Optimization and Engineering

, Volume 12, Issue 1–2, pp 31–54 | Cite as

An adaptive constraint handling technique for differential evolution with dynamic use of variants in engineering optimization

  • Eduardo K. da SilvaEmail author
  • Helio J. C. Barbosa
  • Afonso C. C. Lemonge


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.


Differential evolution Constrained optimization Adaptive penalty 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Eduardo K. da Silva
    • 1
    Email author
  • Helio J. C. Barbosa
    • 1
  • Afonso C. C. Lemonge
    • 2
  1. 1.Laboratório Nacional de Computação Científica—LNCCPetrópolisBrasil
  2. 2.Departamento de Mecânica Aplicada e Computacional, Faculdade de EngenhariaUniversidade Federal de Juiz de ForaJuiz de ForaBrasil

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