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Applied Computational Intelligence and Soft Computing
Volume 2010, Article ID 185063, 11 pages
Review Article

A Review of Constraint-Handling Techniques for Evolution Strategies

International Computer Science Institute, Berkeley, CA 94704, USA

Received 24 September 2009; Accepted 6 January 2010

Academic Editor: Chuan-Kang Ting

Copyright © 2010 Oliver Kramer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Evolution strategies are successful global optimization methods. In many practical numerical problems constraints are not explicitly given. Evolution strategies have to incorporate techniques to optimize in restricted solution spaces. Famous constraint-handling techniques are penalty and multiobjective approaches. Past work has shown that in particular an ill-conditioned alignment between the coordinate system of Gaussian mutation and the constraint boundaries leads to premature convergence. Covariance matrix adaptation evolution strategies offer a solution to this alignment problem. Last, metamodeling of the constraint boundary leads to significant savings of constraint function calls and to a speedup by repairing infeasible solutions. This work gives a brief overview over constraint-handling methods for evolution strategies by demonstrating the approaches experimentally on two exemplary constrained problems.