Numerical Comparison of Some Penalty-Based Constraint Handling Techniques in Genetic Algorithms

We study five penalty function-based constraint handling techniques to be used with genetic algorithms in global optimization. Three of them, the method of superiority of feasible points, the method of parameter free penalties and the method of adaptive penalties have already been considered in the literature. In addition, we introduce two new modifications of these methods. We compare all the five methods numerically in 33 test problems and report and analyze the results obtained in terms of accuracy, efficiency and reliability. The method of adaptive penalties turned out to be most efficient while the method of parameter free penalties was the most reliable.

[1]  Carlos Artemio Coello-Coello,et al.  Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art , 2002 .

[2]  Zbigniew Michalewicz,et al.  A Note on Usefulness of Geometrical Crossover for Numerical Optimization Problems , 1996, Evolutionary Programming.

[3]  Xin Yao,et al.  Stochastic ranking for constrained evolutionary optimization , 2000, IEEE Trans. Evol. Comput..

[4]  Kaisa Miettinen,et al.  Evolutionary algorithms in engineering and computer science : recent advances in genetic algorithms, evolution strategies, evolutionary programming, genetic programming and industrial applications , 1999 .

[5]  Zbigniew Michalewicz,et al.  Evolutionary optimization of constrained problems , 1994 .

[6]  Robert L. Smith,et al.  Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed over Bounded Regions , 1984, Oper. Res..

[7]  Sana Ben Hamida,et al.  An Adaptive Algorithm for Constrained Optimization Problems , 2000, PPSN.

[8]  Kaisa Miettinen,et al.  Interactive multiobjective optimization system WWW-NIMBUS on the Internet , 2000, Comput. Oper. Res..

[9]  Mitsuo Gen,et al.  A survey of penalty techniques in genetic algorithms , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[10]  Vassilios Petridis,et al.  Varying Fitness Functions in Genetic Algorithms: Studying the Rate of Increase of the Dynamic Penalty Terms , 1998, PPSN.

[11]  J. Périaux,et al.  Multidisciplinary shape optimization in aerodynamics and electromagnetics using genetic algorithms , 1999 .

[12]  Hector A. Rosales-Macedo.  Nonlinear Programming: Theory and Algorithms (2nd Edition) , 1993 .

[13]  Hyun Myung,et al.  Evolutionary programming techniques for constrained optimization problems , 1997, IEEE Trans. Evol. Comput..

[14]  Zbigniew Michalewicz,et al.  Boundary Operators for Constrained Parameter Optimization Problems , 1997, ICGA.

[15]  Panos M. Pardalos,et al.  A Collection of Test Problems for Constrained Global Optimization Algorithms , 1990, Lecture Notes in Computer Science.

[16]  Alice E. Smith,et al.  Genetic Optimization Using A Penalty Function , 1993, ICGA.

[17]  Zbigniew Michalewicz,et al.  Genetic AlgorithmsNumerical Optimizationand Constraints , 1995, ICGA.

[18]  Michael M. Skolnick,et al.  Using Genetic Algorithms in Engineering Design Optimization with Non-Linear Constraints , 1993, ICGA.

[19]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .

[20]  Raphael T. Haftka,et al.  A Segregated Genetic Algorithm for Constrained Structural Optimization , 1995, ICGA.

[21]  H. Adeli,et al.  Augmented Lagrangian genetic algorithm for structural optimization , 1994 .

[22]  Carlos A. Coello Coello,et al.  THEORETICAL AND NUMERICAL CONSTRAINT-HANDLING TECHNIQUES USED WITH EVOLUTIONARY ALGORITHMS: A SURVEY OF THE STATE OF THE ART , 2002 .

[23]  K. Miettinen,et al.  Interactive bundle-based method for nondifferentiable multiobjeective optimization: nimbus § , 1995 .

[24]  K. Deb.  An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

[25]  Zbigniew Michalewicz,et al.  A Survey of Constraint Handling Techniques in Evolutionary Computation Methods , 1995 .

[26]  Keigo Watanabe,et al.  Evolutionary Optimization of Constrained Problems , 2004 .

[27]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms for Constrained Parameter Optimization Problems , 1996, Evolutionary Computation.

[28]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[29]  P. Pardalos,et al.  Handbook of global optimization , 1995 .

[30]  James C. Bean,et al.  A Genetic Algorithm for the Multiple-Choice Integer Program , 1997, Oper. Res..

[31]  Alice E. Smith,et al.  Penalty guided genetic search for reliability design optimization , 1996 .

[32]  Abdollah Homaifar,et al.  Constrained Optimization Via Genetic Algorithms , 1994, Simul..

[33]  Marc Schoenauer,et al.  Constrained GA Optimization , 1993, ICGA.

[34]  Z. Michalewicz.  Genetic Algorithms , Numerical Optimization , and Constraints , 1995 .