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Showing papers on "Discrete optimization published in 1991"


Book
01 Jan 1991
TL;DR: In this paper, the Lovasz Extensions of Submodular Functions are extended to include nonlinear weight functions and linear weight functions with continuous variables, and a Decomposition Algorithm is proposed.
Abstract: Introduction. 1. Mathematical Preliminaries. Submodular Systems and Base Polyhedra. 2. From Matroids to Submodular Systems. Matroids. Polymatroids. Submodular Systems. 3. Submodular Systems and Base Polyhedra. Fundamental Operations on Submodular Systems. Greedy Algorithm. Structures of Base Polyhedra. Intersecting- and Crossing-Submodular Functions. Related Polyhedra. Submodular Systems of Network Type. Neoflows. 4. The Intersection Problem. The Intersection Theorem. The Discrete Separation Theorem. The Common Base Problem. 5. Neoflows. The Equivalence of the Neoflow Problems. Feasibility for Submodular Flows. Optimality for Submodular Flows. Algorithms for Neoflows. Matroid Optimization. Submodular Analysis. 6. Submodular Functions and Convexity. Conjugate Functions and a Fenchel-Type Min-Max Theorem for Submodular and Supermodular Functions. Subgradients of Submodular Functions. The Lovasz Extensions of Submodular Functions. 7. Submodular Programs. Submodular Programs - Unconstrained Optimization. Submodular Programs - Constrained Optimization. Nonlinear Optimization with Submodular Constraints. 8. Separable Convex Optimization. Optimality Conditions. A Decomposition Algorithm. Discrete Optimization. 9. The Lexicographically Optimal Base Problem. Nonlinear Weight Functions. Linear Weight Functions. 10. The Weighted Max-Min and Min-Max Problems. Continuous Variables. Discrete Variables. 11. The Fair Resource Allocation Problem. Continuous Variables. Discrete Variables. 12. The Neoflow Problem with a Separable Convex Cost Function. References. Index.

505 citations


Journal ArticleDOI
TL;DR: An algorithm for solving non-linear programming problems containing integer, discrete and continuous variables is presented and penalties on integer and/or discrete violations are imposed on the objective function to force the search to converge upon standard values.
Abstract: An algorithm for solving non-linear programming problems containing integer, discrete and continuous variables is presented. Based on a commonly employed optimization algorithm, penalties on integer and/or discrete violations are imposed on the objective function to force the search to converge upon standard values. Examples are included to illustrate the practical use of this algorithm in the area of engineering design.

148 citations


Journal ArticleDOI
TL;DR: In this article, a simulated annealing strategy is developed for use in the discrete optimization of three-dimensional steel frames, which randomly perturbs the current design to create a candidate design.
Abstract: A simulated annealing strategy is developed for use in the discrete optimization of three-dimensional steel frames. This strategy randomly perturbs the current design to create a candidate design. A probabilistic acceptance criterion is then employed to determine whether the candidate design should replace the current design or be rejected. This acceptance criterion allows worse designs to be accepted in the initial stages of the strategy. The likelihood of accepting worse designs is small in the final stages of the strategy. The strategy is presented and illustrated on a three-dimensional, six-story, unsymmetrical frame. The frame is realistically loaded with gravity and seismic loads. Members in the frame must be selected from among discrete standardized shapes. The strategy is able to treat multiple section properties per member without having to curve-fit dependent properties as functions of a single independent property. Performance of the strategy is compared to that of the branch-and-bound method. Approximation techniques aimed at reducing computation time are investigated.

121 citations


Journal ArticleDOI
TL;DR: A general optimization framework for discrete and continuous problems based on genetic algorithmic techniques is presented and the proposed framework exhi is presented.

110 citations


Journal ArticleDOI
TL;DR: A new approach for solving nonlinear mixed-discrete problems with no particular structure is presented here, motivated by its efficiency for models with extensive monotonicities of the problem’s objective and constraint functions with respect to the design variables.
Abstract: Design optimization models of often contain variables that must take only discrete values, such as standard sizes. Nonlinear optimization problems with a mixture of discrete and continuous variables are very difficult, and existing algorithms are either computationally intensive or applicable to models with special structure. A new approach for solving nonlinear mixed-discrete problems with no particular structure is presented here, motivated by its efficiency for models with extensive monotonicities of the problem’s objective and constraint functions with respect to the design variables. It involves solving a sequence of mixed-discrete linear approximations of the original nonlinear model. In this article, a review of previous approaches is followed by description of the resulting algorithm, its convergence properties and limitations. Several illustrative examples are given. A sequel article presents a detailed algorithmic implementation and extensive computational results.

94 citations


Book
01 Jul 1991
TL;DR: This is an unpublished monograph that was widely distributed (and cited) and was first written in August 1988 and subseqently revised in August 1989.
Abstract: This is an unpublished monograph that was widely distributed (and cited). It was first written in August 1988 and subseqently revised.

73 citations


Journal ArticleDOI
TL;DR: In this paper, a tutorial survey of finite dimensional optimization problems which depend on parameters is presented, focusing on unfolding and singularity theory, structural analysis of families of constraint sets, constrained optimization problems and semi-infinite optimization.
Abstract: In this tutorial survey we study finite dimensional optimization problems which depend on parameters. It is our aim to work out several basic connections with different mathematical areas. In particular, attention will be paid to unfolding and singularity theory, structural analysis of families of constraint sets, constrained optimization problems and semi-infinite optimization.

60 citations


Book
01 Jan 1991
TL;DR: Part 1 Optimization as a circuit design tool: a generalized strategy for engineering design optimization and function minimization function space and the optimization problem of computer-aided design scope of the book.
Abstract: Part 1 Optimization as a circuit design tool: a generalized strategy for engineering design optimization and function minimization function space and the optimization problem of computer-aided design scope of the book. Part 2 Preliminary concepts: stationary points of functions unidirectional search classification of optimization methods. Part 3 Direct search optimization methods: tabulation methods sequential methods linear methods quadratically terminating direct search methods. Part 4 Gradient optimization methods: steepest descent Newton's method quasi-Newton methods least squares (Gauss-Newton) methods. Part 5 Unconstrained optimization in practice: local minima selection of an algorithm gradient evaluation. Part 6 Constrained optimization methods: classes of constrained optimization method linear programming quadratic and nonlinear programming commercial availability of constrained optimization algorithms. Part 7 Applications in electronic circuit design: optimization of linear frequency-selective networks optimization of nonlinear networks multiple-criterion optimization and statistical design of integrated circuits simulated annealing - a global optimization method? the future of optimization in electronic systems design.

52 citations


Journal ArticleDOI
TL;DR: Generalized simulated annealing is an optimization procedure for locating the global optimum (maximum or minimum) of multidimenisonal continuous functions and is applied to near‐infrared spectra.
Abstract: Generalized simulated annealing (GSA) is an optimization procedure for locating the global optimum (maximum or minimum) of multidimenisonal continuous functions. GSA has been modified for optimization of discrete functions. Selection of calibration samples from an existing set defines discrete optimization and GSA is used to select optimal sets of calibration samples for specific analysis samples. The procedure is applied to near-infrared spectra. When compared to using the complete set of 37 calibration samples, concentration prediction errors were reduced 50%–100% by using select sets of two to seven calibration samples. Additionally, GSA was able to improve a poorly designed experiment. GSA devised augmented experimental designs such that the overall experimental design (original plus augmented) was more orthogonal than the original.

43 citations


Journal ArticleDOI
TL;DR: An overview of interval arithmetical tools and basic techniques that can be used to construct deterministic global optimization algorithms and are applicable to unconstrained and constrained optimization as well as to nonsmooth optimization and to problems over unbounded domains is presented.
Abstract: An overview of interval arithmetical tools and basic techniques is presented that can be used to construct deterministic global optimization algorithms. These tools are applicable to unconstrained and constrained optimization as well as to nonsmooth optimization and to problems over unbounded domains. Since almost all interval based global optimization algorithms use branch-and-bound methods with iterated bisection of the problem domain we also embed our overview in such a setting.

41 citations


Journal ArticleDOI
TL;DR: In this article, a branch and bound method for solving continuous global optimization problems can be adapted to the discrete case, and an algorithm for minimizing a concave function over the integers contained in a compact polyhedron is presented.
Abstract: In this note we show that various branch and bound methods for solving continuous global optimization problems can be readily adapted to the discrete case. As an illustration, we present an algorithm for minimizing a concave function over the integers contained in a compact polyhedron. Computational experience with this algorithm is reported.

Book ChapterDOI
01 Jan 1991
TL;DR: Emphasis is on various approaches to fuzzy linear programming as the most important from both the practical point of view and the purpose and scope fo the volume.
Abstract: A brief survey of various concepts, problem classes, issues, etc related to fuzzy optimization and fuzzy mathematical programming is provided Emphasis is on various approaches to fuzzy linear programming as the most important from both the practical point of view and the purpose and scope fo the volume

Journal ArticleDOI
TL;DR: A short overview of the general ideas involved in solving optimization problems using interval arithmetic can be found in this article, where a discussion of a few prototype optimization algorithms are also presented, as well as a comparison of the two algorithms.
Abstract: We give a short overview of the general ideas involved in solving optimization problems using interval arithmetic. We include a discussion of a few prototype optimization algorithms.

Journal ArticleDOI
TL;DR: The methodology involves the solution of a sequence of high-quality approximate problems using a global optimization algorithm based on the interval evaluation of the objective function and constraint functions, combined with a local feasible directions algorithm.
Abstract: A global optimization strategy for structural synthesis based on approximation concepts is presented. The methodology involves the solution of a sequence of highly accurate approximate problems using a global optimization algorithm. The global optimization algorithm implemented consists of a branch and bound strategy based on the interval evaluation of the objective function and constraint functions, combined with a local feasible directions algorithm. The approximate design optimization problems are constructed using first order approximations of selected intermediate response quantities in terms of intermediate design variables. Some numerical results for example problems are presented to illustrate the efficacy of the design procedure setforth.


Journal Article
TL;DR: In this paper, a review of structural optimization methods for discrete variable structural optimization is presented, which are classified according to three categories: branch and bound, approximations using Branch and Bound, and ad-hoc methods.
Abstract: Available methods for discrete variable structural optimization are reviewed. Methods are classified according to three categories: branch and bound, approximations using branch and bound, and ad-hoc methods. The branch and bound method is theoretically correct for convex design tasks, but is costly to use. Approximation methods provide efficiency, but do not guarantee an optimum discrete solution. Ad-hoc methods attempt to solve the discrete variable problem without resorting to branch and bound methods and do not guarantee an optimum discrete solution. However, these latter two methods often provide a reasonable solution at an acceptable cost.

Journal ArticleDOI
TL;DR: The classical set covering problem is one of the well known NP-hard problems from discrete optimization and has been investigated by many authors in various formulations.
Abstract: The classical set covering problem is one of the well known NP-hard problems from discrete optimization. It consists of finding the cheapest covering of a finite set with a subsystem of a finite system of its subsets and has been investigated by many authors in various formulations. Here, two formulations are considered and corresponding results are presented.

Book
01 Feb 1991
TL;DR: This paper presents the main types of conflict situation and the criteria for optimal decision-making in economic decision- making, as well as a selection of suitable combination of solutions obtained by partial optimization in Linear Programming Models.
Abstract: Introduction. 1. Optimization Models and Their Role in Economic Decision-Making. 2. Some Aspects of Model Construction in Agriculture. Theoretical Parameters of the Systems Approach. Economic-Mathematical Model as a Tool for Representing Economic Systems. Economic-Mathematical Modelling in Retrospective and Perspective Views. 3. Goal-Directed Character of Economic Systems and its Relation to Optimization Criteria. Basic Terms and Some Aspects of Problems in Goal Analysis. Classification of Goals and Its Importance to Economic-Mathematical Modelling. Evaluation, Formalization and Properties of Goals. Goal Boundaries and Goal Changes. 4. Optimization Criteria in Mathematical Modelling of Economic Systems. The Choice and the Postulated Properties of Optimization Criteria. Classification, Mathematical Formulation and Interpretation of Optimization. Criteria. Optimization Criteria in Economic-Mathematical Models Applied to Agricultural Conditions. Simple optimization criteria. Simple maximization criteria of optimality. Simple minimization criteria of optimality. Compound optimization criteria. 5. Multicriterion Optimization. The Problems and Importance of Multicriterion Optimization. Methods (Procedures) of Multicriterion Optimization in Linear Programming Models. Methods based on the aggregation of criterion functions. Aggregation on the basis of the products (quotients) of coefficients of criterion functions. Aggregation on the basis of the convex combination of criterion functions. Aggregation based on the construction of the difference (sum) criterion functions. Aggregation of optimization criteria based on the construction of fractional linear function. Procedures based on the interchange of criterion. Procedures based on the comparison, analysis and suitable combination of solutions obtained by partial optimization. Procedure based on stepwise partial optimization and simultaneous suboptimization. Procedure based on sensitivity matrix analysis. Procedures based on the comparative and decision-making analysis. Procedure based on the minimization of the deviation function. Procedures based on the formation of convex linear combinations obtained by partial optimization. The method of step-by-step approximation. Minimax method. Multicriterion Optimization and Goal-Programming. Interactive Methods of Multicriterion Optimization. Multicriterion Optimization in Models of Conflict Situations. The substance and significance of conflict situations in economic decision-making. The main types of conflict situation and the criteria for optimal decision-making. Games with goal-directed participants. Games against nature. Decision-making with risks. Decision-making with uncertainty. Evaluation of the Different Procedures of Multicriterion Optimization and Principles of Choosing Them.

Journal Article
TL;DR: In this article, a discrete optimization method for the least-weight design of three-dimensional (3D) steel building frameworks is described. And the design process is iterative in nature and remarkably efficient, with the total number of iterations required to achieve an optimal design being generally small and almost independent of the complexity of the structure.
Abstract: The paper describes a discrete optimization method for the least-weight design of three-dimensional (3D) steel building frameworks. The method involves the coordinated application of structural analysis, sensitivity analysis and optimization techniques to establish an optimal design using standard steel sections that simultaneously satisfies all stiffness and strength provisions of the governing (Canadian or American) steel design code. The design process is iterative in nature and remarkably efficient, with the total number of iterations required to achieve an optimal design being generally small and almost independent of the complexity of the structure. The design of a 3D steel building framework is presented to illustrate the method.

Proceedings ArticleDOI
02 Dec 1991
TL;DR: Joint optimization of capacity and flow assignment (CFA) is considered for high-speed packet-switched networks in which multiple trunk links are modeled by parallel M/M/1 queues.
Abstract: Joint optimization of capacity and flow assignment (CFA) is considered for high-speed packet-switched networks in which multiple trunk links are modeled by parallel M/M/1 queues. A quadratic cost function is considered to reflect both switching and line costs. Queuing, transmission, nodal processing, and propagation delays are all incorporated into the optimization problem. The proposed CFA problem is shown to be a convex optimization problem, thus ensuring a global solution. By invoking optimality of the CFA problem and relaxing the integral channel constraint to a continuous variable, a set of nonlinear equations is derived for the optimal solutions. To circumvent the computational burden involved with the continuous solution approach and to capture the discrete nature of channel allocation, an efficient discrete optimization algorithm is developed based on a marginal analysis approach. >

Proceedings ArticleDOI
18 Nov 1991
TL;DR: A neural network with a three-layer feedback topology is proposed for solving continuous convex optimization problems and computational results are presented to show the usefulness of the proposed approach.
Abstract: A neural network with a three-layer feedback topology is proposed for solving continuous convex optimization problems Unconstrained and constrained optimization and relationships between neural networks and optimization theory are addressed Computational results are presented to show the usefulness of the proposed approach >

Book ChapterDOI
15 Apr 1991
TL;DR: A comprehensive framework for generating a robot's program for an automated production system will require an integration of several layers of system theory-based support methods and tools.
Abstract: A comprehensive framework for generating a robot's program for an automated production system will require an integration of several layers of system theory-based support methods and tools. Each layer of the robot's program synthesis system requires different CAST tools. The tools for each level are: Level 1 :graph search methods Level 2 :Petri net methodology Level 3 :discrete dynamical system methods Level 4 :discrete optimization methods Level 5 :event based system formalism

Journal ArticleDOI
TL;DR: The paper describes the features of the DISNEL package for interactive solution of a wide range of discrete and nonlinear optimization problems of ES computers.
Abstract: The paper describes the features of the DISNEL package for interactive solution of a wide range of discrete and nonlinear optimization problems of ES computers.

Proceedings ArticleDOI
13 Oct 1991
TL;DR: The authors present the basic concepts of a new approach based on the analytic tools peculiar to minimax algebra, which provide an effective way to write the performance indexes, and the relevant constraints of the analysis/optimization problems considered.
Abstract: The authors present the basic concepts of a new approach for the analysis and the optimization of a certain class of discrete event systems modeling manufacturing processes. Performance analysis of discrete event dynamic systems is performed with respect to a set of possible assignment/sequencing or delay perturbations. A model of a discrete event system is considered where some decisions are fixed and others are to be taken regarding the assignment of the tasks to the machines and the sequencing of such tasks on the machines. The approach described is based on the analytic tools peculiar to minimax algebra, which provide an effective way to write the performance indexes, and the relevant constraints of the analysis/optimization problems considered. >


Journal ArticleDOI
TL;DR: In this article, the authors discuss the effects of gender stereotypes on gender stereotypes in the context of gender discrimination in the media and show that gender stereotypes can be used to discriminate between genders.
Abstract: 本研究は, トラス構造物の離散的最適設計法について研究したものである. 本論文の最適化手法は, 初期設計, 応答近似式による検討ランク幅の設定, 連続的近似最適化問題の利用, および部分抽出法より構成される. 列挙法を基本としているが, 近似の概念を随所に利用し, 構造の特性, および連続的近似最適化問題の結果を利用して検討すべき組合せの数を少なくすることに成功し, 実用的な離散的最適設計法を示している.


Journal ArticleDOI
TL;DR: Stability criteria for multi-dimensional discrete system models in the Z-transform variable are considered and a simple algebraic test for two-dimensional, scalar system assessment is derived.
Abstract: Stability criteria for multi-dimensional discrete system models in the Z-transform variable are considered. A simple algebraic test for two-dimensional, scalar system assessment is derived, and illustrative examples are presented.

Book ChapterDOI
01 Jan 1991
TL;DR: The aim of this chapter is to provide the basic concepts and terminology in shape optimization by the mathematical programming method, which will be used throughout the thesis.
Abstract: The aim of this chapter is to provide the basic concepts and terminology in shape optimization by the mathematical programming method, which will be used throughout the thesis. Various algorithms of the mathematical programming methods are presented to give a general view of the numerical methods available today. The information presented here is mainly from References [1]–[5], in which more details can be found.