Showing papers on "Discrete optimization published in 1998"

Handbook of Combinatorial Optimization

Abstract: A Unified Approach for Domination Problems on Different Network Topologies Advanced Techniques for Dynamic Programming Advances in Group Testing Advances in Scheduling Problems Algebrization and Randomization Methods Algorithmic Aspects of Domination in Graphs Algorithms and Metaheuristics for Combinatorial Matrices Algorithms for the Satisfiability Problem Bin Packing Approximation Algorithms: Survey and Classification Binary Unconstrained Quadratic Optimization Problem Combinatorial Optimization Algorithms for Probe Design and Selection Problems Combinatorial Optimization in Data Mining Combinatorial Optimization Techniques for Network-based Data Mining Combinatorial Optimization Techniques in Transportation and Logistic Networks Complexity Issues on PTAS Computing Distances between Evolutionary Trees Connected Dominating Set in Wireless Networks Connections between Continuous and Discrete Extremum Problems, Generalized Systems and Variational Inequalities Coverage Problems in Sensor Networks Data Correcting Approach for Routing and Location in Networks Dual Integrality in Combinatorial Optimization Dynamical System Approaches to Combinatorial Optimization Efficient Algorithms for Geometric Shortest Path Query Problems Energy Efficiency in Wireless Networks Equitable Coloring of Graphs Faster and Space Efficient Exact Exponential Algorithms: Combinatorial and Algebraic Approaches Fault-Tolerant Facility Allocation Fractional Combinatorial Optimization Fuzzy Combinatorial Optimization Problems Geometric Optimization in Wireless Networks Gradient-Constrained Minimum Interconnection Networks Graph Searching and Related Problems Graph Theoretic Clique Relaxations and Applications Greedy Approximation Algorithms Hardness and Approximation of Network Vulnerability Job Shop Scheduling with Petri Nets Key Tree Optimization Linear Programming Analysis of Switching Networks Map of Geometric Minimal Cuts with Applications Max-Coloring Maximum Flow Problems and an NP-complete variant on Edge Labeled Graphs Modern Network Interdiction Problems and Algorithms Network Optimization Neural Network Models in Combinatorial Optimization On Coloring Problems Online and Semi-online Scheduling Online Frequency Allocation and Mechanism Design for Cognitive Radio Wireless Networks Optimal Partitions Optimization in Multi-Channel Wireless Networks Optimization Problems in Data Broadcasting Optimization Problems in Online Social Networks Optimizing Data Collection Capacity in Wireless Networks Packing Circles in Circles and Applications Partition in High Dimensional Spaces Probabilistic Verification and Non-approximability Protein Docking Problem as Combinatorial Optimization Using Beta-complex Quadratic Assignment Problems Reactive Business Intelligence: Combining the Power of Optimization with Machine Learning Reformulation-Linearization Techniques for Discrete Optimization Problems Resource Allocation Problems Rollout Algorithms for Discrete Optimization: A Survey Simplicial Methods for Approximating Fixed Point with Applications in Combinatorial Optimizations Small World Networks in Computational Neuroscience Social Structure Detection Steiner Minimal Trees: An Introduction, Parallel Computation and Future Work Steiner Minimum Trees in E^3 Tabu Search Variations of Dominating Set Problem

A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems

Abstract: Preface. 1. Introduction. Part I: Discrete Nonconvex Programs. 2. RLT Hierarchy for Mixed-Integer Zero-One Problems. 3. Generalized Hierarchy for Exploiting Special Structures in Mixed-Integer Zero-One Problems. 4. RLT Hierarchy for General Discrete Mixed-Integer Problems. 5. Generating Valid Inequalities and Facets Using RLT. 6. Persistency in Discrete Optimization. Part II: Continuous Nonconvex Programs. 7. RLT-Based Global Optimization Algorithms for Nonconvex Polynomial Programming Problems. 8. Reformulation-Convexification Technique for Quadratic Programs and Some Convex Envelope Characterizations. 9. Reformulation-Convexification Technique for Polynomial Programs: Design and Implementation. Part III: Special Applications to Discrete and Continuous Nonconvex Programs. 10. Applications to Discrete Problems. 11. Applications to Continuous Problems. References.

Stochastic Dynamic Programming and the Control of Queueing Systems

Abstract: Optimization Criteria. Finite Horizon Optimization. Infinite Horizon Discounted Cost Optimization. An Inventory Model. Average Cost Optimization for Finite State Spaces. Average Cost Optimization Theory for Countable State Spaces. Computation of Average Cost Optimal Policies for Infinite State Spaces. Optimization Under Actions at Selected Epochs. Average Cost Optimization of Continuous Time Processes. Appendices. Bibliography. Index.

An overview of the simultaneous perturbation method for efficient optimization

Abstract: ultivariate stochastic optimization plays a major role in the analysis and control of many engineering systems. In almost all real-world optimization problems, it is necessary to use a mathematical algorithm that iteratively seeks out the solution because an analytical (closed-form) solution is rarely available. In this spirit, the “simultaneous perturbation stochastic approximation (SPSA)” method for difficult multivariate optimization problems has been developed. SPSA has recently attracted considerable international attention in areas such as statistical parameter estimation, feedback control, simulation-based optimization, signal and image processing, and experimental design. The essential feature of SPSA—which accounts for its power and relative ease of implementation—is the underlying gradient approximation that requires only two measurements of the objective function regardless of the dimension of the optimization problem. This feature allows for a significant decrease in the cost of optimization, especially in problems with a large number of variables to be optimized. (

Optimized Design of Two-Dimensional Structures Using a Genetic Algorithm

Abstract: A design procedure incorporating a simple genetic algorithm (GA) is developed for discrete optimization of two-dimensional structures. The objective function considered is the total weight (or cost...

A review of simulation optimization techniques

Abstract: We present a review of methods for optimizing stochastic systems using simulation. The focus is on gradient based techniques for optimization with respect to continuous decision parameters and on random search methods for optimization with respect to discrete decision parameters.

Genetic Optimization Using Derivatives

Abstract: We describe a new computer program that combines evolutionary algorithm methods with a derivative-based, quasi-Newton method to solve difficult unconstrained optimization problems. The program, called GENOUD (GENetic Optimization Using Derivatives), effectively solves problems that are nonlinear or perhaps even discontinuous in the parameters of the function to be optimized. When a statistical model's estimating function (for example, a log-likelihood) is nonlinear in the model's parameters, the function to be optimized will usually not be globally concave and may contain irregularities such as saddlepoints or discontinuous jumps. Optimization methods that rely on derivatives of the objective function may be unable to find any optimum at all. Or multiple local optima may exist, so that there is no guarantee that a derivative-based method will converge to the global optimum. We discuss the theoretical basis for expecting GENOUD to have a high probability of finding global optima. We conduct Monte Carlo experiments using scalar Normal mixture densities to illustrate this capability. We also use a system of four simultaneous nonlinear equations that has many parameters and multiple local optima to compare the performance of GENOUD to that of the Gauss-Newton algorithm in SAS's PROC MODEL.

Dynamic Optimization in a Discontinuous World

Abstract: Many engineering tasks can be formulated as dynamic optimization or open-loop optimal control problems, where we search a priori for the input profiles to a dynamic system that optimize a given performance measure over a certain time period. Further, many systems of interest in the chemical processing industries experience significant discontinuities during transients of interest in process design and operation. This paper discusses three classes of dynamic optimization problems with discontinuities: path-constrained problems, hybrid discrete/continuous problems, and mixed-integer dynamic optimization problems. In particular, progress toward a general numerical technology for the solution of large-scale discontinuous dynamic optimization problems is discussed.

Algorithm for the instantaneous frequency estimation using time-frequency distributions with adaptive window width

Abstract: A method for minimization of the mean square error (MSE) of the instantaneous frequency estimation using time-frequency distributions, in the case of a discrete optimization parameter, is presented. It does not require a knowledge of the estimation bias. The method is illustrated on adaptive window width determination in the Wigner distribution.

A flexible optimization procedure for mechanical component design based on genetic adaptive search

Abstract: A flexible algorithm for solving nonlinear engineering design optimization problems involving zero-one, discrete, and continuous variables is presented. The algorithm restricts its search only to the permissible values of the variables, thereby reducing the search effort in converging near the optimum solution. The efficiency and ease of application of the proposed method is demonstrated by solving four different mechanical design problems chosen from the optimization literature. These results are encouraging and suggest the use of the technique to other more complex engineering design problems.

Algorithm for the instantaneous frequency estimation using time-frequency distributions with adaptive window width

Abstract: A method for the minimization of mean square error of the instantaneous frequency estimation using time-frequency distributions, in the case of a discrete optimization parameter, is presented. It does not require knowledge of the estimation bias. The method is illustrated on the adaptive window length determination in the Wigner distribution.

Optimization of Models

Abstract: Designing is a complex human process that has resisted comprehensive description and understanding. All artifacts surrounding us are the results of designing. Creating these artifacts involves making a great many decisions, which suggests that designing can be viewed as a decision-making process. In the decision-making paradigm of the design process we examine the intended artifact in order to identify possible alternatives and select the most suitable one. An abstract description of the artifact using mathematical expressions of relevant natural laws, experience, collected data, and geometry is the mathematical model of the artifact. This mathematical model may contain many alternative designs, and so criteria for comparing these alternatives must be introduced in the model. Within the limitations of such a model, the best, or optimum, design can be identiied with the aid of mathematical methods. In this irst chapter we deine the design optimization problem and describe most of the properties and issues that occupy the rest of the book. We outline the limitations of our approach and caution that an " optimum " design should be perceived as such only within the scope of the mathematical model describing it and the inevitable subjective judgment of the modeler. 1.1 Mathematical Modeling Although this book is concerned with design, almost all the concepts and results described can be generalized by replacing the word design by the word system. We will then start by discussing mathematical models for general systems. The System Concept A system may be deined as a collection of entities that perform a speciied set of tasks. For example, an automobile is a system that transports passengers. It follows that a system performs a function, or process, which results in an output.It is implicit that a system operates under causality; that is, the speciied set of tasks

Stochastic Methods for Practical Global Optimization

Abstract: Engineering design problems often involve global optimization of functions that are supplied as ’black box‘ functions. These functions may be nonconvex, nondifferentiable and even discontinuous. In addition, the decision variables may be a combination of discrete and continuous variables. The functions are usually computationally expensive, and may involve finite element methods. An engineering example of this type of problem is to minimize the weight of a structure, while limiting strain to be below a certain threshold. This type of global optimization problem is very difficult to solve, yet design engineers must find some solution to their problem – even if it is a suboptimal one. Sometimes the most difficult part of the problem is finding any feasible solution. Stochastic methods, including sequential random search and simulated annealing, are finding many applications to this type of practical global optimization problem. Improving Hit-and-Run (IHR) is a sequential random search method that has been successfully used in several engineering design applications, such as the optimal design of composite structures. A motivation to IHR is discussed as well as several enhancements. The enhancements include allowing both continuous and discrete variables in the problem formulation. This has many practical advantages, because design variables often involve a mixture of continuous and discrete values. IHR and several variations have been applied to the composites design problem. Some of this practical experience is discussed.

A parametric finite element environment tuned for numerical optimization

Abstract: Nowadays, numerical optimization in combination with finite element (FE) analysis plays an important role in the design of electromagnetic devices. To apply any kind of optimization algorithm, a parametric description of the FE problem is required and the optimization task must be formulated. Most optimization tasks described in the literature, feature either specially developed algorithms for a specific optimization task, or extensions to standard finite element packages. Here, a 2D parametric FE environment is presented, which is designed to be best suited for numerical optimization while maintaining its general applicability. Particular attention is paid to the symbolic description of the model, minimized computation time and the user friendly definition of the optimization task.

Solving discretized optimization problems by partially reduced SQP methods

Abstract: The solution of discretized optimization problems is a major task in many application areas from engineering and science. These optimization problems present various challenges which result from the high number of variables involved as well as from the properties of the underlying process to be optimized. They also provide several strucures which have to be exploited by efficient numerical solution approaches. In this paper we focus on partially reduced SQP methods which are shown to be particularly well suited for this problem class. In practical applications the efficiency of this approach is demonstrated for optimization problems resulting from discretized DAE as well as from discretized PDE. The practically important issues of inexact solution of linearized subproblems and of working range validation are tackled as well.

Reformulation-Linearization Techniques for Discrete Optimization Problems

Abstract: Discrete and continuous nonconvex programming problems arise in a host of practical applications in the context of production, location-allocation, distribution, economics and game theory, process design, and engineering design situations. Several recent advances have been made in the development of branch-and-cut algorithms for discrete optimization problems and in polyhedral outer-approximation methods for continuous nonconvex programming problems. At the heart of these approaches is a sequence of linear programming problems that drive the solution process. The success of such algorithms is strongly tied in with the strength or tightness of the linear programming representations employed.

Min-max optimization of several classical discrete optimization problems

Abstract: In this paper, we study discrete optimization problems with min-max objective functions. This type of problems has direct applications in the recent development of robust optimization. The following well-known classes of problems are discussed: minimum spanning tree problem, resource allocation problem with separable cost functions, and production control problem. Computational complexities of the corresponding min-max version of the above-mentioned problems are analyzed. Pseudopolynomial algorithms for these problems are provided under certain conditions.

Discrete manufacturing process design optimization using computer simulation and generalized hill climbing algorithms

Abstract: Discrete manufacturing process designs can be modelled using computer simulation. Determining optimal designs using such models is very difficult, due to the large number of manufacturing process sequences and associated parameter settings that exist. This has forced researchers to develop heuristic strategies to address such design problems. This paper introduces a new general heuristic strategy for discrete manufacturing process design optimization, called generalised hill climbing (GHC) algorithms. GHC algorithms provide a unifying approach for addressing such problems in particular, and intractable discrete optimization problems in general. Heuristic strategies such as simulated annealing, threshold accepting, Monte Carlo search, local search, and tabu search (among others) can all he formulated as GHC algorithms. Computational results are reported with various GHC algorithms applied to computer simulation models of discrete manufacturing process designs under study at the Materials Process Design Bra...

Design Optimization of Multibody Systems by Sequential Approximation

Abstract: Design optimization of multibody systems is usually established by a direct coupling of multibody system analysis and mathematical programming algorithms. However, a direct coupling is hindered by the transient and computationally complex behavior of many multibody systems. In structural optimization often approximation concepts are used instead to interface numerical analysis and optimization. This paper shows that such an approach is valuable for the optimization of multibody systems as well. A design optimization tool has been developed for multibody systems that generates a sequence of approximate optimization problems. The approach is illustrated by three examples: an impact absorber, a slider-crank mechanism, and a stress-constrained four-bar mechanism. Furthermore, the consequences for an accurate and efficient accompanying design sensitivity analysis are discussed.

Connections between Nonlinear Programming and Discrete Optimization

Abstract: Given a set X,a function f: X→ℝ and a subset S of X –we consider the problem: $$\min f(x)s.t.x \in S$$ (1) Problem (1) is usually called a combinatorial optimization problem when S is finite and a discrete optimization problem when the points of S are isolated in some topology, i.e., every point of S has a neighbourhood which does not contain other points of S. Obviously, all combinatorial optimization problems are also discrete optimization problems but the converse is not true. A simple example is the problem of minimizing a function on the set of integer points contained in an unbounded polyhedron.