Showing papers on "Continuous optimization published in 1991"
TL;DR: In this article, a stochastic approach based on the simulated annealing algorithm is proposed for global optimization problems, which can be defined as the problem of finding points on a bounded subset of Ω(n) points in which some real valued function f assumes its optimal (maximal or minimal) value.
Abstract: In this paper we are concerned with global optimization, which can be defined as the problem of finding points on a bounded subset of ℝ
n
in which some real valued functionf assumes its optimal (maximal or minimal) value. We present a stochastic approach which is based on the simulated annealing algorithm. The approach closely follows the formulation of the simulated annealing algorithm as originally given for discrete optimization problems. The mathematical formulation is extended to continuous optimization problems, and we prove asymptotic convergence to the set of global optima. Furthermore, we discuss an implementation of the algorithm and compare its performance with other well-known algorithms. The performance evaluation is carried out for a standard set of test functions from the literature.
391 citations
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
22 Sep 1991
72 citations
TL;DR: In this article, a branch-and-bound framework is proposed for solving global optimization problems with a few variables and constraints, and the first complete solution of two difficult test problems is presented.
Abstract: Global optimization problems with a few variables and constraints arise in numerous applications but are seldom solved exactly. Most often only a local optimum is found, or if a global optimum is detected no proof is provided that it is one. We study here the extent to which such global optimization problems can be solved exactly using analytical methods. To this effect, we propose a series of tests, similar to those of combinatorial optimization, organized in a branch-and-bound framework. The first complete solution of two difficult test problems illustrates the efficiency of the resulting algorithm. Computational experience with the programbagop, which uses the computer algebra systemmacsyma, is reported on. Many test problems from the compendiums of Hock and Schittkowski and others sources have been solved.
62 citations
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
50 citations
01 Dec 1991
TL;DR: The authors suggest a framework for the multicriteria optimization of simulation models by first discussing the unique difficulties of this problem area along with important problem characteristics, and then discussing the way that these problem characteristics would affect the choice of a particular technique.
Abstract: The authors suggest a framework for the multicriteria optimization of simulation models by first discussing the unique difficulties of this problem area along with important problem characteristics, and then discussing the way that these problem characteristics would affect the choice of a particular technique. The problem of manufacturing system optimization is addressed. Various techniques, along with their advantages and disadvantages, are discussed and categorized according to the timing of the articulation of the required preference (tradeoff) information with respect to the optimization. >
43 citations
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
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.
30 citations
TL;DR: In this paper, the directional derivative of the optimal value of a finite dimensional optimization problem with parameters is studied. But the results on the directional derivatives are not directly comparable to the results in this paper.
Abstract: This paper presents with elementary proofs some results on the directional derivative of the optimal value of a finite dimensional optimization problem with parameters
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.
01 Jan 1991
TL;DR: In this paper, a modified simulated annealing technique was used to optimize the problem with both combinatorial and continuous criteria and with inequality constraints, and the actuator locations were determined by first seeking a near optimum solution using the modified simulated anealing techniques.
Abstract: The development of a lightweight actuation system for maintaining the surface accuracy of a composite honeycomb panel using piezoelectric actuators is discussed A modified simulated annealing technique is used to optimize the problem with both combinatorial and continuous criteria and with inequality constraints Near optimal solutions for the location of the actuators, using combinatorial optimization, and for the required actuator forces, employing continuous optimization, are sought by means of the modified simulated annealing technique The actuator locations are determined by first seeking a near optimum solution using the modified simulated annealing technique The final actuator configuration consists of an arrangement wherein the piezoelectric actuators are placed along six radial lines Numerical results showing the achievable surface correction by means of this configuration are presented
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.
TL;DR: The simplex algorithm for linear programming is based on the well-known equivalence between the problem of maximizing a linear function on a polyhedron and maximizing over the set of all vertices of the polytopes as mentioned in this paper.
Abstract: The simplex algorithm for linear programming is based on the well-known equivalence between the problem of maximizing a linear functionf on a polyhedronP and the problem of maximizingf over the setVP of all vertices ofP. The equivalence between these two problems is also exploited by some methods for maximizing a convex or quasi-convex function on a polyhedron.
TL;DR: In this paper, the authors give an example to illustrate the gap between multiobjective and single-objective optimization, which solves a problem proposed in Ref. 1, and demonstrate a gap between the two types of optimization.
Abstract: We give an example to illustrate a gap between multiobjective optimization and single-objective optimization, which solves a problem proposed in Ref. 1.
TL;DR: In this paper, conditions for stability by vector criterion are derived for the mixed integer problem with mixed (integer and continuous) variables for the vector optimization problem with continuous and continuous variables.
Abstract: Stability of the vector optimization problem with mixed (integer and continuous) variables is considered. Conditions for stability by vector criterion are derived for the mixed integer problem.
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.
31 Oct 1991
TL;DR: In this article, a modification of the Tikhonov regularization method is proposed for a stable recovery of the solution to the Inverse Problem of Electrocardiography, which is tested on a concentric spheres model.
Abstract: A modification of the Tikhonov regularization method is proposed for a stable recovery of the solution to the Inverse Problem of Electrocardiography. It consists of optimization of the Tikhonov functional subject to additional constraints on the amplitudes derived from an overregularized Tikhonov solution. This optimization method, tested on a concentric spheres model, yields solutions that are more accurate than an optimal Tikhonov solution.
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. >
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 >
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.
01 Jan 1991
TL;DR: In this paper, an alternative optimization approach for systematic design of a parametrized engine system was developed and demonstrated through application to a novel conversion device, the patented Stiller-Smith mechanism.
Abstract: This paper develops an alternative optimization approach for systematic design of a parametrized engine system and illustrates the procedure through application to a novel conversion device, the patented Stiller-Smith mechanism (1, 2). Using simultaneous interplay between a simulation scheme, presented in detail elsewhere (3), and an optimization scheme, the proposed structural design process integrates the multiple objectives of structural design. Developed here in detail, optimization involves intermediate continuous optimization via a penalty function method, and integer or discrete programming through the branch-and-bound algorithm. The ensuing application illustrates the approach by optimizing a 16-cylinder Stiller-Smith engine for minimum weight-power and dimensions-power ratios under several types of constraints. In the context of a multi-objective constrained non-linear programming problem, the design example proceeds through three stages: (a) preliminary, in which the designer applies the simulat...
01 May 1991
TL;DR: A 2-phase optimization network is proposed which can obtain both the exact solution, in contrast to the approximate solution by Kennedy and Chua's networks, as well as the corresponding Lagrange multipliers associated with each constraint.
Abstract: Artificial neural networks (ANNs) for optimization are analyzed from the viewpoint of optimization theory. A unifying optimization network theory for linear programming, quadratic programming, convex programming, and nonlinear programming is derived. A 2-phase optimization network is proposed which can obtain both the exact solution, in contrast to the approximate solution by Kennedy and Chua's networks, as well as the corresponding Lagrange multipliers associated with each constraint. The quality of the solutions obtained by the optimization ANNs is quantified through simulation.
The applicability of the optimization ANNs for solving real-world problems is demonstrated with examples of the economic power dispatching problem and the optimal power flow problem. It is shown that the mapping technique of the optimization ANNs is simple and that they are able to handle various kinds of constraint sets. Furthermore, it is demonstrated that the optimization ANNs attain a better objective function value.
Overall, this work lays a solid groundwork for optimization ANNs in both theoretical and practical aspects.
01 Jan 1991
TL;DR: In this article, the authors give an example to illustrate the gap between multiobjective and single-objective optimization, which solves a problem proposed in Ref. 1, and demonstrate a gap between the two types of optimization.
Abstract: We give an example to illustrate a gap between multiobjective optimization and single-objective optimization, which solves a problem proposed in Ref. 1.
01 Jan 1991
TL;DR: A method to replace a single inefficient non-gradient-based optimization by a set of efficient numerical gradient-directed optimizations that can be performed in parallel and yields a 95% speedup over traditional optimization methods and de creases the dependence of the numerical methods on having a good starting point.
Abstract: Many important application problems can be formalized as constrained non-linear optimization tasks. However, numerical methods for solving such problems are brittle and do not scale well. Furthermore, for large classes of engineering problems, the objective function cannot be converted into a differentiable closed form. This prevents the application of efficient gradient optimization methods--only slower, non-gradient methods can be applied. This paper describes a method to speed up and increase the reliability of numerical optimization by (a) optimizing the computation of the objective function, and (b) splitting the objective function into special cases that possess differentiable closed forms. This allows us to replace a single inefficient non-gradient-based optimization by a set of efficient numerical gradient-directed optimizations that can be performed in parallel. In the domain of 2-dimensional structural design, this procedure yields a 95% speedup over traditional optimization methods and de creases the dependence of the numerical methods on having a good starting point.