Functionally specialized CMA-ES: a modification of CMA-ES based on the specialization of the functions of covariance matrix adaptation and step size adaptation

This paper aims the design of efficient and effective optimization algorithms for function optimization. This paper presents a new framework of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Recent studies modified the CMA-ES from the viewpoint of covariance matrix adaptation and resulted in drastic reduction of the number of generations. In addition to their modification, this paper modifies the CMA-ES from the viewpoint of step size adaptation. The main idea of modification is semantically specializing functions of covariance matrix adaptation and step size adaptation. This new method is evaluated on 8 classical unimodal and multimodal test functions and the performance is compared with standard CMA-ES. The experimental result demonstrates an improvement of the search performances in particular with large populations. This result is mainly because the proposed Hybrid-SSA instead of the existing CSA can adjust the global step length more appropriately under large populations and function specialization helps appropriate adaptation of the overall variance of the mutation distribution.

[1]  Nikolaus Hansen,et al.  Step-Size Adaption Based on Non-Local Use of Selection Information , 1994, PPSN.

[2]  Nikolaus Hansen,et al.  Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[3]  N. Hansen Invariance, Self-adaptation and Correlated Mutations in Evolution Strategies Invariance, Self-adaptation and Correlated Mutations in Evolution Strategies , 2000 .

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

[5]  Petros Koumoutsakos,et al.  Increasing the Serial and the Parallel Performance of the CMA-Evolution Strategy with Large Populations , 2002, PPSN.

[6]  Petros Koumoutsakos,et al.  Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES) , 2003, Evolutionary Computation.

[7]  Petros Koumoutsakos,et al.  Learning Probability Distributions in Continuous Evolutionary Algorithms - a Comparative Review , 2004, Nat. Comput..

[8]  Nikolaus Hansen,et al.  Evaluating the CMA Evolution Strategy on Multimodal Test Functions , 2004, PPSN.

[9]  Nikolaus Hansen,et al.  A restart CMA evolution strategy with increasing population size , 2005, 2005 IEEE Congress on Evolutionary Computation.

[10]  Anne Auger,et al.  Performance evaluation of an advanced local search evolutionary algorithm , 2005, 2005 IEEE Congress on Evolutionary Computation.

[11]  Dirk V. Arnold,et al.  Improving Evolution Strategies through Active Covariance Matrix Adaptation , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[12]  Nikolaus Hansen,et al.  The CMA Evolution Strategy: A Comparing Review , 2006, Towards a New Evolutionary Computation.