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Journal ArticleDOI

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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Citations
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Proceedings ArticleDOI
10 Jun 2012
TL;DR: A family of adaptive penalty schemes for steady-state genetic algorithms is proposed here, where a penalty parameter is adaptively computed along the run according to information extracted from the current population, such as the existence of feasible individuals and the level of violation of each constraint.
Abstract: Real world engineering optimization problems are often subject to constraints which are complex implicit functions of the design variables. Frequently, such constrained problems are replaced by unconstrained ones by means of penalty functions. A family of adaptive penalty schemes for steady-state genetic algorithms is proposed here. For each constraint, a penalty parameter is adaptively computed along the run according to information extracted from the current population, such as the existence of feasible individuals and the level of violation of each constraint. The performance of each variant in the family is examined using test problems from the evolutionary computation as well as mechanical and structural optimization literature.

4 citations


Cites methods from "Penalty Function Methods for Constr..."

  • ...Penalty methods for genetic algorithms discussed in [6] were grouped as: i) Death Penalty, ii) Static Penalties, iii) Dynamic Penalties, iv) Annealing Penalties, v) Adaptive Penalties, vi) Segregated GA, and vii) Co-evolutionary Penalties....

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Journal Article
TL;DR: In this paper, the authors proposed new penalty functions which have better convergence properties, as compared to the commonly used exterior and interior penalty functions, have been proposed in this paper, which can also help accomplish optimization in only one round when it is desired to solve a constrained problem by using genetic algorithms.

4 citations

Journal ArticleDOI
TL;DR: In this paper, a penalty function method for solving lexicographic vector equilibrium problems is proposed, and it is shown that every penalty trajectory tends to the solution of the original problem.
Abstract: In this paper, we consider lexicographic vector equilibrium problems. We propose a penalty function method for solving such problems. We show that every penalty trajectory of the penalized lexicographic equilibrium problem tends to the solution of the original problem. Using the regularized gap function to obtain an error bound result for such penalized problems is given.

4 citations

Journal ArticleDOI
TL;DR: In this paper, a deep neural network (DNN) structure was proposed for modeling of the ternary liquid-liquid equilibrium (LLE), which was compared with that of NRTL and UNIQUAC in terms of the root mean square errors (RMSE).

4 citations

Proceedings ArticleDOI
01 Jan 2011
TL;DR: Two heuristics that allow finding a satisfying constraint sequence have been developed and can therefore be easy to implement, and powerful alternatives for solving engineering design problems.
Abstract: Engineering design problems are most frequently charac-terized by constraints that make them hard to solve and time-consuming. When evolutionary algorithms are used to solve these problems, constraints are often handled with the generic weighted sum method or with techniques specific to the prob-lem at hand. Most commonly, all constraints are evaluated at each generation, and it is also necessary to fine-tune different parameters in order to receive good results, which requires in-depth knowledge of the algorithm. The sequential constraint-handling techniques seem to be a promising alternative, be-cause they do not require all constraints to be evaluated at each iteration and they are easy to implement. They neverthe-less require the user to determine the ordering in which those constraints shall be evaluated. Therefore two heuristics that allow finding a satisfying constraint sequence have been developed. Two sequential constraint-handling techniques using the heuristics have been tested against the weighted sum technique with the ten-bar structure benchmark. They both performed better than the weighted sum technique and can therefore be easy to implement, and powerful alternatives for solving engineering design problems.

4 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

Journal ArticleDOI
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