Penalty Function Methods for Constrained Optimization with Genetic Algorithms
01 Apr 2005-Mathematical & Computational Applications (Association for Scientific Research)-Vol. 10, Iss: 1, pp 45-56
TL;DR: These penalty-based methods for handling constraints in Genetic Algorithms are presented and discussed and their strengths and weaknesses are discussed.
Abstract: Genetic Algorithms are most directly suited to unconstrained optimization. Application of Genetic Algorithms to constrained optimization problems is often a challenging effort. Several methods have been proposed for handling constraints. The most common method in Genetic Algorithms to handle constraints is to use penalty functions. In this paper, we present these penalty-based methods and discuss their strengths and weaknesses.
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08 Dec 2020
TL;DR: In this article, the Harris Hawks optimization (HHO) algorithm was applied to the optimization problem of waveguide filters and the results showed that HHO can jump out of a local minimum and converge to the globally optimal solution with higher probability.
Abstract: We apply a novel algorithm, Harris Hawks optimization (HHO), to the optimization problem of waveguide filters In order to investigate the efficiency, particle swarm optimization(PSO), differential evolution(DE), and self-adaptive differential optimization(SaDE) are considered to optimize a fourth-order dual-mode waveguide filter as well Unlike standard PSO, DE, and SaDE, HHO utilizes a hybrid updating strategy to balance the exploiting and exploration phase during the optimization Therefore, HHO can jump out of a local minimum and converge to the globally optimal solution with a higher probability The statistical comparison between different algorithms shows that HHO converges faster than the other algorithms The optimization result also indicates that HHO obtains the best solution, which demonstrates that HHO has the potential to solve sophisticated optimization problems of various electromagnetism devices
3 citations
Journal Article•
TL;DR: A new mathematical model for a redundancyallocation problem (RAP) with cold-standby redundancy strategy and multiple component choices is presented and two metaheuristic algorithms; namely, simulated annealing and genetic algorithm to solve it are proposed.
Abstract: This paper presents a new mathematical model for a redundancyallocation problem (RAP) withcold-standby redundancy strategy and multiple component choices.The applications of the proposed model arecommon in electrical power, transformation,telecommunication systems,etc.Manystudies have concentrated onone type of time-to-failure, butin thispaper, two components of time-to-failures which follow hypo-exponential and exponential distributionare investigated. The goal of the RAP is to select available components and redundancy level for each subsystem for maximizing system reliability under cost and weight constraints.Sincethe proposed model belongs to NP-hard class, we proposed two metaheuristic algorithms; namely, simulated annealing and genetic algorithm to solve it. In addition, a numerical example is presented to demonstrate the application of the proposed solution methodology.
3 citations
Journal Article•
TL;DR: In this paper, a computational approach based on an exterior penalty function MPQI method is given for solving a class of continuous inequality constrained optimization problems, and the essential steps of the partial quadratic interpolation technique and its modified are given.
Abstract: I n this paper, a computational approach based on an exterior penalty function MPQI method is given for solving a class of continuous inequality constrained optimization problems. The essential steps of the partial quadratic interpolation technique and its modified are given. The numerical algorithm and the flowchart of the penalty function method combined with the Modified Partial Quadratic Interpolation Technique are given. For illustration, three examples are solved using the proposed method. From the solutions obtained, we observe that the values of their object functions are amongst the smallest when compared with those obtained by other existing methods available in the literature. More importantly, our method finds solution which satisfies the continuous inequality constraints.
3 citations
Cites background from "Penalty Function Methods for Constr..."
...INTRODUCTION In recent years, there has been a resurgence of interest in penalty methods [1-5] because of their ability to handle degenerate problems and inconsistent constraint linearization....
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01 Jan 2014
TL;DR: This chapter provides a basic overview of the common techniques used with nature-inspired algorithms, including constraint-handling techniques, that are important in problem solving in optimization.
Abstract: Optimization is often subject to complex constraints. Constraint-handling techniques form an important area of problem solving in optimization. There many constraint-handling methods that allow the algorithms to solve unconstrained optimization problems to solve constrained optimization problems efficiently. This chapter provides a basic overview of the common techniques used with nature-inspired algorithms.
3 citations
References
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Book•
01 Sep 1988
TL;DR: In this article, the authors present the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields, including computer programming and mathematics.
Abstract: From the Publisher:
This book brings together - in an informal and tutorial fashion - the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields
Major concepts are illustrated with running examples, and major algorithms are illustrated by Pascal computer programs No prior knowledge of GAs or genetics is assumed, and only a minimum of computer programming and mathematics background is required
52,797 citations
Book•
01 Jan 1992
TL;DR: GAs and Evolution Programs for Various Discrete Problems, a Hierarchy of Evolution Programs and Heuristics, and Conclusions.
Abstract: 1 GAs: What Are They?.- 2 GAs: How Do They Work?.- 3 GAs: Why Do They Work?.- 4 GAs: Selected Topics.- 5 Binary or Float?.- 6 Fine Local Tuning.- 7 Handling Constraints.- 8 Evolution Strategies and Other Methods.- 9 The Transportation Problem.- 10 The Traveling Salesman Problem.- 11 Evolution Programs for Various Discrete Problems.- 12 Machine Learning.- 13 Evolutionary Programming and Genetic Programming.- 14 A Hierarchy of Evolution Programs.- 15 Evolution Programs and Heuristics.- 16 Conclusions.- Appendix A.- Appendix B.- Appendix C.- Appendix D.- References.
12,212 citations
Book•
03 Mar 1993
TL;DR: The book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques.
Abstract: COMPREHENSIVE COVERAGE OF NONLINEAR PROGRAMMING THEORY AND ALGORITHMS, THOROUGHLY REVISED AND EXPANDED"Nonlinear Programming: Theory and Algorithms"--now in an extensively updated Third Edition--addresses the problem of optimizing an objective function in the presence of equality and inequality constraints. Many realistic problems cannot be adequately represented as a linear program owing to the nature of the nonlinearity of the objective function and/or the nonlinearity of any constraints. The "Third Edition" begins with a general introduction to nonlinear programming with illustrative examples and guidelines for model construction.Concentration on the three major parts of nonlinear programming is provided: Convex analysis with discussion of topological properties of convex sets, separation and support of convex sets, polyhedral sets, extreme points and extreme directions of polyhedral sets, and linear programmingOptimality conditions and duality with coverage of the nature, interpretation, and value of the classical Fritz John (FJ) and the Karush-Kuhn-Tucker (KKT) optimality conditions; the interrelationships between various proposed constraint qualifications; and Lagrangian duality and saddle point optimality conditionsAlgorithms and their convergence, with a presentation of algorithms for solving both unconstrained and constrained nonlinear programming problemsImportant features of the "Third Edition" include: New topics such as second interior point methods, nonconvex optimization, nondifferentiable optimization, and moreUpdated discussion and new applications in each chapterDetailed numerical examples and graphical illustrationsEssential coverage of modeling and formulating nonlinear programsSimple numerical problemsAdvanced theoretical exercisesThe book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques. The logical and self-contained format uniquely covers nonlinear programming techniques with a great depth of information and an abundance of valuable examples and illustrations that showcase the most current advances in nonlinear problems.
6,259 citations
TL;DR: GA's population-based approach and ability to make pair-wise comparison in tournament selection operator are exploited to devise a penalty function approach that does not require any penalty parameter to guide the search towards the constrained optimum.
3,495 citations
"Penalty Function Methods for Constr..." refers background in this paper
...These approaches can be grouped in four major categories [28]: Category 1: Methods based on penalty functions - Death Penalty [2] - Static Penalties [15,20] - Dynamic Penalties [16,17] - Annealing Penalties [5,24] - Adaptive Penalties [10,12,35,37] - Segregated GA [21] - Co-evolutionary Penalties [8] Category 2: Methods based on a search of feasible solutions - Repairing unfeasible individuals [27] - Superiority of feasible points [9,32] - Behavioral memory [34]...
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Book•
01 Jan 1996
TL;DR: In this work, the author compares the three most prominent representatives of evolutionary algorithms: genetic algorithms, evolution strategies, and evolutionary programming within a unified framework, thereby clarifying the similarities and differences of these methods.
2,679 citations