A new mutation operator for evolution strategies for constrained problems

We propose a new mutation operator - the biased mutation operator (BMO) -for evolution strategies, which is capable of handling problems for constrained fitness landscapes. The idea of our approach is to bias the mutation ellipsoid in relation to the parent and therefore lead the mutations into a beneficial direction self-adaptively. This helps to improve the success rate to reproduce better offspring. Experimental results show this bias enhances the solution quality within constrained search domains. The number of the additional strategy parameters used in our approach equals to the number of dimensions of the problem. Compared to the correlated mutation, the BMO needs much less memory and supersedes the computation of the rotation matrix of the correlated mutation and the asymmetric probability density function of the directed mutation.

[1]  Atidel B. Hadj-Alouane,et al.  A dual genetic algorithm for bounded integer programs James C. Bean, Atidel Ben Hadj-Alouane. , 1993 .

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

[3]  Dr. Zbigniew Michalewicz,et al.  How to Solve It: Modern Heuristics , 2004 .

[4]  Stefan Berlik.  A Step Size Preserving Directed Mutation Operator , 2004, GECCO.

[5]  Xin Yao,et al.  Fast Evolution Strategies , 1997, Evolutionary Programming.

[6]  Zbigniew Michalewicz,et al.  Evolutionary Computation 2 , 2000 .

[7]  Patrick D. Surry,et al.  A Multi-objective Approach to Constrained Optimisation of Gas Supply Networks: the COMOGA Method , 1995, Evolutionary Computing, AISB Workshop.

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

[9]  J. Rodriguez,et al.  Problem (2) , 1994 .

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

[11]  C. W. Tate.  Solve it. , 2005, Nursing standard (Royal College of Nursing (Great Britain) : 1987).

[12]  Hans-Paul Schwefel,et al.  Evolution strategies – A comprehensive introduction , 2002, Natural Computing.

[13]  Hans-Georg Beyer,et al.  The Theory of Evolution Strategies , 2001, Natural Computing Series.

[14]  E. D. Giorgi.  Selected Papers , 2006 .

[15]  C. Coello.  TREATING CONSTRAINTS AS OBJECTIVES FOR SINGLE-OBJECTIVE EVOLUTIONARY OPTIMIZATION , 2000 .

[16]  Carlos A. Coello Coello,et al.  A simple multimembered evolution strategy to solve constrained optimization problems , 2005, IEEE Transactions on Evolutionary Computation.

[17]  Oliver Kramer,et al.  On three new approaches to handle constraints within evolution strategies , 2006, Natural Computing.

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

[19]  Nikolaus Hansen,et al.  A Derandomized Approach to Self-Adaptation of Evolution Strategies , 1994, Evolutionary Computation.

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

[21]  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 .

[22]  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.

[23]  Ángel Fernando Kuri Morales,et al.  A UNIVERSAL ECLECTIC GENETIC ALGORITHM FOR CONSTRAINED OPTIMIZATION , 2022 .

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

[25]  Lars Hildebrand,et al.  Directed mutation-a new self-adaptation for evolution strategies , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).