Stochastic ranking for constrained evolutionary optimization

Penalty functions are often used in constrained optimization. However, it is very difficult to strike the right balance between objective and penalty functions. This paper introduces a novel approach to balance objective and penalty functions stochastically, i.e., stochastic ranking, and presents a new view on penalty function methods in terms of the dominance of penalty and objective functions. Some of the pitfalls of naive penalty methods are discussed in these terms. The new ranking method is tested using a (/spl mu/, /spl lambda/) evolution strategy on 13 benchmark problems. Our results show that suitable ranking alone (i.e., selection), without the introduction of complicated and specialized variation operators, is capable of improving the search performance significantly.

[1]  Mitsuo Gen,et al.  Genetic algorithms and engineering design , 1997 .

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

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

[4]  Christopher R. Houck,et al.  On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA's , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

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

[6]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[7]  Patrick D. Surry,et al.  The COMOGA Method: Constrained Optimisation by Multi-Objective Genetic Algorithms , 1997 .

[8]  R. Weiner Lecture Notes in Economics and Mathematical Systems , 1985 .

[9]  Jack Sklansky,et al.  Constrained Genetic Optimization via Dynarnic Reward-Penalty Balancing and Its Use in Pattern Recognition , 1989, ICGA.

[10]  Zbigniew Michalewicz,et al.  GENOCOP: a genetic algorithm for numerical optimization problems with linear constraints , 1996, CACM.

[11]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[12]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[13]  Hans-Paul Schwefel,et al.  Evolution and optimum seeking , 1995, Sixth-generation computer technology series.

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

[15]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization , 1999, Evolutionary Computation.

[16]  Alice E. Smith,et al.  Penalty Functions , 1996 .

[17]  Klaus Schittkowski,et al.  More test examples for nonlinear programming codes , 1981 .

[18]  Klaus Schittkowski,et al.  Test examples for nonlinear programming codes , 1980 .

[19]  David Mautner Himmelblau,et al.  Applied Nonlinear Programming , 1972 .

[20]  M. J. D. Powell,et al.  Nonlinear Programming—Sequential Unconstrained Minimization Techniques , 1969 .

[21]  David B. Fogel,et al.  Evolutionary algorithms in theory and practice , 1997, Complex.

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

[23]  Colin R. Reeves,et al.  Genetic Algorithms for the Operations Researcher , 1997, INFORMS J. Comput..

[24]  S. Ben Hamida,et al.  A logarithmic mutation operator to solve constrained optimization problems , 1999 .

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

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

[27]  José L. Verdegay,et al.  Evolutionary Techniques for Constrained Optimization Problems , 1999 .

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