Benchmarking a BI-population CMA-ES on the BBOB-2009 function testbed

ABSTRACT

We propose a multistart CMA-ES with equal budgets for two interlaced restart strategies, one with an increasing population size and one with varying small population sizes. This BI-population CMA-ES is benchmarked on the BBOB-2009 noiseless function testbed and could solve 23, 22 and 20 functions out of 24 in search space dimensions 10, 20 and 40, respectively, within a budget of less than $10^6 D$ function evaluations per trial.

REFERENCES

• 1: A. Auger and N. Hansen. A restart CMA evolution strategy with increasing population size. In Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2005), pages 1769--1776. IEEE Press, 2005.
• 2: S. Finck, N. Hansen, R. Ros, and A. Auger. Real-parameter black-box optimization benchmarking 2009: Presentation of the noiseless functions. Technical Report 2009/20, Research Center PPE, 2009.
• 3: N. Hansen. The CMA evolution strategy: a comparing review. In J. Lozano, P. Larranaga, I. Inza, and E. Bengoetxea, editors, Towards a new evolutionary computation. Advances on estimation of distribution algorithms, pages 75--102. Springer, 2006.
• 4: N. Hansen, A. Auger, S. Finck, and R. Ros. Real-parameter black-box optimization benchmarking 2009: Experimental setup. Technical Report RR-6828, INRIA, 2009.
• 5: N. Hansen, S. Finck, R. Ros, and A. Auger. Real-parameter black-box optimization benchmarking 2009: Noiseless functions definitions. Technical Report RR-6829, INRIA, 2009.
• 6: N. Hansen and S. Kern. Evaluating the CMA evolution strategy on multimodal test functions. In X. Yao et al., editors, Parallel Problem Solving from Nature -- PPSN VIII, LNCS 3242, pages 282--291. Springer, 2004.
• 7: Nikolaus Hansen , Sibylle D. Müller , Petros Koumoutsakos, Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES), Evolutionary Computation, v.11 n.1, p.1-18, Spring 2003 [doi>10.1162/106365603321828970]
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INDEX TERMS

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

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems

General Terms:
Algorithms

Keywords:
CMA-ES, benchmarking, black-box optimization, evolutionary computation