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

ABSTRACT

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.

REFERENCES

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.6 Optimization
          Subjects: Global optimization

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.6 Optimization
          Subjects: Unconstrained optimization
  G.3 PROBABILITY AND STATISTICS
      Subjects: Probabilistic algorithms (including Monte Carlo)

General Terms:
Algorithms, Experimentation, Performance

Keywords:
covariance matrix adaptation, evolution strategy, functional specialization, step size adaptation