Premature Convergence in Constrained Continuous Search Spaces

  • Oliver Kramer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)


The optimum of numerical problems quite often lies on the constraint boundary or even in a vertex of the feasible search space. In such cases the evolutionary algorithm (EA) frequently suffers from premature convergence because of a low success probability near the constraint boundaries. We analyze premature fitness stagnation and the success rates experimentally for an EA using self-adaptive step size control. For a (1+1)-EA with a Rechenberg-like step control mechanism we prove premature step size reduction at the constraint boundary. The proof is based on a success rate analysis considering a simplified mutation distribution model. From the success rates and the possible state transitions, the expected step size change can be derived at each step. We validate the theoretical model with an experimental analysis.


Premature Convergence Constrained Real-Parameter Optimization Evolution Strategies Self-Adaptation 


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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Oliver Kramer
    • 1
  1. 1.Computational Intelligence GroupDortmund University of TechnologyDortmundGermany

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