Showing papers on "Discrete optimization published in 2000"

Nested Partitions Method for Global Optimization

Abstract: We propose a new randomized method for solving global optimization problems. This method, the Nested Partitions (NP) method, systematically partitions the feasible region and concentrates the search in regions that are the most promising. The most promising region is selected in each iteration based on information obtained from random sampling of the entire feasible region and local search. The method hence combines global and local search. We first develop the method for discrete problems and then show that the method can be extended to continuous global optimization. The method is shown to converge with probability one to a global optimum in finite time. In addition, we provide bounds on the expected number of iterations required for convergence, and we suggest two stopping criteria. Numerical examples are also presented to demonstrate the effectiveness of the method.

A survey of simulation optimization techniques and procedures

Abstract: Discrete event simulation optimization is a problem of significant interest to practitioners interested in extracting useful information about an actual (or yet to be designed) system that can be modeled using discrete event simulation. This paper presents a brief survey of the literature on discrete event simulation optimization over the past decade (1988 to the present). Swisher et al. (2000) provides a more comprehensive review of this topic while Jacobson and Schruben (1989) covers the literature preceding 1988. Optimization of both discrete and continuous input parameters are examined. The continuous input parameter case is separated into gradient and non-gradient based optimization procedures. The discrete input parameter case differentiates techniques appropriate for small and for large numbers of feasible input parameter values.

Optimal Reliability Design: Fundamentals and Applications

Abstract: List of figures List of tables Preface Acknowledgments 1 Introduction to reliability systems 2 Analysis and classification of reliability optimization models 3 Redundancy allocation by heuristic methods 4 Redundancy allocation by dynamic programming 5 Redundancy allocation by discrete optimization methods 6 Reliability optimization by nonlinear programming 7 Metaheuristic algorithms for optimization in reliability systems 8 Reliability-redundancy allocation 9 Component assignment in reliability systems 10 Reliability systems with multiple objectives 11 Other methods for system-reliability optimization 12 Burn-in optimization under limited capacity 13 Case study on design for software reliability optimization 14 Case study on an optimal scheduled-maintenance policy 15 Case studies on reliability optimization Appendices References Index

Fuzzy Discrete Multicriteria Cost Optimization of Steel Structures

Abstract: Only a small fraction of the hundreds of papers published on optimization of steel structures deal with cost optimization; the great majority deal only with minimization of the weight of the structure. Those few that are concerned with cost optimization deal with small two-dimensional or academic examples. In this article, the writers present a fuzzy discrete multicriteria cost optimization model for design of space steel structures subjected to the actual constraints of commonly-used design codes such as the AISC ASD code by considering three design criteria: (1) minimum material cost; (2) minimum weight; and (3) minimum number of different section types. The computational model starts with a continuous-variable minimum weight solution with a preemptive constraint violation strategy as the lower bound followed by a fuzzy discrete multicriteria optimization. It is concluded that solving the structural design problem as a cost optimization problem can result in substantial cost savings compared with the tr...

Computing efforts allocation for ordinal optimization and discrete event simulation

Abstract: Ordinal optimization has emerged as an efficient technique for simulation and optimization. Exponential convergence rates can be achieved in many cases. In this paper, we present a new approach that can further enhance the efficiency of ordinal optimization. Our approach intelligently determines the optimal number of simulation replications (or samples) and significantly reduces the total simulation cost. Numerical illustrations are included. The results indicate that our approach can obtain an additional 74% computation time reduction above and beyond the reduction obtained through the use of ordinal optimization for a 10-design example.

A multigrid approach to the optimization of systems governed by differential equations

Abstract: We consider the optimization of systems governed by differential equations. In such problems, one has a set of design variables along with a set of state variables, the two sets of variables being related through a set of differential equation constraints. The overall computational cost of optimization is determined by the level of discretizatio n used to numerically solve the governing differential equations. If a fine discretization is used, one expects a greater degree of physical and mathematical fidelity to the problem under consideration, but the large number of state variables can make the cost of optimization prohibitive. We present here a multigrid algorithm that uses solutions to optimization problems based on coarser discretizations, which are less expensive to compute, in a systematic manner to help us obtain the solution of the optimization problem based on a finer discretization. Of interest is the fact that the approach is applicable in situations where multigrid applied only to the solution of the differential equation might not be applicable or effective. We give evidence (both theoretical and numerical) that a multigrid approach can often be successful in the more general setting of optimization.

Simulation optimization: a survey of simulation optimization techniques and procedures

Abstract: Discrete-event simulation optimization is a problem of significant interest to practitioners interested in extracting useful information about an actual (or yet to be designed) system that can be modeled using discrete-event simulation. This paper presents a brief survey of the literature on discrete-event simulation optimization over the past decade (1988 to the present). Swisher et al. (2000) provides a more comprehensive review of this topic while Jacobson and Schruben (1989) covers the literature preceding 1988. Optimization of both discrete and continuous input parameters are examined herein. The continuous input parameter case is separated into gradient and non-gradient based optimization procedures. The discrete input parameter case differentiates techniques appropriate for small and for large numbers of feasible input parameter values.

Constrained Discounted Markov Decision Processes and Hamiltonian Cycles

Abstract: This paper establishes new links between stochastic and discrete optimization. We consider the following three problems for discrete time Markov Decision Processes with finite states and action sets: i find an optimal deterministic policy for a discounted problem with constraints, ii find an optimal stationary policy for a weighted discounted problem with constraints, iii find an optimal deterministic policy for a weighted discounted problem with constraints. We formulate mathematical programs for problems i--iii and show that the Hamiltonian Cycle Problem is a special case of each of these problems. Therefore problems i--iii are NP-hard. We also provide new mathematical programming formulations for the Hamiltonian Cycle and Traveling Salesman Problems.

Supply-Chain Analysis at Volkswagen of America

Abstract: In 1995, Volkswagen of America began a review of its vehicle-distribution system looking for opportunities to improve customer responsiveness and simultaneously reduce system costs. An analytical tool was required to evaluate alternative designs in terms of cost and customer service level, both of which are functions of probabilistic and dynamic elements. These elements include inventory policies, demand seasonality and volume, customer-choice patterns, and transportation delays. By using an innovative combination of simulation and discrete optimization models, we addressed the problem of analyzing a large number of alternatives efficiently. Our analysis indicated opportunities for significant savings in estimated annual transportation costs, and it provided insights on how to implement the proposed system.

On the core of ordered submodular cost games

Abstract: A general ordertheoretic linear programming model for the study of matroid-type greedy algorithms is introduced. The primal restrictions are given by so-called weakly increasing submodular functions on antichains. The LP-dual is solved by a Monge-type greedy algorithm. The model offers a direct combinatorial explanation for many integrality results in discrete optimization. In particular, the submodular intersection theorem of Edmonds and Giles is seen to extend to the case with a rooted forest as underlying structure. The core of associated polyhedra is introduced and applications to the existence of the core in cooperative game theory are discussed.

A New Algorithm for Stochastic Discrete Resource AllocationOptimization

Abstract: Stochastic discrete resource allocation problems are difficult to solve. In this paper, we propose a new algorithm designed specifically to tackle them. The algorithm combines with the Nested Partitions method, the Ordinal Optimization techniques, and an efficient simulation control technique. The resulting hybrid algorithm retains the global perspective of the Nested Partitions method and the fast convergence properties of the Ordinal Optimization. Numerical results demonstrate that the hybrid algorithm can be effectively used for many large-scale stochastic discrete optimization problems.

Methods for Discrete Variable Structural Optimization

Abstract: Discrete design variables are encountered in most practical design applications. An overview of the optimization methods that can treat such design variables in their solution process is presented. Many times selection of an appropriate method depends on type of discrete variables and problem functions. Therefore, discrete design variable problems are classified into six different types. Methods suitable for each problem type are identified. Some recent applications of discrete variable optimization methods are described. Methods for structural optimization with available sections are discussed.

COPS: Large-scale nonlinearly constrained optimization problems

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

A general parallel simulated annealing library and its application in airline industry

Abstract: To solve real-world discrete optimization problems approximately metaheuristics such as simulated annealing and other local search methods are commonly used. For large instances of these problems or those with a lot of hard constraints even fast heuristics require a considerable amount of computational time. At the same time, especially for sensitivity analyses, fast response times are necessary in real-world applications. Therefore, to speed up the computation a parallelization of metaheuristics is very desirable. We present parSA, an object-oriented simulated annealing library based on C++ and using the MPI message passing interface. It provides an automatic, transparent way of parallelizing simulated annealing. The efficient communication in parSA is the main reason for its success in several real-world applications. To demonstrate performance of parSA we address the weekly fleet assignment problem (FAP) as a real-world application. It is one of the optimization problems which occur in the process of operating an airline. Given a flight schedule and aircraft of different types (subfleets), to each flight leg a subfleet has to be assigned. Large real-world instances have been provided by internationally operating airlines. We show that our heuristic approach using our library parSA is very competitive to the commonly used integer-program (IF) approach.

A Set of Examples of Global and Discrete Optimization: Applications of Bayesian Heuristic Approach

Abstract: The following topics are important teaching operation research: games theory, decision theory, utility theory, queuing theory, scheduling theory, discrete opti­ mization. These topics are illustrated and the connection with global optimization is shown considering the following mathematical models: - competition model with fixed resource prices, Nash equilibrium, - competition model with free resource prices, Walras equilibrium, - inspector's problem, multi-stage game model, - "Star War" problem, differential game model, - "Portfolio" problem, resource investment model, - exchange rate prediction, Auto-Regression-Moving-Average (ARMA) model, - optimal scheduling, Bayesian heuristic model, - "Bride's" problem, sequential statistical decisions model. The first seven models are solved using a set of algorithms of continuous global and stochastic optimization. The global optimization software GM (see (19)) is used. The underlying theory of this software and algorithms of solution are described in (19, 17). The last model is an example of stochastic dynamic programming. For better understanding, all the models are formulated in simplest terms as "class­ room" examples. However, each of these models can be regarded as simple representations of important families of real-life problems. Therefore the models and solution algorithms may be of interest for application experts, too. The paper is split into two parts. In the part one (18) the first five models are de­ scribed. In this part the rest three models and accompanyiing software are considered.

Global Optimization Problems in Optimal Design of Experiments in Regression Models

Abstract: In this paper we show that optimal design of experiments, a specific topic in statistics, constitutes a challenging application field for global optimization. This paper shows how various structures in optimal design of experiments problems determine the structure of corresponding challenging global optimization problems. Three different kinds of experimental designs are discussed: discrete designs, exact designs and replicationfree designs. Finding optimal designs for these three concepts involves different optimization problems.

Dual methods for discrete structural optimization problems

Abstract: The purpose of this paper is to present a mathematical programming method developed to solve structural optimization problems involving discrete variables. We work in the following context: the structural responses are computed by the finite elements method and convex and separable approximation schemes are used to generate a sequence of explicit approximate subproblems.Each of them is solved in the dual space with a subgradient-based algorithm (or with a variant of it) specially developed to maximize the not everywhere differentiable dual function. To show that the application field is large, the presented applications are issued from different domains of structural design, such as sizing of thin-walled structures, geometrical configuration of trusses, topology optimization of membrane or 3-D structures and welding points numbering in car bodies. The main drawback of using the dual approach is that the obtained solution is generally not the global optimum. This is linked to the presence of a duality gap, due to the non-convexity of the primal discrete subproblems. Fortunately, this gap can be quantified: a maximum bound on its value can be computed. Moreover, it turns out that the duality gap is decreasing for higher number of variables; the maximum bound on the duality gap is generally negligible in the treated applications. The developed algorithms are very efficient for 2-D and 3-D topology optimization, where applications involving thousands of binary design variables are solved in a very short time. Copyright © 2000 John Wiley & Sons, Ltd.

Two-level optimization of airframe structures using response surface approximation

Abstract: In this paper, a two-level optimization approach is developed for the preliminary and conceptual design of airframe structures. The preliminary design, involving a single objective multidisciplinary optimization, constitutes the lower level where ASTROS (Automated STRuctural Optimization System) is employed for multidisciplinary optimization. The conceptual design, which is carried out at the upper level, aims mainly at configuration design. The multiple objectives are incorporated as a single objective function by using the K-S function formulation. The objective function and constraints at the upper level are modelled through response surface approximation. During the upper level optimization process, the branch and bound method is applied for solving the problem with discrete design variables. The proposed strategy is demonstrated by the optimization of an Intermediate Complexity Wing (ICW) model.

Discrete Hamiltonian Analysis of Endoreversible Thermal Cascades

Abstract: Endoreversible multistage processes which yield mechanical work are optimized by a relatively little-known discrete maximum principle of Pontryagin’s type. A discrete optimization approach extends the classical method, well known for continuous systems in which a Hamiltonian is maximized with respect to controls. Equations of dynamics which follow from energy balance and transfer equations are difference constraints for optimizing work. Irreversibilites caused by the energy transport are essential. Variation of efficiency is analyzed in terms of the heat flux. Enhanced bounds for the work released from an engine system or added to a heat-pump system are evaluated. Lagrangians of work functionals, canonical equations, and structure of the Hamiltonian function are all discrete characteristics which reach their continuous conterparts in the limit of an infinite number of stages. For a finite-time passage of a resource fluid between two given temperatures, optimality of an irreversible process manifests itself as a connection between the process duration and an optimal intensity expressed in terms of the Hamiltonian. Extremal performance functions that describe extremal work are found in terms of final states, process duration, and number of stages. A discrete extension of classical thermal exergy to systems with a finite number of stages and a finite holdup time of a resource fluid is one of the main results. This extended exergy, that has an irreversible component, simplifies to the classical thermal exergy in the limit of infinite duration and an infinite number of stages. The extended exergy exhibits a hysteretic property as a decrease of maximum work received from a multistage engine system and an increase of minimum work added to a heat-pump system, two properties which are particularly important in high-rate regimes.

Optimization of composite laminates with cutouts using genetic algorithm, variable metric and complex search methods

Abstract: Optimization of composite laminates with cutouts is a complex problem, involving non-differentiable objective function and constraints. Choice of the optimization method is generally based on the nature and complexity of the objective function, constraints and how easily and/or accurately the first derivatives can be found. Many researchers have attempted and applied different classical optimization techniques for non-convex optimization problems. This paper clearly brings out the advantages of a non-traditional optimization method-Genetic algorithm (GA) over conventional techniques, the limitations of conventional techniques and GA's ability to approach the global optimum in an n-dimensional search space, for composite laminates.