multiphysics applications.

Fast Integer Ambiguity Resolution for GPS Attitude Determination

NASA Technical Reports Server (NTRS)

Lightsey, E. Glenn; Crassidis, John L.; Markley, F. Landis

1999-01-01

In this paper, a new algorithm for GPS (Global Positioning System) integer ambiguity resolution is shown. The algorithm first incorporates an instantaneous (static) integer search to significantly reduce the search space using a geometric inequality. Then a batch-type loss function is used to check the remaining integers in order to determine the optimal integer. This batch function represents the GPS sightline vectors in the body frame as the sum of two vectors, one depending on the phase measurements and the other on the unknown integers. The new algorithm has several advantages: it does not require an a-priori estimate of the vehicle's attitude; it provides an inherent integrity check using a covariance-type expression; and it can resolve the integers even when coplanar baselines exist. The performance of the new algorithm is tested on a dynamic hardware simulator.

Comparative Study of Advanced Turbulence Models for Turbomachinery

NASA Technical Reports Server (NTRS)

Hadid, Ali H.; Sindir, Munir M.

1996-01-01

A computational study has been undertaken to study the performance of advanced phenomenological turbulence models coded in a modular form to describe incompressible turbulent flow behavior in two dimensional/axisymmetric and three dimensional complex geometry. The models include a variety of two equation models (single and multi-scale k-epsilon models with different near wall treatments) and second moment algebraic and full Reynolds stress closure models. These models were systematically assessed to evaluate their performance in complex flows with rotation, curvature and separation. The models are coded as self contained modules that can be interfaced with a number of flow solvers. These modules are stand alone satellite programs that come with their own formulation, finite-volume discretization scheme, solver and boundary condition implementation. They will take as input (from any generic Navier-Stokes solver) the velocity field, grid (structured H-type grid) and computational domain specification (boundary conditions), and will deliver, depending on the model used, turbulent viscosity, or the components of the Reynolds stress tensor. There are separate 2D/axisymmetric and/or 3D decks for each module considered. The modules are tested using Rocketdyn's proprietary code REACT. The code utilizes an efficient solution procedure to solve Navier-Stokes equations in a non-orthogonal body-fitted coordinate system. The differential equations are discretized over a finite-volume grid using a non-staggered variable arrangement and an efficient solution procedure based on the SIMPLE algorithm for the velocity-pressure coupling is used. The modules developed have been interfaced and tested using finite-volume, pressure-correction CFD solvers which are widely used in the CFD community. Other solvers can also be used to test these modules since they are independently structured with their own discretization scheme and solver methodology. Many of these modules have been independently tested by Professor C.P. Chen and his group at the University of Alabama at Huntsville (UAH) by interfacing them with own flow solver (MAST).

Learning Integer Addition: Is Later Better?

ERIC Educational Resources Information Center

Aqazade, Mahtob; Bofferding, Laura; Farmer, Sherri

2017-01-01

We investigate thirty-three second and fifth-grade students' solution strategies on integer addition problems before and after analyzing contrasting cases with integer addition and participating in a lesson on integers. The students took a pretest, participated in two small group sessions and a short lesson, and took a posttest. Even though the…

Online with Integers

ERIC Educational Resources Information Center

Siegel, Jonathan W.; Siegel, P. B.

2011-01-01

Integers are sometimes used in physics problems to simplify the mathematics so the arithmetic does not distract students from the physics concepts. This is particularly important in exams where students should not have to spend a lot of time using their calculators. Common uses of integers in physics problems include integer solutions to…

Integers Made Easy: Just Walk It Off

ERIC Educational Resources Information Center

Nurnberger-Haag, Julie

2007-01-01

This article describes a multisensory method for teaching students how to multiply and divide as well as add and subtract integers. The author uses sidewalk chalk and the underlying concept of integers to physically and mentally engage students in understanding the concepts of integers, making connections, and developing computational fluency.…

A mixed integer bi-level DEA model for bank branch performance evaluation by Stackelberg approach

NASA Astrophysics Data System (ADS)

Shafiee, Morteza; Lotfi, Farhad Hosseinzadeh; Saleh, Hilda; Ghaderi, Mehdi

2016-03-01

One of the most complicated decision making problems for managers is the evaluation of bank performance, which involves various criteria. There are many studies about bank efficiency evaluation by network DEA in the literature review. These studies do not focus on multi-level network. Wu (Eur J Oper Res 207:856-864, 2010) proposed a bi-level structure for cost efficiency at the first time. In this model, multi-level programming and cost efficiency were used. He used a nonlinear programming to solve the model. In this paper, we have focused on multi-level structure and proposed a bi-level DEA model. We then used a liner programming to solve our model. In other hand, we significantly improved the way to achieve the optimum solution in comparison with the work by Wu (2010) by converting the NP-hard nonlinear programing into a mixed integer linear programming. This study uses a bi-level programming data envelopment analysis model that embodies internal structure with Stackelberg-game relationships to evaluate the performance of banking chain. The perspective of decentralized decisions is taken in this paper to cope with complex interactions in banking chain. The results derived from bi-level programming DEA can provide valuable insights and detailed information for managers to help them evaluate the performance of the banking chain as a whole using Stackelberg-game relationships. Finally, this model was applied in the Iranian bank to evaluate cost efficiency.

Optimally Scheduling Basic Courses at the Defense Language Institute using Integer Programming

DTIC Science & Technology

2005-09-01

DLI’s manual schedules at best can train 8%, 7% and 64%. 15. NUMBER OF PAGES 59 14. SUBJECT TERMS Operations Research, Linear Programming...class in 2006, 2007, and 2008, whereas DLI’s manual schedules at best can train 8%, 7% and 64%. vi THIS PAGE...ARABIC INSTRUTOR LEVELS .....................................25 FIGURE 2. OCS1 AND OCS2 CHINESE-MANDARIN INSTRUTOR LEVELS ............26 FIGURE 3

Decision support for hospital bed management using adaptable individual length of stay estimations and shared resources

PubMed Central

2013-01-01

Background Elective patient admission and assignment planning is an important task of the strategic and operational management of a hospital and early on became a central topic of clinical operations research. The management of hospital beds is an important subtask. Various approaches have been proposed, involving the computation of efficient assignments with regard to the patients’ condition, the necessity of the treatment, and the patients’ preferences. However, these approaches are mostly based on static, unadaptable estimates of the length of stay and, thus, do not take into account the uncertainty of the patient’s recovery. Furthermore, the effect of aggregated bed capacities have not been investigated in this context. Computer supported bed management, combining an adaptable length of stay estimation with the treatment of shared resources (aggregated bed capacities) has not yet been sufficiently investigated. The aim of our work is: 1) to define a cost function for patient admission taking into account adaptable length of stay estimations and aggregated resources, 2) to define a mathematical program formally modeling the assignment problem and an architecture for decision support, 3) to investigate four algorithmic methodologies addressing the assignment problem and one base-line approach, and 4) to evaluate these methodologies w.r.t. cost outcome, performance, and dismissal ratio. Methods The expected free ward capacity is calculated based on individual length of stay estimates, introducing Bernoulli distributed random variables for the ward occupation states and approximating the probability densities. The assignment problem is represented as a binary integer program. Four strategies for solving the problem are applied and compared: an exact approach, using the mixed integer programming solver SCIP; and three heuristic strategies, namely the longest expected processing time, the shortest expected processing time, and random choice. A baseline approach serves to compare these optimization strategies with a simple model of the status quo. All the approaches are evaluated by a realistic discrete event simulation: the outcomes are the ratio of successful assignments and dismissals, the computation time, and the model’s cost factors. Results A discrete event simulation of 226,000 cases shows a reduction of the dismissal rate compared to the baseline by more than 30 percentage points (from a mean dismissal ratio of 74.7% to 40.06% comparing the status quo with the optimization strategies). Each of the optimization strategies leads to an improved assignment. The exact approach has only a marginal advantage over the heuristic strategies in the model’s cost factors (≤3%). Moreover,this marginal advantage was only achieved at the price of a computational time fifty times that of the heuristic models (an average computing time of 141 s using the exact method, vs. 2.6 s for the heuristic strategy). Conclusions In terms of its performance and the quality of its solution, the heuristic strategy RAND is the preferred method for bed assignment in the case of shared resources. Future research is needed to investigate whether an equally marked improvement can be achieved in a large scale clinical application study, ideally one comprising all the departments involved in admission and assignment planning. PMID:23289448

Decision support for hospital bed management using adaptable individual length of stay estimations and shared resources.

PubMed

Schmidt, Robert; Geisler, Sandra; Spreckelsen, Cord

2013-01-07

Elective patient admission and assignment planning is an important task of the strategic and operational management of a hospital and early on became a central topic of clinical operations research. The management of hospital beds is an important subtask. Various approaches have been proposed, involving the computation of efficient assignments with regard to the patients' condition, the necessity of the treatment, and the patients' preferences. However, these approaches are mostly based on static, unadaptable estimates of the length of stay and, thus, do not take into account the uncertainty of the patient's recovery. Furthermore, the effect of aggregated bed capacities have not been investigated in this context. Computer supported bed management, combining an adaptable length of stay estimation with the treatment of shared resources (aggregated bed capacities) has not yet been sufficiently investigated. The aim of our work is: 1) to define a cost function for patient admission taking into account adaptable length of stay estimations and aggregated resources, 2) to define a mathematical program formally modeling the assignment problem and an architecture for decision support, 3) to investigate four algorithmic methodologies addressing the assignment problem and one base-line approach, and 4) to evaluate these methodologies w.r.t. cost outcome, performance, and dismissal ratio. The expected free ward capacity is calculated based on individual length of stay estimates, introducing Bernoulli distributed random variables for the ward occupation states and approximating the probability densities. The assignment problem is represented as a binary integer program. Four strategies for solving the problem are applied and compared: an exact approach, using the mixed integer programming solver SCIP; and three heuristic strategies, namely the longest expected processing time, the shortest expected processing time, and random choice. A baseline approach serves to compare these optimization strategies with a simple model of the status quo. All the approaches are evaluated by a realistic discrete event simulation: the outcomes are the ratio of successful assignments and dismissals, the computation time, and the model's cost factors. A discrete event simulation of 226,000 cases shows a reduction of the dismissal rate compared to the baseline by more than 30 percentage points (from a mean dismissal ratio of 74.7% to 40.06% comparing the status quo with the optimization strategies). Each of the optimization strategies leads to an improved assignment. The exact approach has only a marginal advantage over the heuristic strategies in the model's cost factors (≤3%). Moreover,this marginal advantage was only achieved at the price of a computational time fifty times that of the heuristic models (an average computing time of 141 s using the exact method, vs. 2.6 s for the heuristic strategy). In terms of its performance and the quality of its solution, the heuristic strategy RAND is the preferred method for bed assignment in the case of shared resources. Future research is needed to investigate whether an equally marked improvement can be achieved in a large scale clinical application study, ideally one comprising all the departments involved in admission and assignment planning.

Solving delay differential equations in S-ADAPT by method of steps.

PubMed

Bauer, Robert J; Mo, Gary; Krzyzanski, Wojciech

2013-09-01

S-ADAPT is a version of the ADAPT program that contains additional simulation and optimization abilities such as parametric population analysis. S-ADAPT utilizes LSODA to solve ordinary differential equations (ODEs), an algorithm designed for large dimension non-stiff and stiff problems. However, S-ADAPT does not have a solver for delay differential equations (DDEs). Our objective was to implement in S-ADAPT a DDE solver using the methods of steps. The method of steps allows one to solve virtually any DDE system by transforming it to an ODE system. The solver was validated for scalar linear DDEs with one delay and bolus and infusion inputs for which explicit analytic solutions were derived. Solutions of nonlinear DDE problems coded in S-ADAPT were validated by comparing them with ones obtained by the MATLAB DDE solver dde23. The estimation of parameters was tested on the MATLB simulated population pharmacodynamics data. The comparison of S-ADAPT generated solutions for DDE problems with the explicit solutions as well as MATLAB produced solutions which agreed to at least 7 significant digits. The population parameter estimates from using importance sampling expectation-maximization in S-ADAPT agreed with ones used to generate the data. Published by Elsevier Ireland Ltd.

Optimization methods for decision making in disease prevention and epidemic control.

PubMed

Deng, Yan; Shen, Siqian; Vorobeychik, Yevgeniy

2013-11-01

This paper investigates problems of disease prevention and epidemic control (DPEC), in which we optimize two sets of decisions: (i) vaccinating individuals and (ii) closing locations, given respective budgets with the goal of minimizing the expected number of infected individuals after intervention. The spread of diseases is inherently stochastic due to the uncertainty about disease transmission and human interaction. We use a bipartite graph to represent individuals' propensities of visiting a set of location, and formulate two integer nonlinear programming models to optimize choices of individuals to vaccinate and locations to close. Our first model assumes that if a location is closed, its visitors stay in a safe location and will not visit other locations. Our second model incorporates compensatory behavior by assuming multiple behavioral groups, always visiting the most preferred locations that remain open. The paper develops algorithms based on a greedy strategy, dynamic programming, and integer programming, and compares the computational efficacy and solution quality. We test problem instances derived from daily behavior patterns of 100 randomly chosen individuals (corresponding to 195 locations) in Portland, Oregon, and provide policy insights regarding the use of the two DPEC models. Copyright © 2013 Elsevier Inc. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Ozoe, Shunsuke; Tanaka, Yoichi; Fukushima, Masao

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

Making Sense of Integer Arithmetic: The Effect of Using Virtual Manipulatives on Students' Representational Fluency

ERIC Educational Resources Information Center

Bolyard, Johnna; Moyer-Packenham, Patricia

2012-01-01

This study investigated how the use of virtual manipulatives in integer instruction impacts student achievement for integer addition and subtraction. Of particular interest was the influence of using virtual manipulatives on students' ability to create and translate among representations for integer computation. The research employed a…

Teachers' Construction of Meanings of Signed Quantities and Integer Operation

ERIC Educational Resources Information Center

Kumar, Ruchi S.; Subramaniam, K.; Naik, Shweta Shripad

2017-01-01

Understanding signed quantities and its arithmetic is one of the challenging topics of middle school mathematics. The "specialized content knowledge" (SCK) for teaching integers includes understanding of a variety of representations that may be used while teaching. In this study, we argue that meanings of integers and integer operations…

Anisotropic fractal media by vector calculus in non-integer dimensional space

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2014-08-01

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

HONEI: A collection of libraries for numerical computations targeting multiple processor architectures

NASA Astrophysics Data System (ADS)

van Dyk, Danny; Geveler, Markus; Mallach, Sven; Ribbrock, Dirk; Göddeke, Dominik; Gutwenger, Carsten

2009-12-01

We present HONEI, an open-source collection of libraries offering a hardware oriented approach to numerical calculations. HONEI abstracts the hardware, and applications written on top of HONEI can be executed on a wide range of computer architectures such as CPUs, GPUs and the Cell processor. We demonstrate the flexibility and performance of our approach with two test applications, a Finite Element multigrid solver for the Poisson problem and a robust and fast simulation of shallow water waves. By linking against HONEI's libraries, we achieve a two-fold speedup over straight forward C++ code using HONEI's SSE backend, and additional 3-4 and 4-16 times faster execution on the Cell and a GPU. A second important aspect of our approach is that the full performance capabilities of the hardware under consideration can be exploited by adding optimised application-specific operations to the HONEI libraries. HONEI provides all necessary infrastructure for development and evaluation of such kernels, significantly simplifying their development. Program summaryProgram title: HONEI Catalogue identifier: AEDW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPLv2 No. of lines in distributed program, including test data, etc.: 216 180 No. of bytes in distributed program, including test data, etc.: 1 270 140 Distribution format: tar.gz Programming language: C++ Computer: x86, x86_64, NVIDIA CUDA GPUs, Cell blades and PlayStation 3 Operating system: Linux RAM: at least 500 MB free Classification: 4.8, 4.3, 6.1 External routines: SSE: none; [1] for GPU, [2] for Cell backend Nature of problem: Computational science in general and numerical simulation in particular have reached a turning point. The revolution developers are facing is not primarily driven by a change in (problem-specific) methodology, but rather by the fundamental paradigm shift of the underlying hardware towards heterogeneity and parallelism. This is particularly relevant for data-intensive problems stemming from discretisations with local support, such as finite differences, volumes and elements. Solution method: To address these issues, we present a hardware aware collection of libraries combining the advantages of modern software techniques and hardware oriented programming. Applications built on top of these libraries can be configured trivially to execute on CPUs, GPUs or the Cell processor. In order to evaluate the performance and accuracy of our approach, we provide two domain specific applications; a multigrid solver for the Poisson problem and a fully explicit solver for 2D shallow water equations. Restrictions: HONEI is actively being developed, and its feature list is continuously expanded. Not all combinations of operations and architectures might be supported in earlier versions of the code. Obtaining snapshots from http://www.honei.org is recommended. Unusual features: The considered applications as well as all library operations can be run on NVIDIA GPUs and the Cell BE. Running time: Depending on the application, and the input sizes. The Poisson solver executes in few seconds, while the SWE solver requires up to 5 minutes for large spatial discretisations or small timesteps. References:http://www.nvidia.com/cuda. http://www.ibm.com/developerworks/power/cell.

Parallel Gaussian elimination of a block tridiagonal matrix using multiple microcomputers

NASA Technical Reports Server (NTRS)

Blech, Richard A.

1989-01-01

The solution of a block tridiagonal matrix using parallel processing is demonstrated. The multiprocessor system on which results were obtained and the software environment used to program that system are described. Theoretical partitioning and resource allocation for the Gaussian elimination method used to solve the matrix are discussed. The results obtained from running 1, 2 and 3 processor versions of the block tridiagonal solver are presented. The PASCAL source code for these solvers is given in the appendix, and may be transportable to other shared memory parallel processors provided that the synchronization outlines are reproduced on the target system.

Solution of the Generalized Noah's Ark Problem.

PubMed

Billionnet, Alain

2013-01-01

The phylogenetic diversity (PD) of a set of species is a measure of the evolutionary distance among the species in the collection, based on a phylogenetic tree. Such a tree is composed of a root, internal nodes, and leaves that correspond to the set of taxa under study. With each edge of the tree is associated a non-negative branch length (evolutionary distance). If a particular survival probability is associated with each taxon, the PD measure becomes the expected PD measure. In the Noah's Ark Problem (NAP) introduced by Weitzman (1998), these survival probabilities can be increased at some cost. The problem is to determine how best to allocate a limited amount of resources to maximize the expected PD of the considered species. It is easy to formulate the NAP as a (difficult) nonlinear 0-1 programming problem. The aim of this article is to show that a general version of the NAP (GNAP) can be solved simply and efficiently with any set of edge weights and any set of survival probabilities by using standard mixed-integer linear programming software. The crucial point to move from a nonlinear program in binary variables to a mixed-integer linear program, is to approximate the logarithmic function by the lower envelope of a set of tangents to the curve. Solving the obtained mixed-integer linear program provides not only a near-optimal solution but also an upper bound on the value of the optimal solution. We also applied this approach to a generalization of the nature reserve problem (GNRP) that consists of selecting a set of regions to be conserved so that the expected PD of the set of species present in these regions is maximized. In this case, the survival probabilities of different taxa are not independent of each other. Computational results are presented to illustrate potentialities of the approach. Near-optimal solutions with hypothetical phylogenetic trees comprising about 4000 taxa are obtained in a few seconds or minutes of computing time for the GNAP, and in about 30 min for the GNRP. In all the cases the average guarantee varies from 0% to 1.20%.

Multi-vehicle mobility allowance shuttle transit (MAST) system : an analytical model to select the fleet size and a scheduling heuristic.

DOT National Transportation Integrated Search

2012-06-01

The mobility allowance shuttle transit (MAST) system is a hybrid transit system in which vehicles are : allowed to deviate from a fixed route to serve flexible demand. A mixed integer programming (MIP) : formulation for the static scheduling problem ...

A Graphical Teaching Tool for Understanding Two's Complement.

ERIC Educational Resources Information Center

Luck, Carlos L.

As part of the Electrical Engineering program at the Univesity of Southern Maine, students are typically introduced to Two's Complement algebra and representation, a method to include negative numbers in the binary representation of integers that is widely used in microprocessors and related digital systems. The traditional, procedural method to…

Space tug economic analysis study. Volume 2: Tug concepts analysis. Part 2: Economic analysis

NASA Technical Reports Server (NTRS)

1972-01-01

An economic analysis of space tug operations is presented. The subjects discussed are: (1) cost uncertainties, (2) scenario analysis, (3) economic sensitivities, (4) mixed integer programming formulation of the space tug problem, and (5) critical parameters in the evaluation of a public expenditure.

Optimizing efficiency of height modeling for extensive forest inventories.

Treesearch

T.M. Barrett

2006-01-01

Although critical to monitoring forest ecosystems, inventories are expensive. This paper presents a generalizable method for using an integer programming model to examine tradeoffs between cost and estimation error for alternative measurement strategies in forest inventories. The method is applied to an example problem of choosing alternative height-modeling strategies...

Selecting Personal Computers.

ERIC Educational Resources Information Center

Djang, Philipp A.

1993-01-01

Describes a Multiple Criteria Decision Analysis Approach for the selection of personal computers that combines the capabilities of Analytic Hierarchy Process and Integer Goal Programing. An example of how decision makers can use this approach to determine what kind of personal computers and how many of each type to purchase is given. (nine…

Integrated Sensing and Processing (ISP) Phase II: Demonstration and Evaluation for Distributed Sensor Netowrks and Missile Seeker Systems

DTIC Science & Technology

2007-02-28

Shah, D. Waagen, H. Schmitt, S. Bellofiore, A. Spanias, and D. Cochran, 32nd International Conference on Acoustics, Speech , and Signal Processing...Information Exploitation Office kNN k-Nearest Neighbor LEAN Laplacian Eigenmap Adaptive Neighbor LIP Linear Integer Programming ISP

Optimization Research of Generation Investment Based on Linear Programming Model

NASA Astrophysics Data System (ADS)

Wu, Juan; Ge, Xueqian

Linear programming is an important branch of operational research and it is a mathematical method to assist the people to carry out scientific management. GAMS is an advanced simulation and optimization modeling language and it will combine a large number of complex mathematical programming, such as linear programming LP, nonlinear programming NLP, MIP and other mixed-integer programming with the system simulation. In this paper, based on the linear programming model, the optimized investment decision-making of generation is simulated and analyzed. At last, the optimal installed capacity of power plants and the final total cost are got, which provides the rational decision-making basis for optimized investments.

INFORM: An interactive data collection and display program with debugging capability

NASA Technical Reports Server (NTRS)

Cwynar, D. S.

1980-01-01

A computer program was developed to aid ASSEMBLY language programmers of mini and micro computers in solving the man machine communications problems that exist when scaled integers are involved. In addition to producing displays of quasi-steady state values, INFORM provides an interactive mode for debugging programs, making program patches, and modifying the displays. Auxiliary routines SAMPLE and DATAO add dynamic data acquisition and high speed dynamic display capability to the program. Programming information and flow charts to aid in implementing INFORM on various machines together with descriptions of all supportive software are provided. Program modifications to satisfy the individual user's needs are considered.

Simulation of fluid-structure interaction in micropumps by coupling of two commercial finite element programs

NASA Astrophysics Data System (ADS)

Klein, Andreas; Gerlach, Gerald

1998-09-01

This paper deals with the simulation of the fluid-structure interaction phenomena in micropumps. The proposed solution approach is based on external coupling of two different solvers, which are considered here as `black boxes'. Therefore, no specific intervention is necessary into the program code, and solvers can be exchanged arbitrarily. For the realization of the external iteration loop, two algorithms are considered: the relaxation-based Gauss-Seidel method and the computationally more extensive Newton method. It is demonstrated in terms of a simplified test case, that for rather weak coupling, the Gauss-Seidel method is sufficient. However, by simply changing the considered fluid from air to water, the two physical domains become strongly coupled, and the Gauss-Seidel method fails to converge in this case. The Newton iteration scheme must be used instead.

Experimental evaluation of model predictive control and inverse dynamics control for spacecraft proximity and docking maneuvers

NASA Astrophysics Data System (ADS)

Virgili-Llop, Josep; Zagaris, Costantinos; Park, Hyeongjun; Zappulla, Richard; Romano, Marcello

2018-03-01

An experimental campaign has been conducted to evaluate the performance of two different guidance and control algorithms on a multi-constrained docking maneuver. The evaluated algorithms are model predictive control (MPC) and inverse dynamics in the virtual domain (IDVD). A linear-quadratic approach with a quadratic programming solver is used for the MPC approach. A nonconvex optimization problem results from the IDVD approach, and a nonlinear programming solver is used. The docking scenario is constrained by the presence of a keep-out zone, an entry cone, and by the chaser's maximum actuation level. The performance metrics for the experiments and numerical simulations include the required control effort and time to dock. The experiments have been conducted in a ground-based air-bearing test bed, using spacecraft simulators that float over a granite table.

"The NASA Sci Files": The Case of the Biological Biosphere. [Videotape].

ERIC Educational Resources Information Center

National Aeronautics and Space Administration, Hampton, VA. Langley Research Center.

The NASA Science Files is a series of instructional programs consisting of broadcast, print, and online elements. Emphasizing standards-based instruction, problem-based learning, and science as inquiry, the series seeks to motivate students in grades 3-5 to become critical thinkers and active problem solvers. Each program supports the national…

A non-linear regression analysis program for describing electrophysiological data with multiple functions using Microsoft Excel.

PubMed

Brown, Angus M

2006-04-01

The objective of this present study was to demonstrate a method for fitting complex electrophysiological data with multiple functions using the SOLVER add-in of the ubiquitous spreadsheet Microsoft Excel. SOLVER minimizes the difference between the sum of the squares of the data to be fit and the function(s) describing the data using an iterative generalized reduced gradient method. While it is a straightforward procedure to fit data with linear functions, and we have previously demonstrated a method of non-linear regression analysis of experimental data based upon a single function, it is more complex to fit data with multiple functions, usually requiring specialized expensive computer software. In this paper we describe an easily understood program for fitting experimentally acquired data, in this case the stimulus-evoked compound action potential from the mouse optic nerve, with multiple Gaussian functions. The program is flexible and can be applied to describe data with a wide variety of user-input functions.

Solving Partial Differential Equations in a data-driven multiprocessor environment

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

Gaudiot, J.L.; Lin, C.M.; Hosseiniyar, M.

1988-12-31

Partial differential equations can be found in a host of engineering and scientific problems. The emergence of new parallel architectures has spurred research in the definition of parallel PDE solvers. Concurrently, highly programmable systems such as data-how architectures have been proposed for the exploitation of large scale parallelism. The implementation of some Partial Differential Equation solvers (such as the Jacobi method) on a tagged token data-flow graph is demonstrated here. Asynchronous methods (chaotic relaxation) are studied and new scheduling approaches (the Token No-Labeling scheme) are introduced in order to support the implementation of the asychronous methods in a data-driven environment.more » New high-level data-flow language program constructs are introduced in order to handle chaotic operations. Finally, the performance of the program graphs is demonstrated by a deterministic simulation of a message passing data-flow multiprocessor. An analysis of the overhead in the data-flow graphs is undertaken to demonstrate the limits of parallel operations in dataflow PDE program graphs.« less

Software Technology for Adaptable, Reliable Systems (STARS) (User Manual). Ada Command Environment (ACE) Version 8.0 Sun OS Implementation

DTIC Science & Technology

1990-10-29

the equivalent type names in the basic X libary . 37. Intrinsics Contains the type declarations common to all Xt toolkit routines. 38. Widget-Package...Memory-Size constant Integer 1; MinInt constant I-reger Integer’First; MaxInt const-i’ integer Integer’Last; -- Max- Digits constant Integer 1; -- MaxMan...connection between some type names used by Xt routines and the equivalent type names in the basic X libary . .package RenamedXlibTypes is P;’ge 65 29

CUMBIN - CUMULATIVE BINOMIAL PROGRAMS

NASA Technical Reports Server (NTRS)

Bowerman, P. N.

1994-01-01

The cumulative binomial program, CUMBIN, is one of a set of three programs which calculate cumulative binomial probability distributions for arbitrary inputs. The three programs, CUMBIN, NEWTONP (NPO-17556), and CROSSER (NPO-17557), can be used independently of one another. CUMBIN can be used by statisticians and users of statistical procedures, test planners, designers, and numerical analysts. The program has been used for reliability/availability calculations. CUMBIN calculates the probability that a system of n components has at least k operating if the probability that any one operating is p and the components are independent. Equivalently, this is the reliability of a k-out-of-n system having independent components with common reliability p. CUMBIN can evaluate the incomplete beta distribution for two positive integer arguments. CUMBIN can also evaluate the cumulative F distribution and the negative binomial distribution, and can determine the sample size in a test design. CUMBIN is designed to work well with all integer values 0 < k <= n. To run the program, the user simply runs the executable version and inputs the information requested by the program. The program is not designed to weed out incorrect inputs, so the user must take care to make sure the inputs are correct. Once all input has been entered, the program calculates and lists the result. The CUMBIN program is written in C. It was developed on an IBM AT with a numeric co-processor using Microsoft C 5.0. Because the source code is written using standard C structures and functions, it should compile correctly with most C compilers. The program format is interactive. It has been implemented under DOS 3.2 and has a memory requirement of 26K. CUMBIN was developed in 1988.

Operational Planning for Multiple Heterogeneous Unmanned Aerial Vehicles in Three Dimensions

DTIC Science & Technology

2009-06-01

human input in the planning process. Two solution methods are presented: (1) a mixed-integer program, and (2) an algorithm that utilizes a metaheuristic ...and (2) an algorithm that utilizes a metaheuristic to generate composite variables for a linear program, called the Composite Operations Planning...that represent a path and an associated type of UAV. The reformulation is incorporated into an algorithm that uses a metaheuristic to generate the

Forest management and economics

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

Buongiorno, J.; Gilless, J.K.

1987-01-01

This volume provides a survey of quantitative methods, guiding the reader through formulation and analysis of models that address forest management problems. The authors use simple mathematics, graphics, and short computer programs to explain each method. Emphasizing applications, they discuss linear, integer, dynamic, and goal programming; simulation; network modeling; and econometrics, as these relate to problems of determining economic harvest schedules in even-aged and uneven-aged forests, the evaluation of forest policies, multiple-objective decision making, and more.

Modeling Road Vulnerability to Snow Using Mixed Integer Optimization

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

Rodriguez, Tony K; Omitaomu, Olufemi A; Ostrowski, James A

As the number and severity of snowfall events continue to grow, the need to intelligently direct road maintenance during these snowfall events will also grow. In several locations, local governments lack the resources to completely treat all roadways during snow events. Furthermore, some governments utilize only traffic data to determine which roads should be treated. As a result, many schools, businesses, and government offices must be unnecessarily closed, which directly impacts the social, educational, and economic well-being of citizens and institutions. In this work, we propose a mixed integer programming formulation to optimally allocate resources to manage snowfall on roadsmore » using meteorological, geographical, and environmental parameters. Additionally, we evaluate the impacts of an increase in budget for winter road maintenance on snow control resources.« less

DORMAN computer program (study 2.5). Volume 2: User's guide and programmer's guide. [development of data bank for computerized information storage of NASA programs

NASA Technical Reports Server (NTRS)

Wray, S. T., Jr.

1973-01-01

The DORMAN program was developed to create and modify a data bank containing data decks which serve as input to the DORCA Computer Program. Via a remote terminal a user can access the bank, extract any data deck, modify that deck, output the modified deck to be input to the DORCA program, and save the modified deck in the data bank. This computer program is an assist in the utilization of the DORCA program. The program is dimensionless and operates almost entirely in integer mode. The program was developed on the CDC 6400/7600 complex for implementation on a UNIVAC 1108 computer.

Acceleration of aircraft-level Traffic Flow Management

NASA Astrophysics Data System (ADS)

Rios, Joseph Lucio

This dissertation describes novel approaches to solving large-scale, high fidelity, aircraft-level Traffic Flow Management scheduling problems. Depending on the methods employed, solving these problems to optimality can take longer than the length of the planning horizon in question. Research in this domain typically focuses on the quality of the modeling used to describe the problem and the benefits achieved from the optimized solution, often treating computational aspects as secondary or tertiary. The work presented here takes the complementary view and considers the computational aspect as the primary concern. To this end, a previously published model for solving this Traffic Flow Management scheduling problem is used as starting point for this study. The model proposed by Bertsimas and Stock-Patterson is a binary integer program taking into account all major resource capacities and the trajectories of each flight to decide which flights should be held in which resource for what amount of time in order to satisfy all capacity requirements. For large instances, the solve time using state-of-the-art solvers is prohibitive for use within a potential decision support tool. With this dissertation, however, it will be shown that solving can be achieved in reasonable time for instances of real-world size. Five other techniques developed and tested for this dissertation will be described in detail. These are heuristic methods that provide good results. Performance is measured in terms of runtime and "optimality gap." We then describe the most successful method presented in this dissertation: Dantzig-Wolfe Decomposition. Results indicate that a parallel implementation of Dantzig-Wolfe Decomposition optimally solves the original problem in much reduced time and with better integrality and smaller optimality gap than any of the heuristic methods or state-of-the-art, commercial solvers. The solution quality improves in every measureable way as the number of subproblems solved in parallel increases. A maximal decomposition provides the best results of any method tested. The convergence qualities of Dantzig-Wolfe Decomposition have been criticized in the past, so we examine what makes the Bertsimas-Stock Patterson model so amenable to use of this method. These mathematical qualities of the model are generalized to provide guidance on other problems that may benefit from massively parallel Dantzig-Wolfe Decomposition. This result, together with the development of the software, and the experimental results indicating the feasibility of real-time, nationwide Traffic Flow Management scheduling represent the major contributions of this dissertation.

Counting Triangles to Sum Squares

ERIC Educational Resources Information Center

DeMaio, Joe

2012-01-01

Counting complete subgraphs of three vertices in complete graphs, yields combinatorial arguments for identities for sums of squares of integers, odd integers, even integers and sums of the triangular numbers.

Slip and Slide Method of Factoring Trinomials with Integer Coefficients over the Integers

ERIC Educational Resources Information Center

Donnell, William A.

2012-01-01

In intermediate and college algebra courses there are a number of methods for factoring quadratic trinomials with integer coefficients over the integers. Some of these methods have been given names, such as trial and error, reversing FOIL, AC method, middle term splitting method and slip and slide method. The purpose of this article is to discuss…

Obstacles and Affordances for Integer Reasoning: An Analysis of Children's Thinking and the History of Mathematics

ERIC Educational Resources Information Center

Bishop, Jessica Pierson; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P.; Lewis, Melinda L.

2014-01-01

We identify and document 3 cognitive obstacles, 3 cognitive affordances, and 1 type of integer understanding that can function as either an obstacle or affordance for learners while they extend their numeric domains from whole numbers to include negative integers. In particular, we highlight 2 key subsets of integer reasoning: understanding or…

Anisotropic fractal media by vector calculus in non-integer dimensional space

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

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2014-08-15

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensionalmore » space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.« less

A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows

NASA Astrophysics Data System (ADS)

Zhou, Qiang; Fan, Liang-Shih

2014-07-01

A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The immersed boundary method (IBM) recently developed by Breugem (2012) [19] is adopted in the present method, development including the retraction technique, the multi-direct forcing method and the direct account of the inertia of the fluid contained within the particles. The present IB-LBM is, however, formulated with further improvement with the implementation of the high-order Runge-Kutta schemes in the coupled fluid-particle interaction. The major challenge to implement high-order Runge-Kutta schemes in the LBM is that the flow information such as density and velocity cannot be directly obtained at a fractional time step from the LBM since the LBM only provides the flow information at an integer time step. This challenge can be, however, overcome as given in the present IB-LBM by extrapolating the flow field around particles from the known flow field at the previous integer time step. The newly calculated fluid-particle interactions from the previous fractional time steps of the current integer time step are also accounted for in the extrapolation. The IB-LBM with high-order Runge-Kutta schemes developed in this study is validated by several benchmark applications. It is demonstrated, for the first time, that the IB-LBM has the capacity to resolve the translational and rotational motion of particles with the second-order accuracy. The optimal retraction distances for spheres and tubes that help the method achieve the second-order accuracy are found to be around 0.30 and -0.47 times of the lattice spacing, respectively. Simulations of the Stokes flow through a simple cubic lattice of rotational spheres indicate that the lift force produced by the Magnus effect can be very significant in view of the magnitude of the drag force when the practical rotating speed of the spheres is encountered. This finding may lead to more comprehensive studies of the effect of the particle rotation on fluid-solid drag laws. It is also demonstrated that, when the third-order or the fourth-order Runge-Kutta scheme is used, the numerical stability of the present IB-LBM is better than that of all methods in the literature, including the previous IB-LBMs and also the methods with the combination of the IBM and the traditional incompressible Navier-Stokes solver.

Techniques for computing the discrete Fourier transform using the quadratic residue Fermat number systems

NASA Technical Reports Server (NTRS)

Truong, T. K.; Chang, J. J.; Hsu, I. S.; Pei, D. Y.; Reed, I. S.

1986-01-01

The complex integer multiplier and adder over the direct sum of two copies of finite field developed by Cozzens and Finkelstein (1985) is specialized to the direct sum of the rings of integers modulo Fermat numbers. Such multiplication over the rings of integers modulo Fermat numbers can be performed by means of two integer multiplications, whereas the complex integer multiplication requires three integer multiplications. Such multiplications and additions can be used in the implementation of a discrete Fourier transform (DFT) of a sequence of complex numbers. The advantage of the present approach is that the number of multiplications needed to compute a systolic array of the DFT can be reduced substantially. The architectural designs using this approach are regular, simple, expandable and, therefore, naturally suitable for VLSI implementation.

Scheduling algorithms for rapid imaging using agile Cubesat constellations

NASA Astrophysics Data System (ADS)

Nag, Sreeja; Li, Alan S.; Merrick, James H.

2018-02-01

Distributed Space Missions such as formation flight and constellations, are being recognized as important Earth Observation solutions to increase measurement samples over space and time. Cubesats are increasing in size (27U, ∼40 kg in development) with increasing capabilities to host imager payloads. Given the precise attitude control systems emerging in the commercial market, Cubesats now have the ability to slew and capture images within short notice. We propose a modular framework that combines orbital mechanics, attitude control and scheduling optimization to plan the time-varying, full-body orientation of agile Cubesats in a constellation such that they maximize the number of observed images and observation time, within the constraints of Cubesat hardware specifications. The attitude control strategy combines bang-bang and PD control, with constraints such as power consumption, response time, and stability factored into the optimality computations and a possible extension to PID control to account for disturbances. Schedule optimization is performed using dynamic programming with two levels of heuristics, verified and improved upon using mixed integer linear programming. The automated scheduler is expected to run on ground station resources and the resultant schedules uplinked to the satellites for execution, however it can be adapted for onboard scheduling, contingent on Cubesat hardware and software upgrades. The framework is generalizable over small steerable spacecraft, sensor specifications, imaging objectives and regions of interest, and is demonstrated using multiple 20 kg satellites in Low Earth Orbit for two case studies - rapid imaging of Landsat's land and coastal images and extended imaging of global, warm water coral reefs. The proposed algorithm captures up to 161% more Landsat images than nadir-pointing sensors with the same field of view, on a 2-satellite constellation over a 12-h simulation. Integer programming was able to verify that optimality of the dynamic programming solution for single satellites was within 10%, and find up to 5% more optimal solutions. The optimality gap for constellations was found to be 22% at worst, but the dynamic programming schedules were found at nearly four orders of magnitude better computational speed than integer programming. The algorithm can include cloud cover predictions, ground downlink windows or any other spatial, temporal or angular constraints into the orbital module and be integrated into planning tools for agile constellations.

Case study and lessons learned for the Great Lakes ITS Program, Airport ITS Integration and the Road Infrastructure Management System projects, final report, Wayne County, Michigan

DOT National Transportation Integrated Search

2007-03-02

This report presents the case study and lessons learned for the national evaluation of the Great Lakes Intelligent Transportation Systems (GLITS) Airport ITS Integration and Road Infrastructure Management System (RIMS) projects. The Airport ITS Integ...

A Procedure Using Calculators to Express Answers in Fractional Form.

ERIC Educational Resources Information Center

Carlisle, Earnest

A procedure is described that enables students to perform operations on fractions with a calculator, expressing the answer as a fraction. Patterns using paper-and-pencil procedures for each operation with fractions are presented. A microcomputer software program illustrates how the answer can be found using integer values of the numerators and…

Automated Test-Form Generation

ERIC Educational Resources Information Center

van der Linden, Wim J.; Diao, Qi

2011-01-01

In automated test assembly (ATA), the methodology of mixed-integer programming is used to select test items from an item bank to meet the specifications for a desired test form and optimize its measurement accuracy. The same methodology can be used to automate the formatting of the set of selected items into the actual test form. Three different…

A strategic assessment of biofuels development in the Western States

Treesearch

Kenneth E. Skog; Robert Rummer; Bryan Jenkins; Nathan Parker; Peter Tittman; Quinn Hart; Richard Nelson; Ed Gray; Anneliese Schmidt; Marcia Patton-Mallory; Gordon Gayle

2009-01-01

The Western Governors' Association assessment of biofuels potential in western states estimated the location and capacity of biofuels plants that could potentially be built for selected gasoline prices in 2015 using a mixed integer programming model. The model included information on forest biomass supply curves by county (developed using Forest Service FIA data...

An Integer Programming-Based Generalized Vehicle Routing Approach for Printed Circuit Board Assembly Optimization

ERIC Educational Resources Information Center

Seth, Anupam

2009-01-01

Production planning and scheduling for printed circuit, board assembly has so far defied standard operations research approaches due to the size and complexity of the underlying problems, resulting in unexploited automation flexibility. In this thesis, the increasingly popular collect-and-place machine configuration is studied and the assembly…

Elements of Mathematics, Book O: Intuitive Background. Chapter 2, The Integers.

ERIC Educational Resources Information Center

Exner, Robert; And Others

The sixteen chapters of this book provide the core materials for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

Algorithms for Scheduling and Network Problems

DTIC Science & Technology

1991-09-01

time. We already know, by Lemma 2.2.1, that WOPT = O(log( mpU )), so if we could solve this integer program optimally we would be done. However, the...Folydirat, 15:177-191, 1982. [6] I.S. Belov and Ya. N. Stolin. An algorithm in a single path operations scheduling problem. In Mathematical Economics and

Enhancing Autonomy of Aerial Systems Via Integration of Visual Sensors into Their Avionics Suite

DTIC Science & Technology

2016-09-01

aerial platform for subsequent visual sensor integration. 14. SUBJECT TERMS autonomous system, quadrotors, direct method, inverse ...CONTROLLER ARCHITECTURE .....................................................43 B. INVERSE DYNAMICS IN THE VIRTUAL DOMAIN ......................45 1...control station GPS Global-Positioning System IDVD inverse dynamics in the virtual domain ILP integer linear program INS inertial-navigation system

The Efficiency of Split Panel Designs in an Analysis of Variance Model

PubMed Central

Wang, Wei-Guo; Liu, Hai-Jun

2016-01-01

We consider split panel design efficiency in analysis of variance models, that is, the determination of the cross-sections series optimal proportion in all samples, to minimize parametric best linear unbiased estimators of linear combination variances. An orthogonal matrix is constructed to obtain manageable expression of variances. On this basis, we derive a theorem for analyzing split panel design efficiency irrespective of interest and budget parameters. Additionally, relative estimator efficiency based on the split panel to an estimator based on a pure panel or a pure cross-section is present. The analysis shows that the gains from split panel can be quite substantial. We further consider the efficiency of split panel design, given a budget, and transform it to a constrained nonlinear integer programming. Specifically, an efficient algorithm is designed to solve the constrained nonlinear integer programming. Moreover, we combine one at time designs and factorial designs to illustrate the algorithm’s efficiency with an empirical example concerning monthly consumer expenditure on food in 1985, in the Netherlands, and the efficient ranges of the algorithm parameters are given to ensure a good solution. PMID:27163447

A farm-level precision land management framework based on integer programming

PubMed Central

Li, Qi; Hu, Guiping; Jubery, Talukder Zaki; Ganapathysubramanian, Baskar

2017-01-01

Farmland management involves several planning and decision making tasks including seed selection and irrigation management. A farm-level precision farmland management model based on mixed integer linear programming is proposed in this study. Optimal decisions are designed for pre-season planning of crops and irrigation water allocation. The model captures the effect of size and shape of decision scale as well as special irrigation patterns. The authors illustrate the model with a case study on a farm in the state of California in the U.S. and show the model can capture the impact of precision farm management on profitability. The results show that threefold increase of annual net profit for farmers could be achieved by carefully choosing irrigation and seed selection. Although farmers could increase profits by applying precision management to seed or irrigation alone, profit increase is more significant if farmers apply precision management on seed and irrigation simultaneously. The proposed model can also serve as a risk analysis tool for farmers facing seasonal irrigation water limits as well as a quantitative tool to explore the impact of precision agriculture. PMID:28346499

Microgrid Optimal Scheduling With Chance-Constrained Islanding Capability

DOE PAGES

Liu, Guodong; Starke, Michael R.; Xiao, B.; ...

2017-01-13

To facilitate the integration of variable renewable generation and improve the resilience of electricity sup-ply in a microgrid, this paper proposes an optimal scheduling strategy for microgrid operation considering constraints of islanding capability. A new concept, probability of successful islanding (PSI), indicating the probability that a microgrid maintains enough spinning reserve (both up and down) to meet local demand and accommodate local renewable generation after instantaneously islanding from the main grid, is developed. The PSI is formulated as mixed-integer linear program using multi-interval approximation taking into account the probability distributions of forecast errors of wind, PV and load. With themore » goal of minimizing the total operating cost while preserving user specified PSI, a chance-constrained optimization problem is formulated for the optimal scheduling of mirogrids and solved by mixed integer linear programming (MILP). Numerical simulations on a microgrid consisting of a wind turbine, a PV panel, a fuel cell, a micro-turbine, a diesel generator and a battery demonstrate the effectiveness of the proposed scheduling strategy. Lastly, we verify the relationship between PSI and various factors.« less

A hybrid inventory management system respondingto regular demand and surge demand

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

Mohammad S. Roni; Mingzhou Jin; Sandra D. Eksioglu

2014-06-01

This paper proposes a hybrid policy for a stochastic inventory system facing regular demand and surge demand. The combination of two different demand patterns can be observed in many areas, such as healthcare inventory and humanitarian supply chain management. The surge demand has a lower arrival rate but higher demand volume per arrival. The solution approach proposed in this paper incorporates the level crossing method and mixed integer programming technique to optimize the hybrid inventory policy with both regular orders and emergency orders. The level crossing method is applied to obtain the equilibrium distributions of inventory levels under a givenmore » policy. The model is further transformed into a mixed integer program to identify an optimal hybrid policy. A sensitivity analysis is conducted to investigate the impact of parameters on the optimal inventory policy and minimum cost. Numerical results clearly show the benefit of using the proposed hybrid inventory model. The model and solution approach could help healthcare providers or humanitarian logistics providers in managing their emergency supplies in responding to surge demands.« less

Chemotherapy appointment scheduling under uncertainty using mean-risk stochastic integer programming.

PubMed

Alvarado, Michelle; Ntaimo, Lewis

2018-03-01

Oncology clinics are often burdened with scheduling large volumes of cancer patients for chemotherapy treatments under limited resources such as the number of nurses and chairs. These cancer patients require a series of appointments over several weeks or months and the timing of these appointments is critical to the treatment's effectiveness. Additionally, the appointment duration, the acuity levels of each appointment, and the availability of clinic nurses are uncertain. The timing constraints, stochastic parameters, rising treatment costs, and increased demand of outpatient oncology clinic services motivate the need for efficient appointment schedules and clinic operations. In this paper, we develop three mean-risk stochastic integer programming (SIP) models, referred to as SIP-CHEMO, for the problem of scheduling individual chemotherapy patient appointments and resources. These mean-risk models are presented and an algorithm is devised to improve computational speed. Computational results were conducted using a simulation model and results indicate that the risk-averse SIP-CHEMO model with the expected excess mean-risk measure can decrease patient waiting times and nurse overtime when compared to deterministic scheduling algorithms by 42 % and 27 %, respectively.

Supporting Dynamic Spectrum Access in Heterogeneous LTE+ Networks

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

Luiz A. DaSilva; Ryan E. Irwin; Mike Benonis

As early as 2014, mobile network operators’ spectral capac- ity is expected to be overwhelmed by the demand brought on by new devices and applications. With Long Term Evo- lution Advanced (LTE+) networks likely as the future one world 4G standard, network operators may need to deploy a Dynamic Spectrum Access (DSA) overlay in Heterogeneous Networks (HetNets) to extend coverage, increase spectrum efficiency, and increase the capacity of these networks. In this paper, we propose three new management frameworks for DSA in an LTE+ HetNet: Spectrum Accountability Client, Cell Spectrum Management, and Domain Spectrum Man- agement. For these spectrum managementmore » frameworks, we define protocol interfaces and operational signaling scenar- ios to support cooperative sensing, spectrum lease manage- ment, and alarm scenarios for rule adjustment. We also quan- tify, through integer programs, the benefits of using DSA in an LTE+ HetNet, that can opportunistically reuse vacant TV and GSM spectrum. Using integer programs, we consider a topology using Geographic Information System data from the Blacksburg, VA metro area to assess the realistic benefits of DSA in an LTE+ HetNet.« less

Two Methods for Efficient Solution of the Hitting-Set Problem

NASA Technical Reports Server (NTRS)

Vatan, Farrokh; Fijany, Amir

2005-01-01

A paper addresses much of the same subject matter as that of Fast Algorithms for Model-Based Diagnosis (NPO-30582), which appears elsewhere in this issue of NASA Tech Briefs. However, in the paper, the emphasis is more on the hitting-set problem (also known as the transversal problem), which is well known among experts in combinatorics. The authors primary interest in the hitting-set problem lies in its connection to the diagnosis problem: it is a theorem of model-based diagnosis that in the set-theory representation of the components of a system, the minimal diagnoses of a system are the minimal hitting sets of the system. In the paper, the hitting-set problem (and, hence, the diagnosis problem) is translated from a combinatorial to a computational problem by mapping it onto the Boolean satisfiability and integer- programming problems. The paper goes on to describe developments nearly identical to those summarized in the cited companion NASA Tech Briefs article, including the utilization of Boolean-satisfiability and integer- programming techniques to reduce the computation time and/or memory needed to solve the hitting-set problem.

Integer-Linear-Programing Optimization in Scalable Video Multicast with Adaptive Modulation and Coding in Wireless Networks

PubMed Central

Lee, Chaewoo

2014-01-01

The advancement in wideband wireless network supports real time services such as IPTV and live video streaming. However, because of the sharing nature of the wireless medium, efficient resource allocation has been studied to achieve a high level of acceptability and proliferation of wireless multimedia. Scalable video coding (SVC) with adaptive modulation and coding (AMC) provides an excellent solution for wireless video streaming. By assigning different modulation and coding schemes (MCSs) to video layers, SVC can provide good video quality to users in good channel conditions and also basic video quality to users in bad channel conditions. For optimal resource allocation, a key issue in applying SVC in the wireless multicast service is how to assign MCSs and the time resources to each SVC layer in the heterogeneous channel condition. We formulate this problem with integer linear programming (ILP) and provide numerical results to show the performance under 802.16 m environment. The result shows that our methodology enhances the overall system throughput compared to an existing algorithm. PMID:25276862

Checking Equivalence of SPMD Programs Using Non-Interference

DTIC Science & Technology

2010-01-29

with it hopes to go beyond the limits of Moore’s law, but also worries that programming will become harder [5]. One of the reasons why parallel...array name in G or L, and e is an arithmetic expression of integer type. In the CUDA code shown in Section 3, b and t are represented by coreId and...b+ t. A second, optimized version of the program (using function “reverse2”, see Section 3) can be modeled as a tuple P2 = ( G ,L2, F 2), with G same

Parallel scheduling of recursively defined arrays

NASA Technical Reports Server (NTRS)

Myers, T. J.; Gokhale, M. B.

1986-01-01

A new method of automatic generation of concurrent programs which constructs arrays defined by sets of recursive equations is described. It is assumed that the time of computation of an array element is a linear combination of its indices, and integer programming is used to seek a succession of hyperplanes along which array elements can be computed concurrently. The method can be used to schedule equations involving variable length dependency vectors and mutually recursive arrays. Portions of the work reported here have been implemented in the PS automatic program generation system.

Towards Real-Time Pilot-in-the-Loop Simulation of Rotorcraft With Fully-Coupled CFD Solutions of Rotor / Terrain Interactions

NASA Astrophysics Data System (ADS)

Oruc, Ilker

This thesis presents the development of computationally efficient coupling of Navier-Stokes CFD with a helicopter flight dynamics model, with the ultimate goal of real-time simulation of fully coupled aerodynamic interactions between rotor flow and the surrounding terrain. A particular focus of the research is on coupled airwake effects in the helicopter / ship dynamic interface. A computationally efficient coupling interface was developed between the helicopter flight dynamics model, GENHEL-PSU and the Navier-Stokes solvers, CRUNCH/CRAFT-CFD using both FORTRAN and C/C++ programming languages. In order to achieve real-time execution speeds, the main rotor was modeled with a simplified actuator disk using unsteady momentum sources, instead of resolving the full blade geometry in the CFD. All the airframe components, including the fuselage are represented by single aerodynamic control points in the CFD calculations. The rotor downwash influence on the fuselage and empennage are calculated by using the CFD predicted local flow velocities at these aerodynamic control points defined on the helicopter airframe. In the coupled simulations, the flight dynamics model is free to move within a computational domain, where the main rotor forces are translated into source terms in the momentum equations of the Navier-Stokes equations. Simultaneously, the CFD calculates induced velocities those are fed back to the simulation and affect the aerodynamic loads in the flight dynamics. The CFD solver models the inflow, ground effect, and interactional aerodynamics in the flight dynamics simulation, and these calculations can be coupled with solution of the external flow (e.g. ship airwake effects). The developed framework was utilized for various investigations of hovering, forward flight and helicopter/terrain interaction simulations including standard ground effect, partial ground effect, sloped terrain, and acceleration in ground effect; and results compared with different flight and experimental data. In near ground cases, the fully-coupled flight dynamics and CFD simulations predicted roll oscillations due to interactions of the rotor downwash, ground plane, and the feedback controller, which are not predicted by the conventional simulation models. Fully coupled simulations of a helicopter accelerating near ground predicted flow formations similar to the recirculation and ground vortex flow regimes observed in experiments. The predictions of hover power reductions due to ground effect compared well to a recent experimental data and the results showed 22% power reduction for a hover flight z/R=0.55 above ground level. Fully coupled simulations performed for a helicopter hovering over and approaching to a ship flight deck and results compared with the standalone GENHEL-PSU simulations without ship airwake and one-way coupled simulations. The fully-coupled simulations showed higher pilot workload compared to the other two cases. In order to increase the execution speeds of the CFD calculations, several improvements were made on the CFD solver. First, the initial coupling approach File I/O was replaced with a more efficient method called Multiple Program Multiple Data MPI framework, where the two executables communicate with each other by MPI calls. Next, the unstructured solver (CRUNCH CFD), which is 2nd-order accurate in space, was replaced with the faster running structured solver (CRAFT CFD) that is 5th-order accurate in space. Other improvements including a more efficient k-d tree search algorithm and the bounding of the source term search space within a small region of the grid surrounding the rotor were made on the CFD solver. The final improvement was to parallelize the search task with the CFD solver tasks within the solver. To quantify the speed-up of the improvements to the coupling interface described above, a study was performed to demonstrate the speedup achieved from each of the interface improvements. The improvements made on the CFD solver showed more than 40 times speedup from the baseline file I/O and unstructured solver CRUNCH CFD. Using a structured CFD solver with 5th-order spacial accuracy provided the largest reductions in execution times. Disregarding the solver numeric, the total speedup of all of the interface improvements including the MPMD rotor point exchange, k-d tree search algorithm, bounded search space, and paralleled search task, was approximately 231%, more than a factor of 2. All these improvements provided the necessary speedup for approach real-time CFD. (Abstract shortened by ProQuest.).

Sums of Consecutive Integers

ERIC Educational Resources Information Center

Pong, Wai Yan

2007-01-01

We begin by answering the question, "Which natural numbers are sums of consecutive integers?" We then go on to explore the set of lengths (numbers of summands) in the decompositions of an integer as such sums.

lsjk—a C++ library for arbitrary-precision numeric evaluation of the generalized log-sine functions

NASA Astrophysics Data System (ADS)

Kalmykov, M. Yu.; Sheplyakov, A.

2005-10-01

Generalized log-sine functions Lsj(k)(θ) appear in higher order ɛ-expansion of different Feynman diagrams. We present an algorithm for the numerical evaluation of these functions for real arguments. This algorithm is implemented as a C++ library with arbitrary-precision arithmetics for integer 0⩽k⩽9 and j⩾2. Some new relations and representations of the generalized log-sine functions are given. Program summaryTitle of program:lsjk Catalogue number:ADVS Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVS Program obtained from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing terms: GNU General Public License Computers:all Operating systems:POSIX Programming language:C++ Memory required to execute:Depending on the complexity of the problem, at least 32 MB RAM recommended No. of lines in distributed program, including testing data, etc.:41 975 No. of bytes in distributed program, including testing data, etc.:309 156 Distribution format:tar.gz Other programs called:The CLN library for arbitrary-precision arithmetics is required at version 1.1.5 or greater External files needed:none Nature of the physical problem:Numerical evaluation of the generalized log-sine functions for real argument in the region 0<θ<π. These functions appear in Feynman integrals Method of solution:Series representation for the real argument in the region 0<θ<π Restriction on the complexity of the problem:Limited up to Lsj(9)(θ), and j is an arbitrary integer number. Thus, all function up to the weight 12 in the region 0<θ<π can be evaluated. The algorithm can be extended up to higher values of k(k>9) without modification Typical running time:Depending on the complexity of problem. See text below.

A FEniCS-based programming framework for modeling turbulent flow by the Reynolds-averaged Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Mortensen, Mikael; Langtangen, Hans Petter; Wells, Garth N.

2011-09-01

Finding an appropriate turbulence model for a given flow case usually calls for extensive experimentation with both models and numerical solution methods. This work presents the design and implementation of a flexible, programmable software framework for assisting with numerical experiments in computational turbulence. The framework targets Reynolds-averaged Navier-Stokes models, discretized by finite element methods. The novel implementation makes use of Python and the FEniCS package, the combination of which leads to compact and reusable code, where model- and solver-specific code resemble closely the mathematical formulation of equations and algorithms. The presented ideas and programming techniques are also applicable to other fields that involve systems of nonlinear partial differential equations. We demonstrate the framework in two applications and investigate the impact of various linearizations on the convergence properties of nonlinear solvers for a Reynolds-averaged Navier-Stokes model.

Discrete sensitivity derivatives of the Navier-Stokes equations with a parallel Krylov solver

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Taylor, Arthur C., III

1994-01-01

This paper solves an 'incremental' form of the sensitivity equations derived by differentiating the discretized thin-layer Navier Stokes equations with respect to certain design variables of interest. The equations are solved with a parallel, preconditioned Generalized Minimal RESidual (GMRES) solver on a distributed-memory architecture. The 'serial' sensitivity analysis code is parallelized by using the Single Program Multiple Data (SPMD) programming model, domain decomposition techniques, and message-passing tools. Sensitivity derivatives are computed for low and high Reynolds number flows over a NACA 1406 airfoil on a 32-processor Intel Hypercube, and found to be identical to those computed on a single-processor Cray Y-MP. It is estimated that the parallel sensitivity analysis code has to be run on 40-50 processors of the Intel Hypercube in order to match the single-processor processing time of a Cray Y-MP.

Improve Problem Solving Skills through Adapting Programming Tools

NASA Technical Reports Server (NTRS)

Shaykhian, Linda H.; Shaykhian, Gholam Ali

2007-01-01

There are numerous ways for engineers and students to become better problem-solvers. The use of command line and visual programming tools can help to model a problem and formulate a solution through visualization. The analysis of problem attributes and constraints provide insight into the scope and complexity of the problem. The visualization aspect of the problem-solving approach tends to make students and engineers more systematic in their thought process and help them catch errors before proceeding too far in the wrong direction. The problem-solver identifies and defines important terms, variables, rules, and procedures required for solving a problem. Every step required to construct the problem solution can be defined in program commands that produce intermediate output. This paper advocates improved problem solving skills through using a programming tool. MatLab created by MathWorks, is an interactive numerical computing environment and programming language. It is a matrix-based system that easily lends itself to matrix manipulation, and plotting of functions and data. MatLab can be used as an interactive command line or a sequence of commands that can be saved in a file as a script or named functions. Prior programming experience is not required to use MatLab commands. The GNU Octave, part of the GNU project, a free computer program for performing numerical computations, is comparable to MatLab. MatLab visual and command programming are presented here.

ASTROP2-LE: A Mistuned Aeroelastic Analysis System Based on a Two Dimensional Linearized Euler Solver

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Srivastava, R.; Mehmed, Oral

2002-01-01

An aeroelastic analysis system for flutter and forced response analysis of turbomachines based on a two-dimensional linearized unsteady Euler solver has been developed. The ASTROP2 code, an aeroelastic stability analysis program for turbomachinery, was used as a basis for this development. The ASTROP2 code uses strip theory to couple a two dimensional aerodynamic model with a three dimensional structural model. The code was modified to include forced response capability. The formulation was also modified to include aeroelastic analysis with mistuning. A linearized unsteady Euler solver, LINFLX2D is added to model the unsteady aerodynamics in ASTROP2. By calculating the unsteady aerodynamic loads using LINFLX2D, it is possible to include the effects of transonic flow on flutter and forced response in the analysis. The stability is inferred from an eigenvalue analysis. The revised code, ASTROP2-LE for ASTROP2 code using Linearized Euler aerodynamics, is validated by comparing the predictions with those obtained using linear unsteady aerodynamic solutions.

DB90: A Fortran Callable Relational Database Routine for Scientific and Engineering Computer Programs

NASA Technical Reports Server (NTRS)

Wrenn, Gregory A.

2005-01-01

This report describes a database routine called DB90 which is intended for use with scientific and engineering computer programs. The software is written in the Fortran 90/95 programming language standard with file input and output routines written in the C programming language. These routines should be completely portable to any computing platform and operating system that has Fortran 90/95 and C compilers. DB90 allows a program to supply relation names and up to 5 integer key values to uniquely identify each record of each relation. This permits the user to select records or retrieve data in any desired order.

Synchronic interval Gaussian mixed-integer programming for air quality management.

PubMed

Cheng, Guanhui; Huang, Guohe Gordon; Dong, Cong

2015-12-15

To reveal the synchronism of interval uncertainties, the tradeoff between system optimality and security, the discreteness of facility-expansion options, the uncertainty of pollutant dispersion processes, and the seasonality of wind features in air quality management (AQM) systems, a synchronic interval Gaussian mixed-integer programming (SIGMIP) approach is proposed in this study. A robust interval Gaussian dispersion model is developed for approaching the pollutant dispersion process under interval uncertainties and seasonal variations. The reflection of synchronic effects of interval uncertainties in the programming objective is enabled through introducing interval functions. The proposition of constraint violation degrees helps quantify the tradeoff between system optimality and constraint violation under interval uncertainties. The overall optimality of system profits of an SIGMIP model is achieved based on the definition of an integrally optimal solution. Integer variables in the SIGMIP model are resolved by the existing cutting-plane method. Combining these efforts leads to an effective algorithm for the SIGMIP model. An application to an AQM problem in a region in Shandong Province, China, reveals that the proposed SIGMIP model can facilitate identifying the desired scheme for AQM. The enhancement of the robustness of optimization exercises may be helpful for increasing the reliability of suggested schemes for AQM under these complexities. The interrelated tradeoffs among control measures, emission sources, flow processes, receptors, influencing factors, and economic and environmental goals are effectively balanced. Interests of many stakeholders are reasonably coordinated. The harmony between economic development and air quality control is enabled. Results also indicate that the constraint violation degree is effective at reflecting the compromise relationship between constraint-violation risks and system optimality under interval uncertainties. This can help decision makers mitigate potential risks, e.g. insufficiency of pollutant treatment capabilities, exceedance of air quality standards, deficiency of pollution control fund, or imbalance of economic or environmental stress, in the process of guiding AQM. Copyright © 2015 Elsevier B.V. All rights reserved.

TH-EF-BRB-04: 4π Dynamic Conformal Arc Therapy Dynamic Conformal Arc Therapy (DCAT) for SBRT

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

Chiu, T; Long, T; Tian, Z.

2016-06-15

Purpose: To develop an efficient and effective trajectory optimization methodology for 4π dynamic conformal arc treatment (4π DCAT) with synchronized gantry and couch motion; and to investigate potential clinical benefits for stereotactic body radiation therapy (SBRT) to breast, lung, liver and spine tumors. Methods: The entire optimization framework for 4π DCAT inverse planning consists of two parts: 1) integer programming algorithm and 2) particle swarm optimization (PSO) algorithm. The integer programming is designed to find an optimal solution for arc delivery trajectory with both couch and gantry rotation, while PSO minimize a non-convex objective function based on the selected trajectorymore » and dose-volume constraints. In this study, control point interaction is explicitly taken into account. Beam trajectory was modeled as a series of control points connected together to form a deliverable path. With linear treatment planning objectives, a mixed-integer program (MIP) was formulated. Under mild assumptions, the MIP is tractable. Assigning monitor units to control points along the path can be integrated into the model and done by PSO. The developed 4π DCAT inverse planning strategy is evaluated on SBRT cases and compared to clinically treated plans. Results: The resultant dose distribution of this technique was evaluated between 3D conformal treatment plan generated by Pinnacle treatment planning system and 4π DCAT on a lung SBRT patient case. Both plans share the same scale of MU, 3038 and 2822 correspondingly to 3D conformal plan and 4π DCAT. The mean doses for most of OARs were greatly reduced at 32% (cord), 70% (esophagus), 2.8% (lung) and 42.4% (stomach). Conclusion: Initial results in this study show the proposed 4π DCAT treatment technique can achieve better OAR sparing and lower MUs, which indicates that the developed technique is promising for high dose SBRT to reduce the risk of secondary cancer.« less

Bi-objective integer programming for RNA secondary structure prediction with pseudoknots.

PubMed

Legendre, Audrey; Angel, Eric; Tahi, Fariza

2018-01-15

RNA structure prediction is an important field in bioinformatics, and numerous methods and tools have been proposed. Pseudoknots are specific motifs of RNA secondary structures that are difficult to predict. Almost all existing methods are based on a single model and return one solution, often missing the real structure. An alternative approach would be to combine different models and return a (small) set of solutions, maximizing its quality and diversity in order to increase the probability that it contains the real structure. We propose here an original method for predicting RNA secondary structures with pseudoknots, based on integer programming. We developed a generic bi-objective integer programming algorithm allowing to return optimal and sub-optimal solutions optimizing simultaneously two models. This algorithm was then applied to the combination of two known models of RNA secondary structure prediction, namely MEA and MFE. The resulting tool, called BiokoP, is compared with the other methods in the literature. The results show that the best solution (structure with the highest F 1 -score) is, in most cases, given by BiokoP. Moreover, the results of BiokoP are homogeneous, regardless of the pseudoknot type or the presence or not of pseudoknots. Indeed, the F 1 -scores are always higher than 70% for any number of solutions returned. The results obtained by BiokoP show that combining the MEA and the MFE models, as well as returning several optimal and several sub-optimal solutions, allow to improve the prediction of secondary structures. One perspective of our work is to combine better mono-criterion models, in particular to combine a model based on the comparative approach with the MEA and the MFE models. This leads to develop in the future a new multi-objective algorithm to combine more than two models. BiokoP is available on the EvryRNA platform: https://EvryRNA.ibisc.univ-evry.fr .

AKLSQF - LEAST SQUARES CURVE FITTING

NASA Technical Reports Server (NTRS)

Kantak, A. V.

1994-01-01

The Least Squares Curve Fitting program, AKLSQF, computes the polynomial which will least square fit uniformly spaced data easily and efficiently. The program allows the user to specify the tolerable least squares error in the fitting or allows the user to specify the polynomial degree. In both cases AKLSQF returns the polynomial and the actual least squares fit error incurred in the operation. The data may be supplied to the routine either by direct keyboard entry or via a file. AKLSQF produces the least squares polynomial in two steps. First, the data points are least squares fitted using the orthogonal factorial polynomials. The result is then reduced to a regular polynomial using Sterling numbers of the first kind. If an error tolerance is specified, the program starts with a polynomial of degree 1 and computes the least squares fit error. The degree of the polynomial used for fitting is then increased successively until the error criterion specified by the user is met. At every step the polynomial as well as the least squares fitting error is printed to the screen. In general, the program can produce a curve fitting up to a 100 degree polynomial. All computations in the program are carried out under Double Precision format for real numbers and under long integer format for integers to provide the maximum accuracy possible. AKLSQF was written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler. It has been implemented under DOS 3.2.1 using 23K of RAM. AKLSQF was developed in 1989.

Analysis misconception of integers in microteaching activities

NASA Astrophysics Data System (ADS)

Setyawati, R. D.; Indiati, I.

2018-05-01

This study view to analyse student misconceptions on integers in microteaching activities. This research used qualitative research design. An integers test contained questions from eight main areas of integers. The Integers material test includes (a) converting the image into fractions, (b) examples of positive numbers including rational numbers, (c) operations in fractions, (d) sorting fractions from the largest to the smallest, and vice versa; e) equate denominator, (f) concept of ratio mark, (g) definition of fraction, and (h) difference between fractions and parts. The results indicated an integers concepts: (1) the students have not been able to define concepts well based on the classification of facts in organized part; (2) The correlational concept: students have not been able to combine interrelated events in the form of general principles; and (3) theoretical concepts: students have not been able to use concepts that facilitate in learning the facts or events in an organized system.

Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK

PubMed Central

2014-01-01

Background Investigation of the nonlinear pattern dynamics of a reaction-diffusion system almost always requires numerical solution of the system’s set of defining differential equations. Traditionally, this would be done by selecting an appropriate differential equation solver from a library of such solvers, then writing computer codes (in a programming language such as C or Matlab) to access the selected solver and display the integrated results as a function of space and time. This “code-based” approach is flexible and powerful, but requires a certain level of programming sophistication. A modern alternative is to use a graphical programming interface such as Simulink to construct a data-flow diagram by assembling and linking appropriate code blocks drawn from a library. The result is a visual representation of the inter-relationships between the state variables whose output can be made completely equivalent to the code-based solution. Results As a tutorial introduction, we first demonstrate application of the Simulink data-flow technique to the classical van der Pol nonlinear oscillator, and compare Matlab and Simulink coding approaches to solving the van der Pol ordinary differential equations. We then show how to introduce space (in one and two dimensions) by solving numerically the partial differential equations for two different reaction-diffusion systems: the well-known Brusselator chemical reactor, and a continuum model for a two-dimensional sheet of human cortex whose neurons are linked by both chemical and electrical (diffusive) synapses. We compare the relative performances of the Matlab and Simulink implementations. Conclusions The pattern simulations by Simulink are in good agreement with theoretical predictions. Compared with traditional coding approaches, the Simulink block-diagram paradigm reduces the time and programming burden required to implement a solution for reaction-diffusion systems of equations. Construction of the block-diagram does not require high-level programming skills, and the graphical interface lends itself to easy modification and use by non-experts. PMID:24725437

Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK.

PubMed

Wang, Kaier; Steyn-Ross, Moira L; Steyn-Ross, D Alistair; Wilson, Marcus T; Sleigh, Jamie W; Shiraishi, Yoichi

2014-04-11

Investigation of the nonlinear pattern dynamics of a reaction-diffusion system almost always requires numerical solution of the system's set of defining differential equations. Traditionally, this would be done by selecting an appropriate differential equation solver from a library of such solvers, then writing computer codes (in a programming language such as C or Matlab) to access the selected solver and display the integrated results as a function of space and time. This "code-based" approach is flexible and powerful, but requires a certain level of programming sophistication. A modern alternative is to use a graphical programming interface such as Simulink to construct a data-flow diagram by assembling and linking appropriate code blocks drawn from a library. The result is a visual representation of the inter-relationships between the state variables whose output can be made completely equivalent to the code-based solution. As a tutorial introduction, we first demonstrate application of the Simulink data-flow technique to the classical van der Pol nonlinear oscillator, and compare Matlab and Simulink coding approaches to solving the van der Pol ordinary differential equations. We then show how to introduce space (in one and two dimensions) by solving numerically the partial differential equations for two different reaction-diffusion systems: the well-known Brusselator chemical reactor, and a continuum model for a two-dimensional sheet of human cortex whose neurons are linked by both chemical and electrical (diffusive) synapses. We compare the relative performances of the Matlab and Simulink implementations. The pattern simulations by Simulink are in good agreement with theoretical predictions. Compared with traditional coding approaches, the Simulink block-diagram paradigm reduces the time and programming burden required to implement a solution for reaction-diffusion systems of equations. Construction of the block-diagram does not require high-level programming skills, and the graphical interface lends itself to easy modification and use by non-experts.

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 programming formulation, the solution of which generates feasible and near-optimal routes for individual flights. The algorithm, termed the Lagrangian Generation Algorithm, is used to solve practical problems in the southwestern portion of United States in which the solutions are within 1% of the corresponding lower bounds.

The Computer Bulletin Board.

ERIC Educational Resources Information Center

Batt, Russell H., Ed.

1989-01-01

Describes two chemistry computer programs: (1) "Eureka: A Chemistry Problem Solver" (problem files may be written by the instructor, MS-DOS 2.0, IBM with 384K); and (2) "PC-File+" (database management, IBM with 416K and two floppy drives). (MVL)

MPSalsa Version 1.5: A Finite Element Computer Program for Reacting Flow Problems: Part 1 - Theoretical Development

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

Devine, K.D.; Hennigan, G.L.; Hutchinson, S.A.

1999-01-01

The theoretical background for the finite element computer program, MPSalsa Version 1.5, is presented in detail. MPSalsa is designed to solve laminar or turbulent low Mach number, two- or three-dimensional incompressible and variable density reacting fluid flows on massively parallel computers, using a Petrov-Galerkin finite element formulation. The code has the capability to solve coupled fluid flow (with auxiliary turbulence equations), heat transport, multicomponent species transport, and finite-rate chemical reactions, and to solve coupled multiple Poisson or advection-diffusion-reaction equations. The program employs the CHEMKIN library to provide a rigorous treatment of multicomponent ideal gas kinetics and transport. Chemical reactions occurringmore » in the gas phase and on surfaces are treated by calls to CHEMKIN and SURFACE CHEMK3N, respectively. The code employs unstructured meshes, using the EXODUS II finite element database suite of programs for its input and output files. MPSalsa solves both transient and steady flows by using fully implicit time integration, an inexact Newton method and iterative solvers based on preconditioned Krylov methods as implemented in the Aztec. solver library.« less

Fractal electrodynamics via non-integer dimensional space approach

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-09-01

Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested.

Efficient three-dimensional Poisson solvers in open rectangular conducting pipe

NASA Astrophysics Data System (ADS)

Qiang, Ji

2016-06-01

Three-dimensional (3D) Poisson solver plays an important role in the study of space-charge effects on charged particle beam dynamics in particle accelerators. In this paper, we propose three new 3D Poisson solvers for a charged particle beam in an open rectangular conducting pipe. These three solvers include a spectral integrated Green function (IGF) solver, a 3D spectral solver, and a 3D integrated Green function solver. These solvers effectively handle the longitudinal open boundary condition using a finite computational domain that contains the beam itself. This saves the computational cost of using an extra larger longitudinal domain in order to set up an appropriate finite boundary condition. Using an integrated Green function also avoids the need to resolve rapid variation of the Green function inside the beam. The numerical operational cost of the spectral IGF solver and the 3D IGF solver scales as O(N log(N)) , where N is the number of grid points. The cost of the 3D spectral solver scales as O(Nn N) , where Nn is the maximum longitudinal mode number. We compare these three solvers using several numerical examples and discuss the advantageous regime of each solver in the physical application.

TADS--A CFD-Based Turbomachinery Analysis and Design System with GUI: User's Manual. 2.0

NASA Technical Reports Server (NTRS)

Koiro, M. J.; Myers, R. A.; Delaney, R. A.

1999-01-01

The primary objective of this study was the development of a Computational Fluid Dynamics (CFD) based turbomachinery airfoil analysis and design system, controlled by a Graphical User Interface (GUI). The computer codes resulting from this effort are referred to as TADS (Turbomachinery Analysis and Design System). This document is intended to serve as a User's Manual for the computer programs which comprise the TADS system, developed under Task 18 of NASA Contract NAS3-27350, ADPAC System Coupling to Blade Analysis & Design System GUI and Task 10 of NASA Contract NAS3-27394, ADPAC System Coupling to Blade Analysis & Design System GUI, Phase II-Loss, Design and, Multi-stage Analysis. TADS couples a throughflow solver (ADPAC) with a quasi-3D blade-to-blade solver (RVCQ3D) in an interactive package. Throughflow analysis and design capability was developed in ADPAC through the addition of blade force and blockage terms to the governing equations. A GUI was developed to simplify user input and automate the many tasks required to perform turbomachinery analysis and design. The coupling of the various programs was done in such a way that alternative solvers or grid generators could be easily incorporated into the TADS framework. Results of aerodynamic calculations using the TADS system are presented for a highly loaded fan, a compressor stator, a low speed turbine blade and a transonic turbine vane.

A combinatorial approach to the design of vaccines.

PubMed

Martínez, Luis; Milanič, Martin; Legarreta, Leire; Medvedev, Paul; Malaina, Iker; de la Fuente, Ildefonso M

2015-05-01

We present two new problems of combinatorial optimization and discuss their applications to the computational design of vaccines. In the shortest λ-superstring problem, given a family S1,...,S(k) of strings over a finite alphabet, a set Τ of "target" strings over that alphabet, and an integer λ, the task is to find a string of minimum length containing, for each i, at least λ target strings as substrings of S(i). In the shortest λ-cover superstring problem, given a collection X1,...,X(n) of finite sets of strings over a finite alphabet and an integer λ, the task is to find a string of minimum length containing, for each i, at least λ elements of X(i) as substrings. The two problems are polynomially equivalent, and the shortest λ-cover superstring problem is a common generalization of two well known combinatorial optimization problems, the shortest common superstring problem and the set cover problem. We present two approaches to obtain exact or approximate solutions to the shortest λ-superstring and λ-cover superstring problems: one based on integer programming, and a hill-climbing algorithm. An application is given to the computational design of vaccines and the algorithms are applied to experimental data taken from patients infected by H5N1 and HIV-1.

Examples of Linking Codes Within GeoFramework

NASA Astrophysics Data System (ADS)

Tan, E.; Choi, E.; Thoutireddy, P.; Aivazis, M.; Lavier, L.; Quenette, S.; Gurnis, M.

2003-12-01

Geological processes usually encompass a broad spectrum of length and time scales. Traditionally, a modeling code (solver) is written to solve a problem with specific length and time scales in mind. The utility of the solver beyond the designated purpose is usually limited. Furthermore, two distinct solvers, even if each can solve complementary parts of a new problem, are difficult to link together to solve the problem as a whole. For example, Lagrangian deformation model with visco-elastoplastic crust is used to study deformation near plate boundary. Ideally, the driving force of the deformation should be derived from underlying mantle convection, and it requires linking the Lagrangian deformation model with a Eulerian mantle convection model. As our understanding of geological processes evolves, the need of integrated modeling codes, which should reuse existing codes as much as possible, begins to surface. GeoFramework project addresses this need by developing a suite of reusable and re-combinable tools for the Earth science community. GeoFramework is based on and extends Pyre, a Python-based modeling framework, recently developed to link solid (Lagrangian) and fluid (Eulerian) models, as well as mesh generators, visualization packages, and databases, with one another for engineering applications. Under the framework, a solver is aware of the existence of other solvers and can interact with each other via exchanging information across adjacent boundary. A solver needs to conform a standard interface and provide its own implementation for exchanging boundary information. The framework also provides facilities to control the coordination between interacting solvers. We will show an example of linking two solvers within GeoFramework. CitcomS is a finite element code which solves for thermal convection within a 3D spherical shell. CitcomS can solve for problems either within a full spherical (global) domain or a restricted (regional) domain of a full sphere by using different meshers. We can embed a regional CitcomS solver within a global CitcomS solver. We not that linking instances of the same solver is conceptually equivalent to linking to different solvers. The global solver has a coarser grid and a longer stable time step than the regional solver. Therefore, a global-solver time step consists of several regional-solver time steps. The time-marching scheme is described below. First, the global solver is advanced one global-solver time step. Then, the regional solver is advanced for several regional-solver time steps until it catches up global solver. Within each regional-solver time step, the velocity field of the global solver is interpolated in time and then is imposed to the regional solver as boundary conditions. Finally, the temperature field of the regional solver is extrapolated in space and is fed back to the global. These two solvers are linked and synchronized by the time-marching scheme. An effort to embed a visco-elastoplastic representation of the crust within viscous mantle flow is underway.

Parallelization of elliptic solver for solving 1D Boussinesq model

NASA Astrophysics Data System (ADS)

Tarwidi, D.; Adytia, D.

2018-03-01

In this paper, a parallel implementation of an elliptic solver in solving 1D Boussinesq model is presented. Numerical solution of Boussinesq model is obtained by implementing a staggered grid scheme to continuity, momentum, and elliptic equation of Boussinesq model. Tridiagonal system emerging from numerical scheme of elliptic equation is solved by cyclic reduction algorithm. The parallel implementation of cyclic reduction is executed on multicore processors with shared memory architectures using OpenMP. To measure the performance of parallel program, large number of grids is varied from 28 to 214. Two test cases of numerical experiment, i.e. propagation of solitary and standing wave, are proposed to evaluate the parallel program. The numerical results are verified with analytical solution of solitary and standing wave. The best speedup of solitary and standing wave test cases is about 2.07 with 214 of grids and 1.86 with 213 of grids, respectively, which are executed by using 8 threads. Moreover, the best efficiency of parallel program is 76.2% and 73.5% for solitary and standing wave test cases, respectively.

Density of Primitive Pythagorean Triples

ERIC Educational Resources Information Center

Killen, Duncan A.

2004-01-01

Based on the properties of a Primitive Pythagorean Triple (PPT), a computer program was written to generate, print, and count all PPTs greater than or equal to I[subscript x], where I[subscript x] is an arbitrarily chosen integer. The Density of Primitive Pythagorean Triples may be defined as the ratio of the number of PPTs whose hypotenuse is…

Applying ant colony optimization metaheuristic to solve forest transportation planning problems with side constraints

Treesearch

Marco A. Contreras; Woodam Chung; Greg Jones

2008-01-01

Forest transportation planning problems (FTPP) have evolved from considering only the financial aspects of timber management to more holistic problems that also consider the environmental impacts of roads. These additional requirements have introduced side constraints, making FTPP larger and more complex. Mixed-integer programming (MIP) has been used to solve FTPP, but...

Going Around On Circles: Mathematics and Computer Art. Part 2.

ERIC Educational Resources Information Center

Gordon, Sheldon P.; Gordon, Florence S.

1984-01-01

Discusses properties of epicycloids. (The easiest way to picture them is to think of a piece of radioactive bubble gum attached to a wheel which is rolling around the outside of a larger wheel.) Includes a computer program (TRS-80 color computer) that will graph any epicycloid with integer values for the radii. (JN)

Dynamic reserve selection: Optimal land retention with land-price feedbacks

Treesearch

Sandor F. Toth; Robert G. Haight; Luke W. Rogers

2011-01-01

Urban growth compromises open space and ecosystem functions. To mitigate the negative effects, some agencies use reserve selection models to identify conservation sites for purchase or retention. Existing models assume that conservation has no impact on nearby land prices. We propose a new integer program that relaxes this assumption via adaptive cost coefficients. Our...

Integrating Test-Form Formatting into Automated Test Assembly

ERIC Educational Resources Information Center

Diao, Qi; van der Linden, Wim J.

2013-01-01

Automated test assembly uses the methodology of mixed integer programming to select an optimal set of items from an item bank. Automated test-form generation uses the same methodology to optimally order the items and format the test form. From an optimization point of view, production of fully formatted test forms directly from the item pool using…

Large-Scale Multiobjective Static Test Generation for Web-Based Testing with Integer Programming

ERIC Educational Resources Information Center

Nguyen, M. L.; Hui, Siu Cheung; Fong, A. C. M.

2013-01-01

Web-based testing has become a ubiquitous self-assessment method for online learning. One useful feature that is missing from today's web-based testing systems is the reliable capability to fulfill different assessment requirements of students based on a large-scale question data set. A promising approach for supporting large-scale web-based…

Equitably Distributing Quality of Marine Security Guards Using Integer Programming

DTIC Science & Technology

2013-03-01

Model for Fix-It Shop-Assignment (From Balakrishnan et al ., 2007...LP; Balakrishnan et al ., 2007). The Soviet mathematician A. N. Kolmogorov is recognized as the first person to conceptually develop the idea of LP...commercial sector today. Balakrishnan et al . (2007) captured the three major steps in LP, which are formulation, solution, and interpretation and

Parameterizing by the Number of Numbers

NASA Astrophysics Data System (ADS)

Fellows, Michael R.; Gaspers, Serge; Rosamond, Frances A.

The usefulness of parameterized algorithmics has often depended on what Niedermeier has called "the art of problem parameterization". In this paper we introduce and explore a novel but general form of parameterization: the number of numbers. Several classic numerical problems, such as Subset Sum, Partition, 3-Partition, Numerical 3-Dimensional Matching, and Numerical Matching with Target Sums, have multisets of integers as input. We initiate the study of parameterizing these problems by the number of distinct integers in the input. We rely on an FPT result for Integer Linear Programming Feasibility to show that all the above-mentioned problems are fixed-parameter tractable when parameterized in this way. In various applied settings, problem inputs often consist in part of multisets of integers or multisets of weighted objects (such as edges in a graph, or jobs to be scheduled). Such number-of-numbers parameterized problems often reduce to subproblems about transition systems of various kinds, parameterized by the size of the system description. We consider several core problems of this kind relevant to number-of-numbers parameterization. Our main hardness result considers the problem: given a non-deterministic Mealy machine M (a finite state automaton outputting a letter on each transition), an input word x, and a census requirement c for the output word specifying how many times each letter of the output alphabet should be written, decide whether there exists a computation of M reading x that outputs a word y that meets the requirement c. We show that this problem is hard for W[1]. If the question is whether there exists an input word x such that a computation of M on x outputs a word that meets c, the problem becomes fixed-parameter tractable.

Engineering calculations for solving the orbital allotment problem

NASA Technical Reports Server (NTRS)

Reilly, C.; Walton, E. K.; Mount-Campbell, C.; Caldecott, R.; Aebker, E.; Mata, F.

1988-01-01

Four approaches for calculating downlink interferences for shaped-beam antennas are described. An investigation of alternative mixed-integer programming models for satellite synthesis is summarized. Plans for coordinating the various programs developed under this grant are outlined. Two procedures for ordering satellites to initialize the k-permutation algorithm are proposed. Results are presented for the k-permutation algorithms. Feasible solutions are found for 5 of the 6 problems considered. Finally, it is demonstrated that the k-permutation algorithm can be used to solve arc allotment problems.

Mixed Integer Programming and Heuristic Scheduling for Space Communication

NASA Technical Reports Server (NTRS)

Lee, Charles H.; Cheung, Kar-Ming

2013-01-01

Optimal planning and scheduling for a communication network was created where the nodes within the network are communicating at the highest possible rates while meeting the mission requirements and operational constraints. The planning and scheduling problem was formulated in the framework of Mixed Integer Programming (MIP) to introduce a special penalty function to convert the MIP problem into a continuous optimization problem, and to solve the constrained optimization problem using heuristic optimization. The communication network consists of space and ground assets with the link dynamics between any two assets varying with respect to time, distance, and telecom configurations. One asset could be communicating with another at very high data rates at one time, and at other times, communication is impossible, as the asset could be inaccessible from the network due to planetary occultation. Based on the network's geometric dynamics and link capabilities, the start time, end time, and link configuration of each view period are selected to maximize the communication efficiency within the network. Mathematical formulations for the constrained mixed integer optimization problem were derived, and efficient analytical and numerical techniques were developed to find the optimal solution. By setting up the problem using MIP, the search space for the optimization problem is reduced significantly, thereby speeding up the solution process. The ratio of the dimension of the traditional method over the proposed formulation is approximately an order N (single) to 2*N (arraying), where N is the number of receiving antennas of a node. By introducing a special penalty function, the MIP problem with non-differentiable cost function and nonlinear constraints can be converted into a continuous variable problem, whose solution is possible.

Comparing direct and iterative equation solvers in a large structural analysis software system

NASA Technical Reports Server (NTRS)

Poole, E. L.

1991-01-01

Two direct Choleski equation solvers and two iterative preconditioned conjugate gradient (PCG) equation solvers used in a large structural analysis software system are described. The two direct solvers are implementations of the Choleski method for variable-band matrix storage and sparse matrix storage. The two iterative PCG solvers include the Jacobi conjugate gradient method and an incomplete Choleski conjugate gradient method. The performance of the direct and iterative solvers is compared by solving several representative structural analysis problems. Some key factors affecting the performance of the iterative solvers relative to the direct solvers are identified.

Seven Wonders of the Ancient and Modern Quadratic World.

ERIC Educational Resources Information Center

Taylor, Sharon E.; Mittag, Kathleen Cage

2001-01-01

Presents four methods for solving a quadratic equation using graphing calculator technology: (1) graphing with the CALC feature; (2) quadratic formula program; (3) table; and (4) solver. Includes a worksheet for a lab activity on factoring quadratic equations. (KHR)

News | Argonne National Laboratory

Science.gov Websites

Skip to main content Argonne National Laboratory Toggle Navigation Toggle Search Home Learning solvers Home Learning Center Undergraduates Graduates Faculty Partners News & Events News & Events -4114 Contact Us Argonne Educational Programs is committed to providing a learning environment that

Analysis of Modeling Assumptions used in Production Cost Models for Renewable Integration Studies

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

Stoll, Brady; Brinkman, Gregory; Townsend, Aaron

2016-01-01

Renewable energy integration studies have been published for many different regions exploring the question of how higher penetration of renewable energy will impact the electric grid. These studies each make assumptions about the systems they are analyzing; however the effect of many of these assumptions has not been yet been examined and published. In this paper we analyze the impact of modeling assumptions in renewable integration studies, including the optimization method used (linear or mixed-integer programming) and the temporal resolution of the dispatch stage (hourly or sub-hourly). We analyze each of these assumptions on a large and a small systemmore » and determine the impact of each assumption on key metrics including the total production cost, curtailment of renewables, CO2 emissions, and generator starts and ramps. Additionally, we identified the impact on these metrics if a four-hour ahead commitment step is included before the dispatch step and the impact of retiring generators to reduce the degree to which the system is overbuilt. We find that the largest effect of these assumptions is at the unit level on starts and ramps, particularly for the temporal resolution, and saw a smaller impact at the aggregate level on system costs and emissions. For each fossil fuel generator type we measured the average capacity started, average run-time per start, and average number of ramps. Linear programming results saw up to a 20% difference in number of starts and average run time of traditional generators, and up to a 4% difference in the number of ramps, when compared to mixed-integer programming. Utilizing hourly dispatch instead of sub-hourly dispatch saw no difference in coal or gas CC units for either start metric, while gas CT units had a 5% increase in the number of starts and 2% increase in the average on-time per start. The number of ramps decreased up to 44%. The smallest effect seen was on the CO2 emissions and total production cost, with a 0.8% and 0.9% reduction respectively when using linear programming compared to mixed-integer programming and 0.07% and 0.6% reduction, respectively, in the hourly dispatch compared to sub-hourly dispatch.« less

A model for solving the prescribed burn planning problem.

PubMed

Rachmawati, Ramya; Ozlen, Melih; Reinke, Karin J; Hearne, John W

2015-01-01

The increasing frequency of destructive wildfires, with a consequent loss of life and property, has led to fire and land management agencies initiating extensive fuel management programs. This involves long-term planning of fuel reduction activities such as prescribed burning or mechanical clearing. In this paper, we propose a mixed integer programming (MIP) model that determines when and where fuel reduction activities should take place. The model takes into account multiple vegetation types in the landscape, their tolerance to frequency of fire events, and keeps track of the age of each vegetation class in each treatment unit. The objective is to minimise fuel load over the planning horizon. The complexity of scheduling fuel reduction activities has led to the introduction of sophisticated mathematical optimisation methods. While these approaches can provide optimum solutions, they can be computationally expensive, particularly for fuel management planning which extends across the landscape and spans long term planning horizons. This raises the question of how much better do exact modelling approaches compare to simpler heuristic approaches in their solutions. To answer this question, the proposed model is run using an exact MIP (using commercial MIP solver) and two heuristic approaches that decompose the problem into multiple single-period sub problems. The Knapsack Problem (KP), which is the first heuristic approach, solves the single period problems, using an exact MIP approach. The second heuristic approach solves the single period sub problem using a greedy heuristic approach. The three methods are compared in term of model tractability, computational time and the objective values. The model was tested using randomised data from 711 treatment units in the Barwon-Otway district of Victoria, Australia. Solutions for the exact MIP could be obtained for up to a 15-year planning only using a standard implementation of CPLEX. Both heuristic approaches can solve significantly larger problems, involving 100-year or even longer planning horizons. Furthermore there are no substantial differences in the solutions produced by the three approaches. It is concluded that for practical purposes a heuristic method is to be preferred to the exact MIP approach.

Use of EPANET solver to manage water distribution in Smart City

NASA Astrophysics Data System (ADS)

Antonowicz, A.; Brodziak, R.; Bylka, J.; Mazurkiewicz, J.; Wojtecki, S.; Zakrzewski, P.

2018-02-01

Paper presents a method of using EPANET solver to support manage water distribution system in Smart City. The main task is to develop the application that allows remote access to the simulation model of the water distribution network developed in the EPANET environment. Application allows to perform both single and cyclic simulations with the specified step of changing the values of the selected process variables. In the paper the architecture of application was shown. The application supports the selection of the best device control algorithm using optimization methods. Optimization procedures are possible with following methods: brute force, SLSQP (Sequential Least SQuares Programming), Modified Powell Method. Article was supplemented by example of using developed computer tool.

Oilfield flooding polymer

DOEpatents

Martin, Fred D.; Hatch, Melvin J.; Shepitka, Joel S.; Donaruma, Lorraine G.

1986-01-01

A monomer, polymers containing the monomer, and the use of the polymer in oilfield flooding is disclosed. The subject monomer is represented by the general formula: ##STR1## wherein: n is an integer from 0 to about 4; m is an integer from 0 to about 6; a is an integer equal to at least 1 except where m is equal to 0, a must equal 0 and where m is equal to 1, a must equal 0 or 1; p is an integer from 2 to about 10; b is an integer equal to at least 1 and is of sufficient magnitude that the ratio b/p is at least 0.2; and q is an integer from 0 to 2. The number of hydroxy groups in the monomer is believed to be critical, and therefore the sum of (a+b) divided by the sum (m+p) should be at least 0.2. The moieties linked to the acrylic nitrogen can be joined to provide a ringed structure.

An Ada Linear-Algebra Software Package Modeled After HAL/S

NASA Technical Reports Server (NTRS)

Klumpp, Allan R.; Lawson, Charles L.

1990-01-01

New avionics software written more easily. Software package extends Ada programming language to include linear-algebra capabilities similar to those of HAL/S programming language. Designed for such avionics applications as Space Station flight software. In addition to built-in functions of HAL/S, package incorporates quaternion functions used in Space Shuttle and Galileo projects and routines from LINPAK solving systems of equations involving general square matrices. Contains two generic programs: one for floating-point computations and one for integer computations. Written on IBM/AT personal computer running under PC DOS, v.3.1.

TADS: A CFD-Based Turbomachinery Analysis and Design System with GUI: Methods and Results. 2.0

NASA Technical Reports Server (NTRS)

Koiro, M. J.; Myers, R. A.; Delaney, R. A.

1999-01-01

The primary objective of this study was the development of a Computational Fluid Dynamics (CFD) based turbomachinery airfoil analysis and design system, controlled by a Graphical User Interface (GUI). The computer codes resulting from this effort are referred to as TADS (Turbomachinery Analysis and Design System). This document is the Final Report describing the theoretical basis and analytical results from the TADS system developed under Task 10 of NASA Contract NAS3-27394, ADPAC System Coupling to Blade Analysis & Design System GUI, Phase II-Loss, Design and. Multi-stage Analysis. TADS couples a throughflow solver (ADPAC) with a quasi-3D blade-to-blade solver (RVCQ3D) or a 3-D solver with slip condition on the end walls (B2BADPAC) in an interactive package. Throughflow analysis and design capability was developed in ADPAC through the addition of blade force and blockage terms to the governing equations. A GUI was developed to simplify user input and automate the many tasks required to perform turbomachinery analysis and design. The coupling of the various programs was done in such a way that alternative solvers or grid generators could be easily incorporated into the TADS framework. Results of aerodynamic calculations using the TADS system are presented for a multistage compressor, a multistage turbine, two highly loaded fans, and several single stage compressor and turbine example cases.

The NASA SCI Files[TM]: The Case of the Shaky Quake. A Lesson Guide with Activities in Mathematics, Science, and Technology.

ERIC Educational Resources Information Center

Ricles, Shannon

The NASA SCI Files is a series of instructional programs consisting of broadcast, print, and online elements emphasizing standards-based instruction, problem-based learning, and science as inquiry. The series seeks to motivate students in grades 3-5 to become critical thinkers and active problem solvers. In this program, the tree house detectives…

libmpdata++ 1.0: a library of parallel MPDATA solvers for systems of generalised transport equations

NASA Astrophysics Data System (ADS)

Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.

2015-04-01

This paper accompanies the first release of libmpdata++, a C++ library implementing the multi-dimensional positive-definite advection transport algorithm (MPDATA) on regular structured grid. The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; a shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.

libmpdata++ 0.1: a library of parallel MPDATA solvers for systems of generalised transport equations

NASA Astrophysics Data System (ADS)

Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.

2014-11-01

This paper accompanies first release of libmpdata++, a C++ library implementing the Multidimensional Positive-Definite Advection Transport Algorithm (MPDATA). The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include: homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.

Open Collaboration: A Problem Solving Strategy That Is Redefining NASA's Innovative Spirit

NASA Technical Reports Server (NTRS)

Rando, Cynthia M.; Fogarty, Jennifer A.; Richard, Elizabeth E.; Davis, Jeffrey R.

2011-01-01

In 2010, NASA?s Space Life Sciences Directorate announced the successful results from pilot experiments with open innovation methodologies. Specifically, utilization of internet based external crowd sourcing platforms to solve challenging problems in human health and performance related to the future of spaceflight. The follow-up to this success was an internal crowd sourcing pilot program entitled NASA@work, which was supported by the InnoCentive@work software platform. The objective of the NASA@work pilot was to connect the collective knowledge of individuals from all areas within the NASA organization via a private web based environment. The platform provided a venue for NASA Challenge Owners, those looking for solutions or new ideas, to pose challenges to internal solvers, those within NASA with the skill and desire to create solutions. The pilot was launched in 57 days, a record for InnoCentive and NASA, and ran for three months with a total of 20 challenges posted Agency wide. The NASA@work pilot attracted over 6000 participants throughout NASA with a total of 183 contributing solvers for the 20 challenges posted. At the time of the pilot?s closure, solvers provided viable solutions and ideas for 17 of the 20 posted challenges. The solver community provided feedback on the pilot describing it as a barrier breaking activity, conveying that there was a satisfaction associated with helping co-workers, that it was "fun" to think about problems outside normal work boundaries, and it was nice to learn what challenges others were facing across the agency. The results and the feedback from the solver community have demonstrated the power and utility of an internal collaboration tool, such as NASA@work.

Open Collaboration: A Problem Solving Strategy That is Redefining NASA's Innovative Spirit

NASA Technical Reports Server (NTRS)

Rando, Cynthia M.; Fogarty, Jennifer A.; Richard, E. E.; Davis, Jeffrey R.

2011-01-01

In 2010, NASA's Space Life Sciences Directorate announced the successful results from pilot experiments with open innovation methodologies. Specifically, utilization of internet based external crowdsourcing platforms to solve challenging problems in human health and performance related to the future of spaceflight. The follow-up to this success was an internal crowdsourcing pilot program entitled NASA@work, which was supported by the InnoCentive@work software platform. The objective of the NASA@work pilot was to connect the collective knowledge of individuals from all areas within the NASA organization via a private web based environment. The platform provided a venue for NASA Challenge Owners, those looking for solutions or new ideas, to pose challenges to internal solvers, those within NASA with the skill and desire to create solutions. The pilot was launched in 57 days, a record for InnoCentive and NASA, and ran for three months with a total of 20 challenges posted Agency wide. The NASA@work pilot attracted over 6,000 participants throughout NASA with a total of 183 contributing solvers for the 20 challenges posted. At the time of the pilot's closure, solvers provided viable solutions and ideas for 17 of the 20 posted challenges. The solver community provided feedback on the pilot describing it as a barrier breaking activity, conveying that there was a satisfaction associated with helping co-workers, that it was fun to think about problems outside normal work boundaries, and it was nice to learn what challenges others were facing across the agency. The results and the feedback from the solver community have demonstrated the power and utility of an internal collaboration tool, such as NASA@work.

Increase Workshop | Argonne National Laboratory

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Skip to main content Argonne National Laboratory Toggle Navigation Toggle Search Home Learning solvers Home Learning Center Undergraduates Graduates Faculty Partners News & Events Faculty Visiting Us Argonne Educational Programs is committed to providing a learning environment that emphasizes the

A Paper-and-Pencil gcd Algorithm for Gaussian Integers

ERIC Educational Resources Information Center

Szabo, Sandor

2005-01-01

As with natural numbers, a greatest common divisor of two Gaussian (complex) integers "a" and "b" is a Gaussian integer "d" that is a common divisor of both "a" and "b". This article explores an algorithm for such gcds that is easy to do by hand.

Robust design of (s, S) inventory policy parameters in supply chains with demand and lead time uncertainties

NASA Astrophysics Data System (ADS)

Karimi Movahed, Kamran; Zhang, Zhi-Hai

2015-09-01

Demand and lead time uncertainties have significant effects on supply chain behaviour. In this paper, we present a single-product three-level multi-period supply chain with uncertain demands and lead times by using robust techniques to study the managerial insights of the supply chain inventory system under uncertainty. We formulate this problem as a robust mixed-integer linear program with minimised expected cost and total cost variation to determine the optimal (s, S) values of the inventory parameters. Several numerical studies are performed to investigate the supply chain behaviour. Useful guidelines for the design of a robust supply chain are also provided. Results show that the order variance and the expected cost in a supply chain significantly increase when the manufacturer's review period is an integer ratio of the distributor's and the retailer's review periods.

A new VLSI complex integer multiplier which uses a quadratic-polynomial residue system with Fermat numbers

NASA Technical Reports Server (NTRS)

Truong, T. K.; Hsu, I. S.; Chang, J. J.; Shyu, H. C.; Reed, I. S.

1986-01-01

A quadratic-polynomial Fermat residue number system (QFNS) has been used to compute complex integer multiplications. The advantage of such a QFNS is that a complex integer multiplication requires only two integer multiplications. In this article, a new type Fermat number multiplier is developed which eliminates the initialization condition of the previous method. It is shown that the new complex multiplier can be implemented on a single VLSI chip. Such a chip is designed and fabricated in CMOS-pw technology.

A new VLSI complex integer multiplier which uses a quadratic-polynomial residue system with Fermat numbers

NASA Technical Reports Server (NTRS)

Shyu, H. C.; Reed, I. S.; Truong, T. K.; Hsu, I. S.; Chang, J. J.

1987-01-01

A quadratic-polynomial Fermat residue number system (QFNS) has been used to compute complex integer multiplications. The advantage of such a QFNS is that a complex integer multiplication requires only two integer multiplications. In this article, a new type Fermat number multiplier is developed which eliminates the initialization condition of the previous method. It is shown that the new complex multiplier can be implemented on a single VLSI chip. Such a chip is designed and fabricated in CMOS-Pw technology.

Elasticity of fractal materials using the continuum model with non-integer dimensional space

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-01-01

Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.

Innovative Teaching Games: Climbing the Hills of Math Skills. California Demonstration Mathematics Program.

ERIC Educational Resources Information Center

Pittsburg Unified School District, CA.

The card games in this publication are an alternative activity to help students master computational skills. Games for operations with whole numbers, fractions, decimals, percents, integers, and square roots are included. They can be used to introduce math topics and for practice and review, with either the whole class or in small groups with 2 to…

Optimizing Marine Corps Personnel Assignments Using an Integer Programming Model

DTIC Science & Technology

2012-12-01

Corps. vi THIS PAGE INTENTIONALLY LEFT BLANK vii TABLE OF CONTENTS I. INTRODUCTION ...throughout our careers. xvi THIS PAGE INTENTIONALLY LEFT BLANK 1 I. INTRODUCTION The Marine Corps Manpower and Reserve Affairs (M&RA) office has the...2012 BAH Rates-with Dependents. Defense Travel Mangement Office. (2011, December). 2012 BAH Rates-without Dependents. M ileage C ost 1 Per D iem

Discrete Optimization of Electronic Hyperpolarizabilities in a Chemical Subspace

DTIC Science & Technology

2009-05-01

molecular design. Methods for optimization in discrete spaces have been studied extensively and recently reviewed ( 5). Optimization methods include...integer programming, as in branch-and-bound techniques (including dead-end elimination [ 6]), simulated annealing ( 7), and genetic algorithms ( 8...These algorithms have found renewed interest and application in molecular and materials design (9- 12) . Recently, new approaches have been

Development of a Prototype H-46 Helicopter Diagnostic Expert System.

DTIC Science & Technology

1987-09-01

SQUADRON MAINTEN\\NCE: CURRENT PROCESS AND CA D S INTEG R ,ATIO N ........................................ 14 A. MAINTENANCE DATA SYSTEM...increasce the effectiveness of the maintenance process should enhance the ability of achieving :hee objectives. Artificial intelligence techniques offer a...completeiy validated. G. ORGANIZATION OF STUDY Chapter II contains a description of the Naval Aviation Maintenance Program’s Maintenance Data System (MDS

Learning oncogenetic networks by reducing to mixed integer linear programming.

PubMed

Shahrabi Farahani, Hossein; Lagergren, Jens

2013-01-01

Cancer can be a result of accumulation of different types of genetic mutations such as copy number aberrations. The data from tumors are cross-sectional and do not contain the temporal order of the genetic events. Finding the order in which the genetic events have occurred and progression pathways are of vital importance in understanding the disease. In order to model cancer progression, we propose Progression Networks, a special case of Bayesian networks, that are tailored to model disease progression. Progression networks have similarities with Conjunctive Bayesian Networks (CBNs) [1],a variation of Bayesian networks also proposed for modeling disease progression. We also describe a learning algorithm for learning Bayesian networks in general and progression networks in particular. We reduce the hard problem of learning the Bayesian and progression networks to Mixed Integer Linear Programming (MILP). MILP is a Non-deterministic Polynomial-time complete (NP-complete) problem for which very good heuristics exists. We tested our algorithm on synthetic and real cytogenetic data from renal cell carcinoma. We also compared our learned progression networks with the networks proposed in earlier publications. The software is available on the website https://bitbucket.org/farahani/diprog.

A bi-objective integer programming model for partly-restricted flight departure scheduling

PubMed Central

Guan, Wei; Zhang, Wenyi; Jiang, Shixiong; Fan, Lingling

2018-01-01

The normal studies on air traffic departure scheduling problem (DSP) mainly deal with an independent airport in which the departure traffic is not affected by surrounded airports, which, however, is not a consistent case. In reality, there still exist cases where several commercial airports are closely located and one of them possesses a higher priority. During the peak hours, the departure activities of the lower-priority airports are usually required to give way to those of higher-priority airport. These giving-way requirements can inflict a set of changes on the modeling of departure scheduling problem with respect to the lower-priority airports. To the best of our knowledge, studies on DSP under this condition are scarce. Accordingly, this paper develops a bi-objective integer programming model to address the flight departure scheduling of the partly-restricted (e.g., lower-priority) one among several adjacent airports. An adapted tabu search algorithm is designed to solve the current problem. It is demonstrated from the case study of Tianjin Binhai International Airport in China that the proposed method can obviously improve the operation efficiency, while still realizing superior equity and regularity among restricted flows. PMID:29715299

Accurate construction of consensus genetic maps via integer linear programming.

PubMed

Wu, Yonghui; Close, Timothy J; Lonardi, Stefano

2011-01-01

We study the problem of merging genetic maps, when the individual genetic maps are given as directed acyclic graphs. The computational problem is to build a consensus map, which is a directed graph that includes and is consistent with all (or, the vast majority of) the markers in the input maps. However, when markers in the individual maps have ordering conflicts, the resulting consensus map will contain cycles. Here, we formulate the problem of resolving cycles in the context of a parsimonious paradigm that takes into account two types of errors that may be present in the input maps, namely, local reshuffles and global displacements. The resulting combinatorial optimization problem is, in turn, expressed as an integer linear program. A fast approximation algorithm is proposed, and an additional speedup heuristic is developed. Our algorithms were implemented in a software tool named MERGEMAP which is freely available for academic use. An extensive set of experiments shows that MERGEMAP consistently outperforms JOINMAP, which is the most popular tool currently available for this task, both in terms of accuracy and running time. MERGEMAP is available for download at http://www.cs.ucr.edu/~yonghui/mgmap.html.

Analysis of the single-vehicle cyclic inventory routing problem

NASA Astrophysics Data System (ADS)

Aghezzaf, El-Houssaine; Zhong, Yiqing; Raa, Birger; Mateo, Manel

2012-11-01

The single-vehicle cyclic inventory routing problem (SV-CIRP) consists of a repetitive distribution of a product from a single depot to a selected subset of customers. For each customer, selected for replenishments, the supplier collects a corresponding fixed reward. The objective is to determine the subset of customers to replenish, the quantity of the product to be delivered to each and to design the vehicle route so that the resulting profit (difference between the total reward and the total logistical cost) is maximised while preventing stockouts at each of the selected customers. This problem appears often as a sub-problem in many logistical problems. In this article, the SV-CIRP is formulated as a mixed-integer program with a nonlinear objective function. After a thorough analysis of the structure of the problem and its features, an exact algorithm for its solution is proposed. This exact algorithm requires only solutions of linear mixed-integer programs. Values of a savings-based heuristic for this problem are compared to the optimal values obtained for a set of some test problems. In general, the gap may get as large as 25%, which justifies the effort to continue exploring and developing exact and approximation algorithms for the SV-CIRP.

MIP models for connected facility location: A theoretical and computational study☆

PubMed Central

Gollowitzer, Stefan; Ljubić, Ivana

2011-01-01

This article comprises the first theoretical and computational study on mixed integer programming (MIP) models for the connected facility location problem (ConFL). ConFL combines facility location and Steiner trees: given a set of customers, a set of potential facility locations and some inter-connection nodes, ConFL searches for the minimum-cost way of assigning each customer to exactly one open facility, and connecting the open facilities via a Steiner tree. The costs needed for building the Steiner tree, facility opening costs and the assignment costs need to be minimized. We model ConFL using seven compact and three mixed integer programming formulations of exponential size. We also show how to transform ConFL into the Steiner arborescence problem. A full hierarchy between the models is provided. For two exponential size models we develop a branch-and-cut algorithm. An extensive computational study is based on two benchmark sets of randomly generated instances with up to 1300 nodes and 115,000 edges. We empirically compare the presented models with respect to the quality of obtained bounds and the corresponding running time. We report optimal values for all but 16 instances for which the obtained gaps are below 0.6%. PMID:25009366

Quantum-Inspired Maximizer

NASA Technical Reports Server (NTRS)

Zak, Michail

2008-01-01

A report discusses an algorithm for a new kind of dynamics based on a quantum- classical hybrid-quantum-inspired maximizer. The model is represented by a modified Madelung equation in which the quantum potential is replaced by different, specially chosen 'computational' potential. As a result, the dynamics attains both quantum and classical properties: it preserves superposition and entanglement of random solutions, while allowing one to measure its state variables, using classical methods. Such optimal combination of characteristics is a perfect match for quantum-inspired computing. As an application, an algorithm for global maximum of an arbitrary integrable function is proposed. The idea of the proposed algorithm is very simple: based upon the Quantum-inspired Maximizer (QIM), introduce a positive function to be maximized as the probability density to which the solution is attracted. Then the larger value of this function will have the higher probability to appear. Special attention is paid to simulation of integer programming and NP-complete problems. It is demonstrated that the problem of global maximum of an integrable function can be found in polynomial time by using the proposed quantum- classical hybrid. The result is extended to a constrained maximum with applications to integer programming and TSP (Traveling Salesman Problem).

A bi-objective integer programming model for partly-restricted flight departure scheduling.

PubMed

Zhong, Han; Guan, Wei; Zhang, Wenyi; Jiang, Shixiong; Fan, Lingling

2018-01-01

The normal studies on air traffic departure scheduling problem (DSP) mainly deal with an independent airport in which the departure traffic is not affected by surrounded airports, which, however, is not a consistent case. In reality, there still exist cases where several commercial airports are closely located and one of them possesses a higher priority. During the peak hours, the departure activities of the lower-priority airports are usually required to give way to those of higher-priority airport. These giving-way requirements can inflict a set of changes on the modeling of departure scheduling problem with respect to the lower-priority airports. To the best of our knowledge, studies on DSP under this condition are scarce. Accordingly, this paper develops a bi-objective integer programming model to address the flight departure scheduling of the partly-restricted (e.g., lower-priority) one among several adjacent airports. An adapted tabu search algorithm is designed to solve the current problem. It is demonstrated from the case study of Tianjin Binhai International Airport in China that the proposed method can obviously improve the operation efficiency, while still realizing superior equity and regularity among restricted flows.

Discovery of Boolean metabolic networks: integer linear programming based approach.

PubMed

Qiu, Yushan; Jiang, Hao; Ching, Wai-Ki; Cheng, Xiaoqing

2018-04-11

Traditional drug discovery methods focused on the efficacy of drugs rather than their toxicity. However, toxicity and/or lack of efficacy are produced when unintended targets are affected in metabolic networks. Thus, identification of biological targets which can be manipulated to produce the desired effect with minimum side-effects has become an important and challenging topic. Efficient computational methods are required to identify the drug targets while incurring minimal side-effects. In this paper, we propose a graph-based computational damage model that summarizes the impact of enzymes on compounds in metabolic networks. An efficient method based on Integer Linear Programming formalism is then developed to identify the optimal enzyme-combination so as to minimize the side-effects. The identified target enzymes for known successful drugs are then verified by comparing the results with those in the existing literature. Side-effects reduction plays a crucial role in the study of drug development. A graph-based computational damage model is proposed and the theoretical analysis states the captured problem is NP-completeness. The proposed approaches can therefore contribute to the discovery of drug targets. Our developed software is available at " http://hkumath.hku.hk/~wkc/APBC2018-metabolic-network.zip ".

A combined MOIP-MCDA approach to building and screening atmospheric pollution control strategies in urban regions.

PubMed

Mavrotas, George; Ziomas, Ioannis C; Diakouaki, Danae

2006-07-01

This article presents a methodological approach for the formulation of control strategies capable of reducing atmospheric pollution at the standards set by European legislation. The approach was implemented in the greater area of Thessaloniki and was part of a project aiming at the compliance with air quality standards in five major cities in Greece. The methodological approach comprises two stages: in the first stage, the availability of several measures contributing to a certain extent to reducing atmospheric pollution indicates a combinatorial problem and favors the use of Integer Programming. More specifically, Multiple Objective Integer Programming is used in order to generate alternative efficient combinations of the available policy measures on the basis of two conflicting objectives: public expenditure minimization and social acceptance maximization. In the second stage, these combinations of control measures (i.e., the control strategies) are then comparatively evaluated with respect to a wider set of criteria, using tools from Multiple Criteria Decision Analysis, namely, the well-known PROMETHEE method. The whole procedure is based on the active involvement of local and central authorities in order to incorporate their concerns and preferences, as well as to secure the adoption and implementation of the resulting solution.

Mixed Integer Linear Programming based machine learning approach identifies regulators of telomerase in yeast.

PubMed

Poos, Alexandra M; Maicher, André; Dieckmann, Anna K; Oswald, Marcus; Eils, Roland; Kupiec, Martin; Luke, Brian; König, Rainer

2016-06-02

Understanding telomere length maintenance mechanisms is central in cancer biology as their dysregulation is one of the hallmarks for immortalization of cancer cells. Important for this well-balanced control is the transcriptional regulation of the telomerase genes. We integrated Mixed Integer Linear Programming models into a comparative machine learning based approach to identify regulatory interactions that best explain the discrepancy of telomerase transcript levels in yeast mutants with deleted regulators showing aberrant telomere length, when compared to mutants with normal telomere length. We uncover novel regulators of telomerase expression, several of which affect histone levels or modifications. In particular, our results point to the transcription factors Sum1, Hst1 and Srb2 as being important for the regulation of EST1 transcription, and we validated the effect of Sum1 experimentally. We compiled our machine learning method leading to a user friendly package for R which can straightforwardly be applied to similar problems integrating gene regulator binding information and expression profiles of samples of e.g. different phenotypes, diseases or treatments. © The Author(s) 2016. Published by Oxford University Press on behalf of Nucleic Acids Research.

Optimising the selection of food items for FFQs using Mixed Integer Linear Programming.

PubMed

Gerdessen, Johanna C; Souverein, Olga W; van 't Veer, Pieter; de Vries, Jeanne Hm

2015-01-01

To support the selection of food items for FFQs in such a way that the amount of information on all relevant nutrients is maximised while the food list is as short as possible. Selection of the most informative food items to be included in FFQs was modelled as a Mixed Integer Linear Programming (MILP) model. The methodology was demonstrated for an FFQ with interest in energy, total protein, total fat, saturated fat, monounsaturated fat, polyunsaturated fat, total carbohydrates, mono- and disaccharides, dietary fibre and potassium. The food lists generated by the MILP model have good performance in terms of length, coverage and R 2 (explained variance) of all nutrients. MILP-generated food lists were 32-40 % shorter than a benchmark food list, whereas their quality in terms of R 2 was similar to that of the benchmark. The results suggest that the MILP model makes the selection process faster, more standardised and transparent, and is especially helpful in coping with multiple nutrients. The complexity of the method does not increase with increasing number of nutrients. The generated food lists appear either shorter or provide more information than a food list generated without the MILP model.

A Combined MOIP-MCDA Approach to Building and Screening Atmospheric Pollution Control Strategies in Urban Regions

NASA Astrophysics Data System (ADS)

Mavrotas, George; Ziomas, Ioannis C.; Diakouaki, Danae

2006-07-01

This article presents a methodological approach for the formulation of control strategies capable of reducing atmospheric pollution at the standards set by European legislation. The approach was implemented in the greater area of Thessaloniki and was part of a project aiming at the compliance with air quality standards in five major cities in Greece. The methodological approach comprises two stages: in the first stage, the availability of several measures contributing to a certain extent to reducing atmospheric pollution indicates a combinatorial problem and favors the use of Integer Programming. More specifically, Multiple Objective Integer Programming is used in order to generate alternative efficient combinations of the available policy measures on the basis of two conflicting objectives: public expenditure minimization and social acceptance maximization. In the second stage, these combinations of control measures (i.e., the control strategies) are then comparatively evaluated with respect to a wider set of criteria, using tools from Multiple Criteria Decision Analysis, namely, the well-known PROMETHEE method. The whole procedure is based on the active involvement of local and central authorities in order to incorporate their concerns and preferences, as well as to secure the adoption and implementation of the resulting solution.

Advanced Computational Methods for Security Constrained Financial Transmission Rights: Structure and Parallelism

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

Elbert, Stephen T.; Kalsi, Karanjit; Vlachopoulou, Maria

Financial Transmission Rights (FTRs) help power market participants reduce price risks associated with transmission congestion. FTRs are issued based on a process of solving a constrained optimization problem with the objective to maximize the FTR social welfare under power flow security constraints. Security constraints for different FTR categories (monthly, seasonal or annual) are usually coupled and the number of constraints increases exponentially with the number of categories. Commercial software for FTR calculation can only provide limited categories of FTRs due to the inherent computational challenges mentioned above. In this paper, a novel non-linear dynamical system (NDS) approach is proposed tomore » solve the optimization problem. The new formulation and performance of the NDS solver is benchmarked against widely used linear programming (LP) solvers like CPLEX™ and tested on large-scale systems using data from the Western Electricity Coordinating Council (WECC). The NDS is demonstrated to outperform the widely used CPLEX algorithms while exhibiting superior scalability. Furthermore, the NDS based solver can be easily parallelized which results in significant computational improvement.« less

TADS: A CFD-based turbomachinery and analysis design system with GUI. Volume 1: Method and results

NASA Technical Reports Server (NTRS)

Topp, D. A.; Myers, R. A.; Delaney, R. A.

1995-01-01

The primary objective of this study was the development of a computational fluid dynamics (CFD) based turbomachinery airfoil analysis and design system, controlled by a graphical user interface (GUI). The computer codes resulting from this effort are referred to as the Turbomachinery Analysis and Design System (TADS). This document describes the theoretical basis and analytical results from the TADS system. TADS couples a throughflow solver (ADPAC) with a quasi-3D blade-to-blade solver (RVCQ3D) in an interactive package. Throughflow analysis capability was developed in ADPAC through the addition of blade force and blockage terms to the governing equations. A GUI was developed to simplify user input and automate the many tasks required to perform turbomachinery analysis and design. The coupling of various programs was done in a way that alternative solvers or grid generators could be easily incorporated into the TADS framework. Results of aerodynamic calculations using the TADS system are presented for a highly loaded fan, a compressor stator, a low-speed turbine blade, and a transonic turbine vane.

Recent Advances in Agglomerated Multigrid

NASA Technical Reports Server (NTRS)

Nishikawa, Hiroaki; Diskin, Boris; Thomas, James L.; Hammond, Dana P.

2013-01-01

We report recent advancements of the agglomerated multigrid methodology for complex flow simulations on fully unstructured grids. An agglomerated multigrid solver is applied to a wide range of test problems from simple two-dimensional geometries to realistic three- dimensional configurations. The solver is evaluated against a single-grid solver and, in some cases, against a structured-grid multigrid solver. Grid and solver issues are identified and overcome, leading to significant improvements over single-grid solvers.

Parallel Solver for H(div) Problems Using Hybridization and AMG

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

Lee, Chak S.; Vassilevski, Panayot S.

2016-01-15

In this paper, a scalable parallel solver is proposed for H(div) problems discretized by arbitrary order finite elements on general unstructured meshes. The solver is based on hybridization and algebraic multigrid (AMG). Unlike some previously studied H(div) solvers, the hybridization solver does not require discrete curl and gradient operators as additional input from the user. Instead, only some element information is needed in the construction of the solver. The hybridization results in a H1-equivalent symmetric positive definite system, which is then rescaled and solved by AMG solvers designed for H1 problems. Weak and strong scaling of the method are examinedmore » through several numerical tests. Our numerical results show that the proposed solver provides a promising alternative to ADS, a state-of-the-art solver [12], for H(div) problems. In fact, it outperforms ADS for higher order elements.« less

PowerPlay: Training an Increasingly General Problem Solver by Continually Searching for the Simplest Still Unsolvable Problem

PubMed Central

Schmidhuber, Jürgen

2013-01-01

Most of computer science focuses on automatically solving given computational problems. I focus on automatically inventing or discovering problems in a way inspired by the playful behavior of animals and humans, to train a more and more general problem solver from scratch in an unsupervised fashion. Consider the infinite set of all computable descriptions of tasks with possibly computable solutions. Given a general problem-solving architecture, at any given time, the novel algorithmic framework PowerPlay (Schmidhuber, 2011) searches the space of possible pairs of new tasks and modifications of the current problem solver, until it finds a more powerful problem solver that provably solves all previously learned tasks plus the new one, while the unmodified predecessor does not. Newly invented tasks may require to achieve a wow-effect by making previously learned skills more efficient such that they require less time and space. New skills may (partially) re-use previously learned skills. The greedy search of typical PowerPlay variants uses time-optimal program search to order candidate pairs of tasks and solver modifications by their conditional computational (time and space) complexity, given the stored experience so far. The new task and its corresponding task-solving skill are those first found and validated. This biases the search toward pairs that can be described compactly and validated quickly. The computational costs of validating new tasks need not grow with task repertoire size. Standard problem solver architectures of personal computers or neural networks tend to generalize by solving numerous tasks outside the self-invented training set; PowerPlay’s ongoing search for novelty keeps breaking the generalization abilities of its present solver. This is related to Gödel’s sequence of increasingly powerful formal theories based on adding formerly unprovable statements to the axioms without affecting previously provable theorems. The continually increasing repertoire of problem-solving procedures can be exploited by a parallel search for solutions to additional externally posed tasks. PowerPlay may be viewed as a greedy but practical implementation of basic principles of creativity (Schmidhuber, 2006a, 2010). A first experimental analysis can be found in separate papers (Srivastava et al., 2012a,b, 2013). PMID:23761771

MODFLOW-NWT, A Newton formulation for MODFLOW-2005

USGS Publications Warehouse

Niswonger, Richard G.; Panday, Sorab; Ibaraki, Motomu

2011-01-01

This report documents a Newton formulation of MODFLOW-2005, called MODFLOW-NWT. MODFLOW-NWT is a standalone program that is intended for solving problems involving drying and rewetting nonlinearities of the unconfined groundwater-flow equation. MODFLOW-NWT must be used with the Upstream-Weighting (UPW) Package for calculating intercell conductances in a different manner than is done in the Block-Centered Flow (BCF), Layer Property Flow (LPF), or Hydrogeologic-Unit Flow (HUF; Anderman and Hill, 2000) Packages. The UPW Package treats nonlinearities of cell drying and rewetting by use of a continuous function of groundwater head, rather than the discrete approach of drying and rewetting that is used by the BCF, LPF, and HUF Packages. This further enables application of the Newton formulation for unconfined groundwater-flow problems because conductance derivatives required by the Newton method are smooth over the full range of head for a model cell. The NWT linearization approach generates an asymmetric matrix, which is different from the standard MODFLOW formulation that generates a symmetric matrix. Because all linear solvers presently available for use with MODFLOW-2005 solve only symmetric matrices, MODFLOW-NWT includes two previously developed asymmetric matrix-solver options. The matrix-solver options include a generalized-minimum-residual (GMRES) Solver and an Orthomin / stabilized conjugate-gradient (CGSTAB) Solver. The GMRES Solver is documented in a previously published report, such that only a brief description and input instructions are provided in this report. However, the CGSTAB Solver (called XMD) is documented in this report. Flow-property input for the UPW Package is designed based on the LPF Package and material-property input is identical to that for the LPF Package except that the rewetting and vertical-conductance correction options of the LPF Package are not available with the UPW Package. Input files constructed for the LPF Package can be used with slight modification as input for the UPW Package. This report presents the theory and methods used by MODFLOW-NWT, including the UPW Package. Additionally, this report provides comparisons of the new methodology to analytical solutions of groundwater flow and to standard MODFLOW-2005 results by use of an unconfined aquifer MODFLOW example problem. The standard MODFLOW-2005 simulation uses the LPF Package with the wet/dry option active. A new example problem also is presented to demonstrate MODFLOW-NWT's ability to provide a solution for a difficult unconfined groundwater-flow problem.

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Computational strategies for three-dimensional flow simulations on distributed computer systems. Ph.D. Thesis Semiannual Status Report, 15 Aug. 1993 - 15 Feb. 1994

NASA Technical Reports Server (NTRS)

Weed, Richard Allen; Sankar, L. N.

1994-01-01

An increasing amount of research activity in computational fluid dynamics has been devoted to the development of efficient algorithms for parallel computing systems. The increasing performance to price ratio of engineering workstations has led to research to development procedures for implementing a parallel computing system composed of distributed workstations. This thesis proposal outlines an ongoing research program to develop efficient strategies for performing three-dimensional flow analysis on distributed computing systems. The PVM parallel programming interface was used to modify an existing three-dimensional flow solver, the TEAM code developed by Lockheed for the Air Force, to function as a parallel flow solver on clusters of workstations. Steady flow solutions were generated for three different wing and body geometries to validate the code and evaluate code performance. The proposed research will extend the parallel code development to determine the most efficient strategies for unsteady flow simulations.

Solution of large nonlinear quasistatic structural mechanics problems on distributed-memory multiprocessor computers

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

Blanford, M.

1997-12-31

Most commercially-available quasistatic finite element programs assemble element stiffnesses into a global stiffness matrix, then use a direct linear equation solver to obtain nodal displacements. However, for large problems (greater than a few hundred thousand degrees of freedom), the memory size and computation time required for this approach becomes prohibitive. Moreover, direct solution does not lend itself to the parallel processing needed for today`s multiprocessor systems. This talk gives an overview of the iterative solution strategy of JAS3D, the nonlinear large-deformation quasistatic finite element program. Because its architecture is derived from an explicit transient-dynamics code, it does not ever assemblemore » a global stiffness matrix. The author describes the approach he used to implement the solver on multiprocessor computers, and shows examples of problems run on hundreds of processors and more than a million degrees of freedom. Finally, he describes some of the work he is presently doing to address the challenges of iterative convergence for ill-conditioned problems.« less

An efficient solver for large structured eigenvalue problems in relativistic quantum chemistry

NASA Astrophysics Data System (ADS)

Shiozaki, Toru

2017-01-01

We report an efficient program for computing the eigenvalues and symmetry-adapted eigenvectors of very large quaternionic (or Hermitian skew-Hamiltonian) matrices, using which structure-preserving diagonalisation of matrices of dimension N > 10, 000 is now routine on a single computer node. Such matrices appear frequently in relativistic quantum chemistry owing to the time-reversal symmetry. The implementation is based on a blocked version of the Paige-Van Loan algorithm, which allows us to use the Level 3 BLAS subroutines for most of the computations. Taking advantage of the symmetry, the program is faster by up to a factor of 2 than state-of-the-art implementations of complex Hermitian diagonalisation; diagonalising a 12, 800 × 12, 800 matrix took 42.8 (9.5) and 85.6 (12.6) minutes with 1 CPU core (16 CPU cores) using our symmetry-adapted solver and Intel Math Kernel Library's ZHEEV that is not structure-preserving, respectively. The source code is publicly available under the FreeBSD licence.

A multiblock multigrid three-dimensional Euler equation solver

NASA Technical Reports Server (NTRS)

Cannizzaro, Frank E.; Elmiligui, Alaa; Melson, N. Duane; Vonlavante, E.

1990-01-01

Current aerodynamic designs are often quite complex (geometrically). Flexible computational tools are needed for the analysis of a wide range of configurations with both internal and external flows. In the past, geometrically dissimilar configurations required different analysis codes with different grid topologies in each. The duplicity of codes can be avoided with the use of a general multiblock formulation which can handle any grid topology. Rather than hard wiring the grid topology into the program, it is instead dictated by input to the program. In this work, the compressible Euler equations, written in a body-fitted finite-volume formulation, are solved using a pseudo-time-marching approach. Two upwind methods (van Leer's flux-vector-splitting and Roe's flux-differencing) were investigated. Two types of explicit solvers (a two-step predictor-corrector and a modified multistage Runge-Kutta) were used with multigrid acceleration to enhance convergence. A multiblock strategy is used to allow greater geometric flexibility. A report on simple explicit upwind schemes for solving compressible flows is included.

Sum-Difference Numbers

ERIC Educational Resources Information Center

Shi, Yixun

2010-01-01

Starting with an interesting number game sometimes used by school teachers to demonstrate the factorization of integers, "sum-difference numbers" are defined. A positive integer n is a "sum-difference number" if there exist positive integers "x, y, w, z" such that n = xy = wz and x ? y = w + z. This paper characterizes all sum-difference numbers…

Order and Value: Transitioning to Integers

ERIC Educational Resources Information Center

Bofferding, Laura

2014-01-01

As students progress from working with whole numbers to working with integers, they must wrestle with the big ideas of number values and order. Using objects to show positive quantities is easy, but no physical negative quantities exist. Therefore, when talking about integers, the author refers to number values instead of number quantities. The…

A time series model: First-order integer-valued autoregressive (INAR(1))

NASA Astrophysics Data System (ADS)

Simarmata, D. M.; Novkaniza, F.; Widyaningsih, Y.

2017-07-01

Nonnegative integer-valued time series arises in many applications. A time series model: first-order Integer-valued AutoRegressive (INAR(1)) is constructed by binomial thinning operator to model nonnegative integer-valued time series. INAR (1) depends on one period from the process before. The parameter of the model can be estimated by Conditional Least Squares (CLS). Specification of INAR(1) is following the specification of (AR(1)). Forecasting in INAR(1) uses median or Bayesian forecasting methodology. Median forecasting methodology obtains integer s, which is cumulative density function (CDF) until s, is more than or equal to 0.5. Bayesian forecasting methodology forecasts h-step-ahead of generating the parameter of the model and parameter of innovation term using Adaptive Rejection Metropolis Sampling within Gibbs sampling (ARMS), then finding the least integer s, where CDF until s is more than or equal to u . u is a value taken from the Uniform(0,1) distribution. INAR(1) is applied on pneumonia case in Penjaringan, Jakarta Utara, January 2008 until April 2016 monthly.

Multidimensional Riemann problem with self-similar internal structure - part III - a multidimensional analogue of the HLLI Riemann solver for conservative hyperbolic systems

NASA Astrophysics Data System (ADS)

Balsara, Dinshaw S.; Nkonga, Boniface

2017-10-01

Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional Riemann solver is also similarly improved. Such multidimensional Riemann problems arise when multiple states come together at the vertex of a mesh. The interaction of the resulting one-dimensional Riemann problems gives rise to a strongly-interacting state. We wish to endow this strongly-interacting state with physically-motivated sub-structure. The fastest way of endowing such sub-structure consists of making a multidimensional extension of the HLLI Riemann solver for hyperbolic conservation laws. Presenting such a multidimensional analogue of the HLLI Riemann solver with linear sub-structure for use on structured meshes is the goal of this work. The multidimensional MuSIC Riemann solver documented here is universal in the sense that it can be applied to any hyperbolic conservation law. The multidimensional Riemann solver is made to be consistent with constraints that emerge naturally from the Galerkin projection of the self-similar states within the wave model. When the full eigenstructure in both directions is used in the present Riemann solver, it becomes a complete Riemann solver in a multidimensional sense. I.e., all the intermediate waves are represented in the multidimensional wave model. The work also presents, for the very first time, an important analysis of the dissipation characteristics of multidimensional Riemann solvers. The present Riemann solver results in the most efficient implementation of a multidimensional Riemann solver with sub-structure. Because it preserves stationary linearly degenerate waves, it might also help with well-balancing. Implementation-related details are presented in pointwise fashion for the one-dimensional HLLI Riemann solver as well as the multidimensional MuSIC Riemann solver.

Vector calculus in non-integer dimensional space and its applications to fractal media

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-02-01

We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are defined. For simplification we consider scalar and vector fields that are independent of angles. We formulate a generalization of vector calculus for rotationally covariant scalar and vector functions. This generalization allows us to describe fractal media and materials in the framework of continuum models with non-integer dimensional space. As examples of application of the suggested calculus, we consider elasticity of fractal materials (fractal hollow ball and fractal cylindrical pipe with pressure inside and outside), steady distribution of heat in fractal media, electric field of fractal charged cylinder. We solve the correspondent equations for non-integer dimensional space models.

A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows

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

Zhou, Qiang; Fan, Liang-Shih, E-mail: fan.1@osu.edu

A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The immersed boundary method (IBM) recently developed by Breugem (2012) [19] is adopted in the present method, development including the retraction technique, the multi-direct forcing method and the direct account of the inertia of the fluid contained within the particles. The present IB-LBM is, however, formulated with further improvement with the implementation of the high-order Runge–Kutta schemes in the coupled fluid–particle interaction. The major challenge to implement high-order Runge–Kutta schemes in the LBM is that the flow information suchmore » as density and velocity cannot be directly obtained at a fractional time step from the LBM since the LBM only provides the flow information at an integer time step. This challenge can be, however, overcome as given in the present IB-LBM by extrapolating the flow field around particles from the known flow field at the previous integer time step. The newly calculated fluid–particle interactions from the previous fractional time steps of the current integer time step are also accounted for in the extrapolation. The IB-LBM with high-order Runge–Kutta schemes developed in this study is validated by several benchmark applications. It is demonstrated, for the first time, that the IB-LBM has the capacity to resolve the translational and rotational motion of particles with the second-order accuracy. The optimal retraction distances for spheres and tubes that help the method achieve the second-order accuracy are found to be around 0.30 and −0.47 times of the lattice spacing, respectively. Simulations of the Stokes flow through a simple cubic lattice of rotational spheres indicate that the lift force produced by the Magnus effect can be very significant in view of the magnitude of the drag force when the practical rotating speed of the spheres is encountered. This finding may lead to more comprehensive studies of the effect of the particle rotation on fluid–solid drag laws. It is also demonstrated that, when the third-order or the fourth-order Runge–Kutta scheme is used, the numerical stability of the present IB-LBM is better than that of all methods in the literature, including the previous IB-LBMs and also the methods with the combination of the IBM and the traditional incompressible Navier–Stokes solver. - Highlights: • The IBM is embedded in the LBM using Runge–Kutta time schemes. • The effectiveness of the present IB-LBM is validated by benchmark applications. • For the first time, the IB-LBM achieves the second-order accuracy. • The numerical stability of the present IB-LBM is better than previous methods.« less

Overview of Transonic to Hypersonic Stage Separation Tool Development for Multi-Stage-to-Orbit Concepts

NASA Technical Reports Server (NTRS)

Murphy, Kelly J.; Bunning, Pieter G.; Pamadi, Bandu N.; Scallion, William I.; Jones, Kenneth M.

2004-01-01

An overview of research efforts at NASA in support of the stage separation and ascent aerothermodynamics research program is presented. The objective of this work is to develop a synergistic suite of experimental, computational, and engineering tools and methods to apply to vehicle separation across the transonic to hypersonic speed regimes. Proximity testing of a generic bimese wing-body configuration is on-going in the transonic (Mach numbers 0.6, 1.05, and 1.1), supersonic (Mach numbers 2.3, 3.0, and 4.5) and hypersonic (Mach numbers 6 and 10) speed regimes in four wind tunnel facilities at the NASA Langley Research Center. An overset grid, Navier-Stokes flow solver has been enhanced and demonstrated on a matrix of proximity cases and on a dynamic separation simulation of the bimese configuration. Steady-state predictions with this solver were in excellent agreement with wind tunnel data at Mach 3 as were predictions via a Cartesian-grid Euler solver. Experimental and computational data have been used to evaluate multi-body enhancements to the widely-used Aerodynamic Preliminary Analysis System, an engineering methodology, and to develop a new software package, SepSim, for the simulation and visualization of vehicle motions in a stage separation scenario. Web-based software will be used for archiving information generated from this research program into a database accessible to the user community. Thus, a framework has been established to study stage separation problems using coordinated experimental, computational, and engineering tools.

An adaptive random search for short term generation scheduling with network constraints.

PubMed

Marmolejo, J A; Velasco, Jonás; Selley, Héctor J

2017-01-01

This paper presents an adaptive random search approach to address a short term generation scheduling with network constraints, which determines the startup and shutdown schedules of thermal units over a given planning horizon. In this model, we consider the transmission network through capacity limits and line losses. The mathematical model is stated in the form of a Mixed Integer Non Linear Problem with binary variables. The proposed heuristic is a population-based method that generates a set of new potential solutions via a random search strategy. The random search is based on the Markov Chain Monte Carlo method. The main key of the proposed method is that the noise level of the random search is adaptively controlled in order to exploring and exploiting the entire search space. In order to improve the solutions, we consider coupling a local search into random search process. Several test systems are presented to evaluate the performance of the proposed heuristic. We use a commercial optimizer to compare the quality of the solutions provided by the proposed method. The solution of the proposed algorithm showed a significant reduction in computational effort with respect to the full-scale outer approximation commercial solver. Numerical results show the potential and robustness of our approach.

Enhanced representations of lithium-ion batteries in power systems models and their effect on the valuation of energy arbitrage applications

NASA Astrophysics Data System (ADS)

Sakti, Apurba; Gallagher, Kevin G.; Sepulveda, Nestor; Uckun, Canan; Vergara, Claudio; de Sisternes, Fernando J.; Dees, Dennis W.; Botterud, Audun

2017-02-01

We develop three novel enhanced mixed integer-linear representations of the power limit of the battery and its efficiency as a function of the charge and discharge power and the state of charge of the battery, which can be directly implemented in large-scale power systems models and solved with commercial optimization solvers. Using these battery representations, we conduct a techno-economic analysis of the performance of a 10 MWh lithium-ion battery system testing the effect of a 5-min vs. a 60-min price signal on profits using real time prices from a selected node in the MISO electricity market. Results show that models of lithium-ion batteries where the power limits and efficiency are held constant overestimate profits by 10% compared to those obtained from an enhanced representation that more closely matches the real behavior of the battery. When the battery system is exposed to a 5-min price signal, the energy arbitrage profitability improves by 60% compared to that from hourly price exposure. These results indicate that a more accurate representation of li-ion batteries as well as the market rules that govern the frequency of electricity prices can play a major role on the estimation of the value of battery technologies for power grid applications.

Trace of totally positive algebraic integers and integer transfinite diameter

NASA Astrophysics Data System (ADS)

Flammang, V.

2009-06-01

Explicit auxiliary functions can be used in the ``Schur-Siegel- Smyth trace problem''. In the previous works, these functions were constructed only with polynomials having all their roots positive. Here, we use several polynomials with complex roots, which are found with Wu's algorithm, and we improve the known lower bounds for the absolute trace of totally positive algebraic integers. This improvement has a consequence for the search of Salem numbers that have a negative trace. The same method also gives a small improvement of the upper bound for the integer transfinite diameter of [0,1].

Integer cosine transform for image compression

NASA Technical Reports Server (NTRS)

Cheung, K.-M.; Pollara, F.; Shahshahani, M.

1991-01-01

This article describes a recently introduced transform algorithm called the integer cosine transform (ICT), which is used in transform-based data compression schemes. The ICT algorithm requires only integer operations on small integers and at the same time gives a rate-distortion performance comparable to that offered by the floating-point discrete cosine transform (DCT). The article addresses the issue of implementation complexity, which is of prime concern for source coding applications of interest in deep-space communications. Complexity reduction in the transform stage of the compression scheme is particularly relevant, since this stage accounts for most (typically over 80 percent) of the computational load.

An installed nacelle design code using a multiblock Euler solver. Volume 2: User guide

NASA Technical Reports Server (NTRS)

Chen, H. C.

1992-01-01

This is a user manual for the general multiblock Euler design (GMBEDS) code. The code is for the design of a nacelle installed on a geometrically complex configuration such as a complete airplane with wing/body/nacelle/pylon. It consists of two major building blocks: a design module developed by LaRC using directive iterative surface curvature (DISC); and a general multiblock Euler (GMBE) flow solver. The flow field surrounding a complex configuration is divided into a number of topologically simple blocks to facilitate surface-fitted grid generation and improve flow solution efficiency. This user guide provides input data formats along with examples of input files and a Unix script for program execution in the UNICOS environment.

OVERFLOW-Interaction with Industry

NASA Technical Reports Server (NTRS)

Buning, Pieter G.; George, Michael W. (Technical Monitor)

1996-01-01

A Navier-Stokes flow solver, OVERFLOW, has been developed by researchers at NASA Ames Research Center to use overset (Chimera) grids to simulate the flow about complex aerodynamic shapes. Primary customers of the OVERFLOW flow solver and related software include McDonnell Douglas and Boeing, as well as the NASA Focused Programs for Advanced Subsonic Technology (AST) and High Speed Research (HSR). Code development has focused on customer issues, including improving code performance, ability to run on workstation clusters and the NAS SP2, and direct interaction with industry on accuracy assessment and validation. Significant interaction with NAS has produced a capability tailored to the Ames computing environment, and code contributions have come from a wide range of sources, both within and outside Ames.

Solving Modal Equations of Motion with Initial Conditions Using MSC/NASTRAN DMAP. Part 2; Coupled Versus Uncoupled Integration

NASA Technical Reports Server (NTRS)

Barnett, Alan R.; Ibrahim, Omar M.; Abdallah, Ayman A.; Sullivan, Timothy L.

1993-01-01

By utilizing MSC/NASTRAN DMAP (Direct Matrix Abstraction Program) in an existing NASA Lewis Research Center coupled loads methodology, solving modal equations of motion with initial conditions is possible using either coupled (Newmark-Beta) or uncoupled (exact mode superposition) integration available within module TRD1. Both the coupled and newly developed exact mode superposition methods have been used to perform transient analyses of various space systems. However, experience has shown that in most cases, significant time savings are realized when the equations of motion are integrated using the uncoupled solver instead of the coupled solver. Through the results of a real-world engineering analysis, advantages of using the exact mode superposition methodology are illustrated.

A multistage stochastic programming model for a multi-period strategic expansion of biofuel supply chain under evolving uncertainties

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

Xie, Fei; Huang, Yongxi

Here, we develop a multistage, stochastic mixed-integer model to support biofuel supply chain expansion under evolving uncertainties. By utilizing the block-separable recourse property, we reformulate the multistage program in an equivalent two-stage program and solve it using an enhanced nested decomposition method with maximal non-dominated cuts. We conduct extensive numerical experiments and demonstrate the application of the model and algorithm in a case study based on the South Carolina settings. The value of multistage stochastic programming method is also explored by comparing the model solution with the counterparts of an expected value based deterministic model and a two-stage stochastic model.

A multistage stochastic programming model for a multi-period strategic expansion of biofuel supply chain under evolving uncertainties

DOE PAGES

Xie, Fei; Huang, Yongxi

2018-02-04

Here, we develop a multistage, stochastic mixed-integer model to support biofuel supply chain expansion under evolving uncertainties. By utilizing the block-separable recourse property, we reformulate the multistage program in an equivalent two-stage program and solve it using an enhanced nested decomposition method with maximal non-dominated cuts. We conduct extensive numerical experiments and demonstrate the application of the model and algorithm in a case study based on the South Carolina settings. The value of multistage stochastic programming method is also explored by comparing the model solution with the counterparts of an expected value based deterministic model and a two-stage stochastic model.

Elliptic Curve Integral Points on y2 = x3 + 3x ‑ 14

NASA Astrophysics Data System (ADS)

Zhao, Jianhong

2018-03-01

The positive integer points and integral points of elliptic curves are very important in the theory of number and arithmetic algebra, it has a wide range of applications in cryptography and other fields. There are some results of positive integer points of elliptic curve y 2 = x 3 + ax + b, a, b ∈ Z In 1987, D. Zagier submit the question of the integer points on y 2 = x 3 ‑ 27x + 62, it count a great deal to the study of the arithmetic properties of elliptic curves. In 2009, Zhu H L and Chen J H solved the problem of the integer points on y 2 = x 3 ‑ 27x + 62 by using algebraic number theory and P-adic analysis method. In 2010, By using the elementary method, Wu H M obtain all the integral points of elliptic curves y 2 = x 3 ‑ 27x ‑ 62. In 2015, Li Y Z and Cui B J solved the problem of the integer points on y 2 = x 3 ‑ 21x ‑ 90 By using the elementary method. In 2016, Guo J solved the problem of the integer points on y 2 = x 3 + 27x + 62 by using the elementary method. In 2017, Guo J proved that y 2 = x 3 ‑ 21x + 90 has no integer points by using the elementary method. Up to now, there is no relevant conclusions on the integral points of elliptic curves y 2 = x 3 + 3x ‑ 14, which is the subject of this paper. By using congruence and Legendre Symbol, it can be proved that elliptic curve y 2 = x 3 + 3x ‑ 14 has only one integer point: (x, y) = (2, 0).

Integer aperture ambiguity resolution based on difference test

NASA Astrophysics Data System (ADS)

Zhang, Jingyu; Wu, Meiping; Li, Tao; Zhang, Kaidong

2015-07-01

Carrier-phase integer ambiguity resolution (IAR) is the key to highly precise, fast positioning and attitude determination with Global Navigation Satellite System (GNSS). It can be seen as the process of estimating the unknown cycle ambiguities of the carrier-phase observations as integers. Once the ambiguities are fixed, carrier phase data will act as the very precise range data. Integer aperture (IA) ambiguity resolution is the combination of acceptance testing and integer ambiguity resolution, which can realize better quality control of IAR. Difference test (DT) is one of the most popular acceptance tests. This contribution will give a detailed analysis about the following properties of IA ambiguity resolution based on DT: 1. The sharpest and loose upper bounds of DT are derived from the perspective of geometry. These bounds are very simple and easy to be computed, which give the range for the critical values of DT.

Naval Postgraduate School Aircraft Synthesis Program (User’s Manual)

DTIC Science & Technology

1991-09-01

LOGICAL DVFLAG CHARACTER ANS*6, TITLE*80, PHASE*8 INTEGER EN REAL MACHI, M&CH2 DIMENSION ALTD(6), XM& CH (6) 6590 IF(DVFLAG.EQ. .FALSE.) THEN !GIVE OPTION TO...7800 7840 WRITE (6, 78 45) 7845 FORMAT(/7X,’ENTER THE HORIZONTAL TAIL/CANARD’/ &7X,’WEIGHT SLOPE: ’,$) READ(5,7826,ERR-7840) SLOPE(3) IF((SLOPE(3).LT

Formal Semanol Specification of Ada.

DTIC Science & Technology

1980-09-01

concurrent task modeling involved very little change to the SEMANOL metalanguage. A primitive capable of initiating concurrent SEMANOL task processors...i.e., #CO-COMPUTE) and two primitivc-; corresponding to integer semaphores (i.c., #P and #V) were all that were required. In addition, these changes... synchronization techniques and choice of correct unblocking alternatives. We should note that it had been our original intention to use the Ada Translator program

HIPPO Unit Commitment Version 1

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

2017-01-17

Developed for the Midcontinent Independent System Operator, Inc. (MISO), HIPPO-Unit Commitment Version 1 is for solving security constrained unit commitment problem. The model was developed to solve MISO's cases. This version of codes includes I/O module to read in MISO's csv files, modules to create a state-based mixed integer programming formulation for solving MIP, and modules to test basic procedures to solve MIP via HPC.

Item Selection for the Development of Parallel Forms from an IRT-Based Seed Test Using a Sampling and Classification Approach

ERIC Educational Resources Information Center

Chen, Pei-Hua; Chang, Hua-Hua; Wu, Haiyan

2012-01-01

Two sampling-and-classification-based procedures were developed for automated test assembly: the Cell Only and the Cell and Cube methods. A simulation study based on a 540-item bank was conducted to compare the performance of the procedures with the performance of a mixed-integer programming (MIP) method for assembling multiple parallel test…

Optimum use of air tankers in initial attack: selection, basing, and transfer rules

Treesearch

Francis E. Greulich; William G. O' Regan

1982-01-01

Fire managers face two interrelated problems in deciding the most efficient use of air tankers: where best to base them, and how best to reallocate them each day in anticipation of fire occurrence. A computerized model based on a mixed integer linear program can help in assigning air tankers throughout the fire season. The model was tested using information from...

Towards a theory of automated elliptic mesh generation

NASA Technical Reports Server (NTRS)

Cordova, J. Q.

1992-01-01

The theory of elliptic mesh generation is reviewed and the fundamental problem of constructing computational space is discussed. It is argued that the construction of computational space is an NP-Complete problem and therefore requires a nonstandard approach for its solution. This leads to the development of graph-theoretic, combinatorial optimization and integer programming algorithms. Methods for the construction of two dimensional computational space are presented.

A Generalized Distance’ Estimation Procedure for Intra-Urban Interaction

DTIC Science & Technology

Bettinger . It is found that available estimation techniques necessarily result in non-integer solutions. A mathematical device is therefore...The estimation of urban and regional travel patterns has been a necessary part of current efforts to establish land use guidelines for the Texas...paper details computational experience with travel estimation within Corpus Christi, Texas, using a new convex programming approach of Charnes, Raike and

MIADS2 ... an alphanumeric map information assembly and display system for a large computer

Treesearch

Elliot L. Amidon

1966-01-01

A major improvement and extension of the Map Information Assembly and Display System (MIADS) developed in 1964 is described. Basic principles remain unchanged, but the computer programs have been expanded and rewritten for a large computer, in Fortran IV and MAP languages. The code system is extended from 99 integers to about 2,200 alphanumeric 2-character codes. Hand-...

Cloud-based large-scale air traffic flow optimization

NASA Astrophysics Data System (ADS)

Cao, Yi

The ever-increasing traffic demand makes the efficient use of airspace an imperative mission, and this paper presents an effort in response to this call. Firstly, a new aggregate model, called Link Transmission Model (LTM), is proposed, which models the nationwide traffic as a network of flight routes identified by origin-destination pairs. The traversal time of a flight route is assumed to be the mode of distribution of historical flight records, and the mode is estimated by using Kernel Density Estimation. As this simplification abstracts away physical trajectory details, the complexity of modeling is drastically decreased, resulting in efficient traffic forecasting. The predicative capability of LTM is validated against recorded traffic data. Secondly, a nationwide traffic flow optimization problem with airport and en route capacity constraints is formulated based on LTM. The optimization problem aims at alleviating traffic congestions with minimal global delays. This problem is intractable due to millions of variables. A dual decomposition method is applied to decompose the large-scale problem such that the subproblems are solvable. However, the whole problem is still computational expensive to solve since each subproblem is an smaller integer programming problem that pursues integer solutions. Solving an integer programing problem is known to be far more time-consuming than solving its linear relaxation. In addition, sequential execution on a standalone computer leads to linear runtime increase when the problem size increases. To address the computational efficiency problem, a parallel computing framework is designed which accommodates concurrent executions via multithreading programming. The multithreaded version is compared with its monolithic version to show decreased runtime. Finally, an open-source cloud computing framework, Hadoop MapReduce, is employed for better scalability and reliability. This framework is an "off-the-shelf" parallel computing model that can be used for both offline historical traffic data analysis and online traffic flow optimization. It provides an efficient and robust platform for easy deployment and implementation. A small cloud consisting of five workstations was configured and used to demonstrate the advantages of cloud computing in dealing with large-scale parallelizable traffic problems.

ArraySolver: an algorithm for colour-coded graphical display and Wilcoxon signed-rank statistics for comparing microarray gene expression data.

PubMed

Khan, Haseeb Ahmad

2004-01-01

The massive surge in the production of microarray data poses a great challenge for proper analysis and interpretation. In recent years numerous computational tools have been developed to extract meaningful interpretation of microarray gene expression data. However, a convenient tool for two-groups comparison of microarray data is still lacking and users have to rely on commercial statistical packages that might be costly and require special skills, in addition to extra time and effort for transferring data from one platform to other. Various statistical methods, including the t-test, analysis of variance, Pearson test and Mann-Whitney U test, have been reported for comparing microarray data, whereas the utilization of the Wilcoxon signed-rank test, which is an appropriate test for two-groups comparison of gene expression data, has largely been neglected in microarray studies. The aim of this investigation was to build an integrated tool, ArraySolver, for colour-coded graphical display and comparison of gene expression data using the Wilcoxon signed-rank test. The results of software validation showed similar outputs with ArraySolver and SPSS for large datasets. Whereas the former program appeared to be more accurate for 25 or fewer pairs (n < or = 25), suggesting its potential application in analysing molecular signatures that usually contain small numbers of genes. The main advantages of ArraySolver are easy data selection, convenient report format, accurate statistics and the familiar Excel platform.

ArraySolver: An Algorithm for Colour-Coded Graphical Display and Wilcoxon Signed-Rank Statistics for Comparing Microarray Gene Expression Data

PubMed Central

2004-01-01

The massive surge in the production of microarray data poses a great challenge for proper analysis and interpretation. In recent years numerous computational tools have been developed to extract meaningful interpretation of microarray gene expression data. However, a convenient tool for two-groups comparison of microarray data is still lacking and users have to rely on commercial statistical packages that might be costly and require special skills, in addition to extra time and effort for transferring data from one platform to other. Various statistical methods, including the t-test, analysis of variance, Pearson test and Mann–Whitney U test, have been reported for comparing microarray data, whereas the utilization of the Wilcoxon signed-rank test, which is an appropriate test for two-groups comparison of gene expression data, has largely been neglected in microarray studies. The aim of this investigation was to build an integrated tool, ArraySolver, for colour-coded graphical display and comparison of gene expression data using the Wilcoxon signed-rank test. The results of software validation showed similar outputs with ArraySolver and SPSS for large datasets. Whereas the former program appeared to be more accurate for 25 or fewer pairs (n ≤ 25), suggesting its potential application in analysing molecular signatures that usually contain small numbers of genes. The main advantages of ArraySolver are easy data selection, convenient report format, accurate statistics and the familiar Excel platform. PMID:18629036

Small Internal Combustion Engine Testing for a Hybrid-Electric Remotely-Piloted Aircraft

DTIC Science & Technology

2011-03-01

differential equations (ODEs) were formed and solved for numerically using various solvers in MATLAB . From these solutions, engine performance...program 5. □ Make sure eddy-current absorber and sprockets are free of debris and that no loose materials are close enough to become entangled

Getting the Best out of Excel

ERIC Educational Resources Information Center

Heys, Chris

2008-01-01

Excel, Microsoft's spreadsheet program, offers several tools which have proven useful in solving some optimization problems that arise in operations research. We will look at two such tools, the Excel modules called Solver and Goal Seek--this after deriving an equation, called the "cash accumulation equation", to be used in conjunction with them.

"Radically Different Learning": Implementing Sustainability Pedagogy in a University Peer Mentor Program

ERIC Educational Resources Information Center

Sherman, Jacob D. B.; Burns, Heather L.

2015-01-01

Sustainability education is a growing field within higher education that fosters personal and intellectual engagement with the interconnected tensions of pressing social, ecological, economic, and political issues. Sustainability education aims to prepare learners to become creative problem solvers and active citizens who understand the…

Parallelized CCHE2D flow model with CUDA Fortran on Graphics Process Units

USDA-ARS?s Scientific Manuscript database

This paper presents the CCHE2D implicit flow model parallelized using CUDA Fortran programming technique on Graphics Processing Units (GPUs). A parallelized implicit Alternating Direction Implicit (ADI) solver using Parallel Cyclic Reduction (PCR) algorithm on GPU is developed and tested. This solve...

A Converse of a Result about the Floor Function by Hermite

ERIC Educational Resources Information Center

Mortici, Cristinel

2012-01-01

The floor function maps a real number to the largest previous integer. More precisely, floor(x)=[x] is the largest integer not greater than x. The square bracket notation [x] for the floor function was introduced by Gauss in his third proof of quadratic reciprocity in 1808. The floor function is also called the greatest integer or entier (French…

Using Integer Clocks to Verify the Timing-Sync Sensor Network Protocol

NASA Technical Reports Server (NTRS)

Huang, Xiaowan; Singh, Anu; Smolka, Scott A.

2010-01-01

We use the UPPAAL model checker for Timed Automata to verify the Timing-Sync time-synchronization protocol for sensor networks (TPSN). The TPSN protocol seeks to provide network-wide synchronization of the distributed clocks in a sensor network. Clock-synchronization algorithms for sensor networks such as TPSN must be able to perform arithmetic on clock values to calculate clock drift and network propagation delays. They must be able to read the value of a local clock and assign it to another local clock. Such operations are not directly supported by the theory of Timed Automata. To overcome this formal-modeling obstacle, we augment the UPPAAL specification language with the integer clock derived type. Integer clocks, which are essentially integer variables that are periodically incremented by a global pulse generator, greatly facilitate the encoding of the operations required to synchronize clocks as in the TPSN protocol. With this integer-clock-based model of TPSN in hand, we use UPPAAL to verify that the protocol achieves network-wide time synchronization and is devoid of deadlock. We also use the UPPAAL Tracer tool to illustrate how integer clocks can be used to capture clock drift and resynchronization during protocol execution

System and method for generating attitude determinations using GPS

NASA Technical Reports Server (NTRS)

Cohen, Clark E. (Inventor)

1996-01-01

A GPS attitude receiver for determining the attitude of a moving vehicle in conjunction with a first, a second, a third, and a fourth antenna mounted to the moving vehicle. Each of the antennas receives a plurality of GPS signals that each include a carrier component. For each of the carrier components of the received GPS signals there is an integer ambiguity associated with the first and fourth antennas, an integer ambiguity associated with second and fourth antennas, and an integer ambiguity associated with the third and fourth antennas. The GPS attitude receiver measures phase values for the carrier components of the GPS signals received from each of the antennas at a plurality of measurement epochs during an initialization period and at a measurement epoch after the initialization period. In response to the phase values measured at the measurement epochs during the initialization period, the GPS attitude receiver computes integer ambiguity resolution values representing resolution of the integer ambiguities. Then, in response to the computed integer ambiguity resolution values and the phase value measured at the measurement epoch after the initialization period, it computes values defining the attitude of the moving vehicle at the measurement epoch after the initialization period.

Validation of the United States Marine Corps Qualified Candidate Population Model

DTIC Science & Technology

2003-03-01

time. Fields are created in the database to support this forecasting. User forms and a macro are programmed in Microsoft VBA to develop the...at 0.001. To accomplish 50,000 iterations of a minimization problem, this study wrote a macro in the VBA programming language that guides the solver...success in the commissioning process. **To improve the diagnostics of this propensity model, other factors were considered as well. Applying SQL

Computerized Engineering

NASA Technical Reports Server (NTRS)

1998-01-01

In 1966, MacNeal-Schwendler Corporation (MSC) was awarded a contract by NASA to develop a general purpose structural analysis program dubbed NASTRAN (NASA structural analysis). The first operational version was delivered in 1969. In 1982, MSC procured the rights to market their subsequent version of NASTRAN to industry as a problem solver for applications ranging from acoustics to heat transfer. Known today as MSC/NASTRAN, the program has thousands of users worldwide. NASTRAN is also distributed through COSMIC.

Testing of PVODE, a parallel ODE solver

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

Wittman, M.R.

1996-08-09

The purpose of this paper is to discuss the issues involved with, and the results from, testing of two example programs that use PVODE: pvkx and pvnx. These two programs are intended to provide a template for users for follow when writing their own code. However, we also used them (primarily pvkx) to do performance testing and visualization. This work was done on a Cray T3D, a Sparc 10, and a Sparc 5.

Eigenvalue Solvers for Modeling Nuclear Reactors on Leadership Class Machines

DOE PAGES

Slaybaugh, R. N.; Ramirez-Zweiger, M.; Pandya, Tara; ...

2018-02-20

In this paper, three complementary methods have been implemented in the code Denovo that accelerate neutral particle transport calculations with methods that use leadership-class computers fully and effectively: a multigroup block (MG) Krylov solver, a Rayleigh quotient iteration (RQI) eigenvalue solver, and a multigrid in energy (MGE) preconditioner. The MG Krylov solver converges more quickly than Gauss Seidel and enables energy decomposition such that Denovo can scale to hundreds of thousands of cores. RQI should converge in fewer iterations than power iteration (PI) for large and challenging problems. RQI creates shifted systems that would not be tractable without the MGmore » Krylov solver. It also creates ill-conditioned matrices. The MGE preconditioner reduces iteration count significantly when used with RQI and takes advantage of the new energy decomposition such that it can scale efficiently. Each individual method has been described before, but this is the first time they have been demonstrated to work together effectively. The combination of solvers enables the RQI eigenvalue solver to work better than the other available solvers for large reactors problems on leadership-class machines. Using these methods together, RQI converged in fewer iterations and in less time than PI for a full pressurized water reactor core. These solvers also performed better than an Arnoldi eigenvalue solver for a reactor benchmark problem when energy decomposition is needed. The MG Krylov, MGE preconditioner, and RQI solver combination also scales well in energy. Finally, this solver set is a strong choice for very large and challenging problems.« less

Eigenvalue Solvers for Modeling Nuclear Reactors on Leadership Class Machines

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

Slaybaugh, R. N.; Ramirez-Zweiger, M.; Pandya, Tara

In this paper, three complementary methods have been implemented in the code Denovo that accelerate neutral particle transport calculations with methods that use leadership-class computers fully and effectively: a multigroup block (MG) Krylov solver, a Rayleigh quotient iteration (RQI) eigenvalue solver, and a multigrid in energy (MGE) preconditioner. The MG Krylov solver converges more quickly than Gauss Seidel and enables energy decomposition such that Denovo can scale to hundreds of thousands of cores. RQI should converge in fewer iterations than power iteration (PI) for large and challenging problems. RQI creates shifted systems that would not be tractable without the MGmore » Krylov solver. It also creates ill-conditioned matrices. The MGE preconditioner reduces iteration count significantly when used with RQI and takes advantage of the new energy decomposition such that it can scale efficiently. Each individual method has been described before, but this is the first time they have been demonstrated to work together effectively. The combination of solvers enables the RQI eigenvalue solver to work better than the other available solvers for large reactors problems on leadership-class machines. Using these methods together, RQI converged in fewer iterations and in less time than PI for a full pressurized water reactor core. These solvers also performed better than an Arnoldi eigenvalue solver for a reactor benchmark problem when energy decomposition is needed. The MG Krylov, MGE preconditioner, and RQI solver combination also scales well in energy. Finally, this solver set is a strong choice for very large and challenging problems.« less

General purpose nonlinear system solver based on Newton-Krylov method.

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

2013-12-01

KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation Solvers [1]. KINSOL is a general-purpose nonlinear system solver based on Newton-Krylov and fixed-point solver technologies [2].

Scheduling the resident 80-hour work week: an operations research algorithm.

PubMed

Day, T Eugene; Napoli, Joseph T; Kuo, Paul C

2006-01-01

The resident 80-hour work week requires that programs now schedule duty hours. Typically, scheduling is performed in an empirical "trial-and-error" fashion. However, this is a classic "scheduling" problem from the field of operations research (OR). It is similar to scheduling issues that airlines must face with pilots and planes routing through various airports at various times. The authors hypothesized that an OR approach using iterative computer algorithms could provide a rational scheduling solution. Institution-specific constraints of the residency problem were formulated. A total of 56 residents are rotating through 4 hospitals. Additional constraints were dictated by the Residency Review Committee (RRC) rules or the specific surgical service. For example, at Hospital 1, during the weekday hours between 6 am and 6 pm, there will be a PGY4 or PGY5 and a PGY2 or PGY3 on-duty to cover Service "A." A series of equations and logic statements was generated to satisfy all constraints and requirements. These were restated in the Optimization Programming Language used by the ILOG software suite for solving mixed integer programming problems. An integer programming solution was generated to this resource-constrained assignment problem. A total of 30,900 variables and 12,443 constraints were required. A total of man-hours of programming were used; computer run-time was 25.9 hours. A weekly schedule was generated for each resident that satisfied the RRC regulations while fulfilling all stated surgical service requirements. Each required between 64 and 80 weekly resident duty hours. The authors conclude that OR is a viable approach to schedule resident work hours. This technique is sufficiently robust to accommodate changes in resident numbers, service requirements, and service and hospital rotations.

An HLLC Riemann solver for resistive relativistic magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Miranda-Aranguren, S.; Aloy, M. A.; Rembiasz, T.

2018-05-01

We present a new approximate Riemann solver for the augmented system of equations of resistive relativistic magnetohydrodynamics that belongs to the family of Harten-Lax-van Leer contact wave (HLLC) solvers. In HLLC solvers, the solution is approximated by two constant states flanked by two shocks separated by a contact wave. The accuracy of the new approximate solver is calibrated through 1D and 2D test problems.

A Comparison of Three Navier-Stokes Solvers for Exhaust Nozzle Flowfields

NASA Technical Reports Server (NTRS)

Georgiadis, Nicholas J.; Yoder, Dennis A.; Debonis, James R.

1999-01-01

A comparison of the NPARC, PAB, and WIND (previously known as NASTD) Navier-Stokes solvers is made for two flow cases with turbulent mixing as the dominant flow characteristic, a two-dimensional ejector nozzle and a Mach 1.5 elliptic jet. The objective of the work is to determine if comparable predictions of nozzle flows can be obtained from different Navier-Stokes codes employed in a multiple site research program. A single computational grid was constructed for each of the two flows and used for all of the Navier-Stokes solvers. In addition, similar k-e based turbulence models were employed in each code, and boundary conditions were specified as similarly as possible across the codes. Comparisons of mass flow rates, velocity profiles, and turbulence model quantities are made between the computations and experimental data. The computational cost of obtaining converged solutions with each of the codes is also documented. Results indicate that all of the codes provided similar predictions for the two nozzle flows. Agreement of the Navier-Stokes calculations with experimental data was good for the ejector nozzle. However, for the Mach 1.5 elliptic jet, the calculations were unable to accurately capture the development of the three dimensional elliptic mixing layer.

TADS: A CFD-based turbomachinery and analysis design system with GUI. Volume 1: Method and results

NASA Technical Reports Server (NTRS)

Topp, D. A.; Myers, R. A.; Delaney, R. A.

1995-01-01

The primary objective of this study was the development of a CFD (Computational Fluid Dynamics) based turbomachinery airfoil analysis and design system, controlled by a GUI (Graphical User Interface). The computer codes resulting from this effort are referred to as TADS (Turbomachinery Analysis and Design System). This document is the Final Report describing the theoretical basis and analytical results from the TADS system, developed under Task 18 of NASA Contract NAS3-25950, ADPAC System Coupling to Blade Analysis & Design System GUI. TADS couples a throughflow solver (ADPAC) with a quasi-3D blade-to-blade solver (RVCQ3D) in an interactive package. Throughflow analysis capability was developed in ADPAC through the addition of blade force and blockage terms to the governing equations. A GUI was developed to simplify user input and automate the many tasks required to perform turbomachinery analysis and design. The coupling of the various programs was done in such a way that alternative solvers or grid generators could be easily incorporated into the TADS framework. Results of aerodynamic calculations using the TADS system are presented for a highly loaded fan, a compressor stator, a low speed turbine blade and a transonic turbine vane.

Energy consumption optimization of the total-FETI solver by changing the CPU frequency

NASA Astrophysics Data System (ADS)

Horak, David; Riha, Lubomir; Sojka, Radim; Kruzik, Jakub; Beseda, Martin; Cermak, Martin; Schuchart, Joseph

2017-07-01

The energy consumption of supercomputers is one of the critical problems for the upcoming Exascale supercomputing era. The awareness of power and energy consumption is required on both software and hardware side. This paper deals with the energy consumption evaluation of the Finite Element Tearing and Interconnect (FETI) based solvers of linear systems, which is an established method for solving real-world engineering problems. We have evaluated the effect of the CPU frequency on the energy consumption of the FETI solver using a linear elasticity 3D cube synthetic benchmark. In this problem, we have evaluated the effect of frequency tuning on the energy consumption of the essential processing kernels of the FETI method. The paper provides results for two types of frequency tuning: (1) static tuning and (2) dynamic tuning. For static tuning experiments, the frequency is set before execution and kept constant during the runtime. For dynamic tuning, the frequency is changed during the program execution to adapt the system to the actual needs of the application. The paper shows that static tuning brings up 12% energy savings when compared to default CPU settings (the highest clock rate). The dynamic tuning improves this further by up to 3%.

Large-Eddy Simulation of Subsonic Jets

NASA Astrophysics Data System (ADS)

Vuorinen, Ville; Wehrfritz, Armin; Yu, Jingzhou; Kaario, Ossi; Larmi, Martti; Boersma, Bendiks Jan

2011-12-01

The present study deals with development and validation of a fully explicit, compressible Runge-Kutta-4 (RK4) Navier-Stokes solver in the opensource CFD programming environment OpenFOAM. The background motivation is to shift towards explicit density based solution strategy and thereby avoid using the pressure based algorithms which are currently proposed in the standard OpenFOAM release for Large-Eddy Simulation (LES). This shift is considered necessary in strongly compressible flows when Ma > 0.5. Our application of interest is related to the pre-mixing stage in direct injection gas engines where high injection pressures are typically utilized. First, the developed flow solver is discussed and validated. Then, the implementation of subsonic inflow conditions using a forcing region in combination with a simplified nozzle geometry is discussed and validated. After this, LES of mixing in compressible, round jets at Ma = 0.3, 0.5 and 0.65 are carried out. Respectively, the Reynolds numbers of the jets correspond to Re = 6000, 10000 and 13000. Results for two meshes are presented. The results imply that the present solver produces turbulent structures, resolves a range of turbulent eddy frequencies and gives also mesh independent results within satisfactory limits for mean flow and turbulence statistics.

An Overview of Ares-I CFD Ascent Aerodynamic Data Development And Analysis Based on USM3D

NASA Technical Reports Server (NTRS)

Abdol-Hamid, Khaled S.; Ghaffari, Farhad; Parlette, Edward B.

2011-01-01

An overview of the computational results obtained from the NASA Langley developed unstructured grid, Reynolds-averaged Navier-Stokes flow solver USM3D, in support of the Ares-I project within the NASA s Constellation program, are presented. The numerical data are obtained for representative flow conditions pertinent to the ascent phase of the trajectory at both wind tunnel and flight Reynolds number without including any propulsion effects. The USM3D flow solver has been designated to have the primary role within the Ares-I project in developing the computational aerodynamic data for the vehicle while other flow solvers, namely OVERFLOW and FUN3D, have supporting roles to provide complementary results for fewer cases as part of the verification process to ensure code-to-code solution consistency. Similarly, as part of the solution validation efforts, the predicted numerical results are correlated with the aerodynamic wind tunnel data that have been generated within the project in the past few years. Sample aerodynamic results and the processes established for the computational solution/data development for the evolving Ares-I design cycles are presented.

Fuel Optimal, Finite Thrust Guidance Methods to Circumnavigate with Lighting Constraints

NASA Astrophysics Data System (ADS)

Prince, E. R.; Carr, R. W.; Cobb, R. G.

This paper details improvements made to the authors' most recent work to find fuel optimal, finite-thrust guidance to inject an inspector satellite into a prescribed natural motion circumnavigation (NMC) orbit about a resident space object (RSO) in geosynchronous orbit (GEO). Better initial guess methodologies are developed for the low-fidelity model nonlinear programming problem (NLP) solver to include using Clohessy- Wiltshire (CW) targeting, a modified particle swarm optimization (PSO), and MATLAB's genetic algorithm (GA). These initial guess solutions may then be fed into the NLP solver as an initial guess, where a different NLP solver, IPOPT, is used. Celestial lighting constraints are taken into account in addition to the sunlight constraint, ensuring that the resulting NMC also adheres to Moon and Earth lighting constraints. The guidance is initially calculated given a fixed final time, and then solutions are also calculated for fixed final times before and after the original fixed final time, allowing mission planners to choose the lowest-cost solution in the resulting range which satisfies all constraints. The developed algorithms provide computationally fast and highly reliable methods for determining fuel optimal guidance for NMC injections while also adhering to multiple lighting constraints.

A simple GPU-accelerated two-dimensional MUSCL-Hancock solver for ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Bard, Christopher M.; Dorelli, John C.

2014-02-01

We describe our experience using NVIDIA's CUDA (Compute Unified Device Architecture) C programming environment to implement a two-dimensional second-order MUSCL-Hancock ideal magnetohydrodynamics (MHD) solver on a GTX 480 Graphics Processing Unit (GPU). Taking a simple approach in which the MHD variables are stored exclusively in the global memory of the GTX 480 and accessed in a cache-friendly manner (without further optimizing memory access by, for example, staging data in the GPU's faster shared memory), we achieved a maximum speed-up of ≈126 for a 10242 grid relative to the sequential C code running on a single Intel Nehalem (2.8 GHz) core. This speedup is consistent with simple estimates based on the known floating point performance, memory throughput and parallel processing capacity of the GTX 480.

SMITHERS: An object-oriented modular mapping methodology for MCNP-based neutronic–thermal hydraulic multiphysics

DOE PAGES

Richard, Joshua; Galloway, Jack; Fensin, Michael; ...

2015-04-04

A novel object-oriented modular mapping methodology for externally coupled neutronics–thermal hydraulics multiphysics simulations was developed. The Simulator using MCNP with Integrated Thermal-Hydraulics for Exploratory Reactor Studies (SMITHERS) code performs on-the-fly mapping of material-wise power distribution tallies implemented by MCNP-based neutron transport/depletion solvers for use in estimating coolant temperature and density distributions with a separate thermal-hydraulic solver. The key development of SMITHERS is that it reconstructs the hierarchical geometry structure of the material-wise power generation tallies from the depletion solver automatically, with only a modicum of additional information required from the user. In addition, it performs the basis mapping from themore » combinatorial geometry of the depletion solver to the required geometry of the thermal-hydraulic solver in a generalizable manner, such that it can transparently accommodate varying levels of thermal-hydraulic solver geometric fidelity, from the nodal geometry of multi-channel analysis solvers to the pin-cell level of discretization for sub-channel analysis solvers.« less

Dynamic Distributed Cooperative Control of Multiple Heterogeneous Resources

DTIC Science & Technology

2012-10-01

of the UAVs to maximize the total sensor footprint over the region of interest. The algorithm utilized to solve this problem was based on sampling a...and moving obstacles. Obstacle positions were assumed known a priori. Kingston and Beard [22] presented an algorithm to keep moving UAVs equally spaced...Planning Algorithms , Cambridge University Press, 2006. 11. Ma, C. S. and Miller, R. H., “Mixed integer linear programming trajectory generation for

An Advanced Tabu Search Approach to Solving the Mixed Payload Airlift Load Planning Problem

DTIC Science & Technology

2009-03-01

cargo, and the problem therefore becomes trivial. 3. Shoring: Some cargo requires shoring which is small planks of plywood stacked on top of each...Integer Programming Method In 1989, Kevin Ng examined the bin-packing MPALP for Canada’s C-130 aircraft (Ng 1992). His goal was to move a set of... leadership & ethics [ ] warfighting [ ] international security [ ] doctrine [X] other (specify): Military Airlift

Optimal Partitioning of a Surveillance Space for Persistent Coverage Using Multiple Autonomous Unmanned Aerial Vehicles: An Integer Programming Approach

DTIC Science & Technology

2014-03-27

asymptotically equal. Carlsson shows that the problem is solved by treating each subregion Ri as a traveling salesman problem (TSP) with a set of points that...terminal state to the goal. If no- travel zones are repre- sented as the union of regions Akx > Bk, the coverage problem can be expressed as an IP [14...3 1.2 Problem Statement

Optimized Waterspace Management and Scheduling Using Mixed-Integer Linear Programming

DTIC Science & Technology

2016-01-01

Complete [30]. Proposition 4.1 satisfies the first criterion. For the second criterion, we will use the Traveling Salesman Problem (TSP), which has been...A branch and cut algorithm for the symmetric generalized traveling salesman problem , Operations Research 45 (1997) 378–394. [33] J. Silberholz, B...Golden, The generalized traveling salesman problem : A new genetic algorithm ap- proach, Extended Horizons: Advances in Computing, Optimization, and

Uncluttered Single-Image Visualization of Vascular Structures using GPU and Integer Programming

PubMed Central

Won, Joong-Ho; Jeon, Yongkweon; Rosenberg, Jarrett; Yoon, Sungroh; Rubin, Geoffrey D.; Napel, Sandy

2013-01-01

Direct projection of three-dimensional branching structures, such as networks of cables, blood vessels, or neurons onto a 2D image creates the illusion of intersecting structural parts and creates challenges for understanding and communication. We present a method for visualizing such structures, and demonstrate its utility in visualizing the abdominal aorta and its branches, whose tomographic images might be obtained by computed tomography or magnetic resonance angiography, in a single two-dimensional stylistic image, without overlaps among branches. The visualization method, termed uncluttered single-image visualization (USIV), involves optimization of geometry. This paper proposes a novel optimization technique that utilizes an interesting connection of the optimization problem regarding USIV to the protein structure prediction problem. Adopting the integer linear programming-based formulation for the protein structure prediction problem, we tested the proposed technique using 30 visualizations produced from five patient scans with representative anatomical variants in the abdominal aortic vessel tree. The novel technique can exploit commodity-level parallelism, enabling use of general-purpose graphics processing unit (GPGPU) technology that yields a significant speedup. Comparison of the results with the other optimization technique previously reported elsewhere suggests that, in most aspects, the quality of the visualization is comparable to that of the previous one, with a significant gain in the computation time of the algorithm. PMID:22291148

An integer programming formulation of the parsimonious loss of heterozygosity problem.

PubMed

Catanzaro, Daniele; Labbé, Martine; Halldórsson, Bjarni V

2013-01-01

A loss of heterozygosity (LOH) event occurs when, by the laws of Mendelian inheritance, an individual should be heterozygote at a given site but, due to a deletion polymorphism, is not. Deletions play an important role in human disease and their detection could provide fundamental insights for the development of new diagnostics and treatments. In this paper, we investigate the parsimonious loss of heterozygosity problem (PLOHP), i.e., the problem of partitioning suspected polymorphisms from a set of individuals into a minimum number of deletion areas. Specifically, we generalize Halldórsson et al.'s work by providing a more general formulation of the PLOHP and by showing how one can incorporate different recombination rates and prior knowledge about the locations of deletions. Moreover, we show that the PLOHP can be formulated as a specific version of the clique partition problem in a particular class of graphs called undirected catch-point interval graphs and we prove its general $({\\cal NP})$-hardness. Finally, we provide a state-of-the-art integer programming (IP) formulation and strengthening valid inequalities to exactly solve real instances of the PLOHP containing up to 9,000 individuals and 3,000 SNPs. Our results give perspectives on the mathematics of the PLOHP and suggest new directions on the development of future efficient exact solution approaches.

Automatic design of synthetic gene circuits through mixed integer non-linear programming.

PubMed

Huynh, Linh; Kececioglu, John; Köppe, Matthias; Tagkopoulos, Ilias

2012-01-01

Automatic design of synthetic gene circuits poses a significant challenge to synthetic biology, primarily due to the complexity of biological systems, and the lack of rigorous optimization methods that can cope with the combinatorial explosion as the number of biological parts increases. Current optimization methods for synthetic gene design rely on heuristic algorithms that are usually not deterministic, deliver sub-optimal solutions, and provide no guaranties on convergence or error bounds. Here, we introduce an optimization framework for the problem of part selection in synthetic gene circuits that is based on mixed integer non-linear programming (MINLP), which is a deterministic method that finds the globally optimal solution and guarantees convergence in finite time. Given a synthetic gene circuit, a library of characterized parts, and user-defined constraints, our method can find the optimal selection of parts that satisfy the constraints and best approximates the objective function given by the user. We evaluated the proposed method in the design of three synthetic circuits (a toggle switch, a transcriptional cascade, and a band detector), with both experimentally constructed and synthetic promoter libraries. Scalability and robustness analysis shows that the proposed framework scales well with the library size and the solution space. The work described here is a step towards a unifying, realistic framework for the automated design of biological circuits.

Predicting protein contact map using evolutionary and physical constraints by integer programming.

PubMed

Wang, Zhiyong; Xu, Jinbo

2013-07-01

Protein contact map describes the pairwise spatial and functional relationship of residues in a protein and contains key information for protein 3D structure prediction. Although studied extensively, it remains challenging to predict contact map using only sequence information. Most existing methods predict the contact map matrix element-by-element, ignoring correlation among contacts and physical feasibility of the whole-contact map. A couple of recent methods predict contact map by using mutual information, taking into consideration contact correlation and enforcing a sparsity restraint, but these methods demand for a very large number of sequence homologs for the protein under consideration and the resultant contact map may be still physically infeasible. This article presents a novel method PhyCMAP for contact map prediction, integrating both evolutionary and physical restraints by machine learning and integer linear programming. The evolutionary restraints are much more informative than mutual information, and the physical restraints specify more concrete relationship among contacts than the sparsity restraint. As such, our method greatly reduces the solution space of the contact map matrix and, thus, significantly improves prediction accuracy. Experimental results confirm that PhyCMAP outperforms currently popular methods no matter how many sequence homologs are available for the protein under consideration. http://raptorx.uchicago.edu.

Variational calculation of second-order reduced density matrices by strong N-representability conditions and an accurate semidefinite programming solver.

PubMed

Nakata, Maho; Braams, Bastiaan J; Fujisawa, Katsuki; Fukuda, Mituhiro; Percus, Jerome K; Yamashita, Makoto; Zhao, Zhengji

2008-04-28

The reduced density matrix (RDM) method, which is a variational calculation based on the second-order reduced density matrix, is applied to the ground state energies and the dipole moments for 57 different states of atoms, molecules, and to the ground state energies and the elements of 2-RDM for the Hubbard model. We explore the well-known N-representability conditions (P, Q, and G) together with the more recent and much stronger T1 and T2(') conditions. T2(') condition was recently rederived and it implies T2 condition. Using these N-representability conditions, we can usually calculate correlation energies in percentage ranging from 100% to 101%, whose accuracy is similar to CCSD(T) and even better for high spin states or anion systems where CCSD(T) fails. Highly accurate calculations are carried out by handling equality constraints and/or developing multiple precision arithmetic in the semidefinite programming (SDP) solver. Results show that handling equality constraints correctly improves the accuracy from 0.1 to 0.6 mhartree. Additionally, improvements by replacing T2 condition with T2(') condition are typically of 0.1-0.5 mhartree. The newly developed multiple precision arithmetic version of SDP solver calculates extraordinary accurate energies for the one dimensional Hubbard model and Be atom. It gives at least 16 significant digits for energies, where double precision calculations gives only two to eight digits. It also provides physically meaningful results for the Hubbard model in the high correlation limit.

FoSSI: the family of simplified solver interfaces for the rapid development of parallel numerical atmosphere and ocean models

NASA Astrophysics Data System (ADS)

Frickenhaus, Stephan; Hiller, Wolfgang; Best, Meike

The portable software FoSSI is introduced that—in combination with additional free solver software packages—allows for an efficient and scalable parallel solution of large sparse linear equations systems arising in finite element model codes. FoSSI is intended to support rapid model code development, completely hiding the complexity of the underlying solver packages. In particular, the model developer need not be an expert in parallelization and is yet free to switch between different solver packages by simple modifications of the interface call. FoSSI offers an efficient and easy, yet flexible interface to several parallel solvers, most of them available on the web, such as PETSC, AZTEC, MUMPS, PILUT and HYPRE. FoSSI makes use of the concept of handles for vectors, matrices, preconditioners and solvers, that is frequently used in solver libraries. Hence, FoSSI allows for a flexible treatment of several linear equations systems and associated preconditioners at the same time, even in parallel on separate MPI-communicators. The second special feature in FoSSI is the task specifier, being a combination of keywords, each configuring a certain phase in the solver setup. This enables the user to control a solver over one unique subroutine. Furthermore, FoSSI has rather similar features for all solvers, making a fast solver intercomparison or exchange an easy task. FoSSI is a community software, proven in an adaptive 2D-atmosphere model and a 3D-primitive equation ocean model, both formulated in finite elements. The present paper discusses perspectives of an OpenMP-implementation of parallel iterative solvers based on domain decomposition methods. This approach to OpenMP solvers is rather attractive, as the code for domain-local operations of factorization, preconditioning and matrix-vector product can be readily taken from a sequential implementation that is also suitable to be used in an MPI-variant. Code development in this direction is in an advanced state under the name ScOPES: the Scalable Open Parallel sparse linear Equations Solver.

The whole number axis integer linear transformation reversible information hiding algorithm on wavelet domain

NASA Astrophysics Data System (ADS)

Jiang, Zhuo; Xie, Chengjun

2013-12-01

This paper improved the algorithm of reversible integer linear transform on finite interval [0,255], which can realize reversible integer linear transform in whole number axis shielding data LSB (least significant bit). Firstly, this method use integer wavelet transformation based on lifting scheme to transform the original image, and select the transformed high frequency areas as information hiding area, meanwhile transform the high frequency coefficients blocks in integer linear way and embed the secret information in LSB of each coefficient, then information hiding by embedding the opposite steps. To extract data bits and recover the host image, a similar reverse procedure can be conducted, and the original host image can be lossless recovered. The simulation experimental results show that this method has good secrecy and concealment, after conducted the CDF (m, n) and DD (m, n) series of wavelet transformed. This method can be applied to information security domain, such as medicine, law and military.

Extending substructure based iterative solvers to multiple load and repeated analyses

NASA Technical Reports Server (NTRS)

Farhat, Charbel

1993-01-01

Direct solvers currently dominate commercial finite element structural software, but do not scale well in the fine granularity regime targeted by emerging parallel processors. Substructure based iterative solvers--often called also domain decomposition algorithms--lend themselves better to parallel processing, but must overcome several obstacles before earning their place in general purpose structural analysis programs. One such obstacle is the solution of systems with many or repeated right hand sides. Such systems arise, for example, in multiple load static analyses and in implicit linear dynamics computations. Direct solvers are well-suited for these problems because after the system matrix has been factored, the multiple or repeated solutions can be obtained through relatively inexpensive forward and backward substitutions. On the other hand, iterative solvers in general are ill-suited for these problems because they often must restart from scratch for every different right hand side. In this paper, we present a methodology for extending the range of applications of domain decomposition methods to problems with multiple or repeated right hand sides. Basically, we formulate the overall problem as a series of minimization problems over K-orthogonal and supplementary subspaces, and tailor the preconditioned conjugate gradient algorithm to solve them efficiently. The resulting solution method is scalable, whereas direct factorization schemes and forward and backward substitution algorithms are not. We illustrate the proposed methodology with the solution of static and dynamic structural problems, and highlight its potential to outperform forward and backward substitutions on parallel computers. As an example, we show that for a linear structural dynamics problem with 11640 degrees of freedom, every time-step beyond time-step 15 is solved in a single iteration and consumes 1.0 second on a 32 processor iPSC-860 system; for the same problem and the same parallel processor, a pair of forward/backward substitutions at each step consumes 15.0 seconds.

A GA based penalty function technique for solving constrained redundancy allocation problem of series system with interval valued reliability of components

NASA Astrophysics Data System (ADS)

Gupta, R. K.; Bhunia, A. K.; Roy, D.

2009-10-01

In this paper, we have considered the problem of constrained redundancy allocation of series system with interval valued reliability of components. For maximizing the overall system reliability under limited resource constraints, the problem is formulated as an unconstrained integer programming problem with interval coefficients by penalty function technique and solved by an advanced GA for integer variables with interval fitness function, tournament selection, uniform crossover, uniform mutation and elitism. As a special case, considering the lower and upper bounds of the interval valued reliabilities of the components to be the same, the corresponding problem has been solved. The model has been illustrated with some numerical examples and the results of the series redundancy allocation problem with fixed value of reliability of the components have been compared with the existing results available in the literature. Finally, sensitivity analyses have been shown graphically to study the stability of our developed GA with respect to the different GA parameters.

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

NASA Astrophysics Data System (ADS)

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

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

Java Programming Language

NASA Technical Reports Server (NTRS)

Shaykhian, Gholam Ali

2007-01-01

The Java seminar covers the fundamentals of Java programming language. No prior programming experience is required for participation in the seminar. The first part of the seminar covers introductory concepts in Java programming including data types (integer, character, ..), operators, functions and constants, casts, input, output, control flow, scope, conditional statements, and arrays. Furthermore, introduction to Object-Oriented programming in Java, relationships between classes, using packages, constructors, private data and methods, final instance fields, static fields and methods, and overloading are explained. The second part of the seminar covers extending classes, inheritance hierarchies, polymorphism, dynamic binding, abstract classes, protected access. The seminar conclude by introducing interfaces, properties of interfaces, interfaces and abstract classes, interfaces and cailbacks, basics of event handling, user interface components with swing, applet basics, converting applications to applets, the applet HTML tags and attributes, exceptions and debugging.

Edgelist phase unwrapping algorithm for time series InSAR analysis.

PubMed

Shanker, A Piyush; Zebker, Howard

2010-03-01

We present here a new integer programming formulation for phase unwrapping of multidimensional data. Phase unwrapping is a key problem in many coherent imaging systems, including time series synthetic aperture radar interferometry (InSAR), with two spatial and one temporal data dimensions. The minimum cost flow (MCF) [IEEE Trans. Geosci. Remote Sens. 36, 813 (1998)] phase unwrapping algorithm describes a global cost minimization problem involving flow between phase residues computed over closed loops. Here we replace closed loops by reliable edges as the basic construct, thus leading to the name "edgelist." Our algorithm has several advantages over current methods-it simplifies the representation of multidimensional phase unwrapping, it incorporates data from external sources, such as GPS, where available to better constrain the unwrapped solution, and it treats regularly sampled or sparsely sampled data alike. It thus is particularly applicable to time series InSAR, where data are often irregularly spaced in time and individual interferograms can be corrupted with large decorrelated regions. We show that, similar to the MCF network problem, the edgelist formulation also exhibits total unimodularity, which enables us to solve the integer program problem by using efficient linear programming tools. We apply our method to a persistent scatterer-InSAR data set from the creeping section of the Central San Andreas Fault and find that the average creep rate of 22 mm/Yr is constant within 3 mm/Yr over 1992-2004 but varies systematically with ground location, with a slightly higher rate in 1992-1998 than in 1999-2003.

Introducing difference recurrence relations for faster semi-global alignment of long sequences.

PubMed

Suzuki, Hajime; Kasahara, Masahiro

2018-02-19

The read length of single-molecule DNA sequencers is reaching 1 Mb. Popular alignment software tools widely used for analyzing such long reads often take advantage of single-instruction multiple-data (SIMD) operations to accelerate calculation of dynamic programming (DP) matrices in the Smith-Waterman-Gotoh (SWG) algorithm with a fixed alignment start position at the origin. Nonetheless, 16-bit or 32-bit integers are necessary for storing the values in a DP matrix when sequences to be aligned are long; this situation hampers the use of the full SIMD width of modern processors. We proposed a faster semi-global alignment algorithm, "difference recurrence relations," that runs more rapidly than the state-of-the-art algorithm by a factor of 2.1. Instead of calculating and storing all the values in a DP matrix directly, our algorithm computes and stores mainly the differences between the values of adjacent cells in the matrix. Although the SWG algorithm and our algorithm can output exactly the same result, our algorithm mainly involves 8-bit integer operations, enabling us to exploit the full width of SIMD operations (e.g., 32) on modern processors. We also developed a library, libgaba, so that developers can easily integrate our algorithm into alignment programs. Our novel algorithm and optimized library implementation will facilitate accelerating nucleotide long-read analysis algorithms that use pairwise alignment stages. The library is implemented in the C programming language and available at https://github.com/ocxtal/libgaba .