SUMMARYA parameter-less adaptive penalty scheme for genetic algorithms applied to constrained optimization problems is proposed. Using feedback from the evolutionary process the procedure automatically defines a penalty parameter for each constraint. The user is thus relieved from the burden of having to determine sensitive parameter(s) when dealing with every new constrained optimization problem. The procedure is shown to be effective and robust when applied to test problems from the evolutionary computation literature as well as several optimization problems from the structural engineering literature.

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Differential Evolution is a simple and efficient stochastic population-based heuristics for global optimization over continuous spaces. As with other nature inspired techniques, there is no provision for constraint handling in its original formulation, and a few possibilities have been proposed in the literature. In this paper an adaptive penalty technique (APM), which has been shown to be quite effective within genetic algorithms, is adopted for constraint handling within differential evolution. The technique, which requires no extra parameters, is based on feedback obtained from the current status of the population of candidate solutions, and automatically defines, for each constraint, its corresponding penalty coefficient. Equality as well as inequality constraints can be dealt with. In this paper we additionally introduce a mechanism for dynamically selecting the mutation operator, according to its performance, among several variants commonly used in the literature. In order to assess the applicability and performance of the proposed procedure, several test-problems from the structural and mechanical engineering optimization literature are considered.

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