Increasing Population (μ + λ)-CMA-ES with Centre and Elitism (IPOP!+)

  • Mark Wineberg
  • Samuel Opawale
Keywords: CMA-ES, center, elitism, restart, selection, IPOP, IPOP!

Abstract

Elitism has previously been introduced to the CMA-ES family of algorithms, where the “’,’ selection operator is replaced by the “+” selection operator. Here we investigate in detailed the addition of elitism to IPOP. Furthermore, a new selection operator was added: the “!” operator (pronounced “bang” or “here”). This operator includes the results of ES recombination into the population for selection, unmodified by mutation, and evaluated separately. From the analysis, we noticed a remarkable improvement in the behavior of IPOP with or without elitism. Only one function (Levy) proved difficult when elitism was used. Under close examination, it was determined that for this function, the population under elitism converges prematurely, and stalled out. Currently we do not know what is the cause of this difference. Perhaps in the future this effect could be avoided or detected and remedial measures applied.

References

Auger, A., Hansen, N.: Performance evaluation of an advanced local search evolutionary algorithm. In:Evolutionary Computation, 2005. The 2005 IEEE Congress on, vol. 2, pp. 1777–1784. IEEE (2005)

Auger, A., Hansen, N.: A restart cma evolution strategy with increasing population size. In: EvolutionaryComputation, 2005. The 2005 IEEE Congress on, vol. 2, pp. 1769–1776. IEEE (2005)

Auger, A., Schoenauer, M., Vanhaecke, N.: Ls-cma-es: A second-order algorithm for covariance matrixadaptation. In: International Conference on Parallel Problem Solving from Nature, pp. 182–191. Springer(2004)

Back, T.: Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming,genetic algorithms. Oxford university press (1996)

Hansen, N., Ostermeier, A.: Adapting arbitrary normal mutation distributions in evolution strategies: Thecovariance matrix adaptation. In: Evolutionary Computation, 1996., Proceedings of IEEE InternationalConference on, pp. 312–317. IEEE (1996)

Igel, C., Hansen, N., Roth, S.: Covariance matrix adaptation for multi-objective optimization. Evolutionarycomputation15(1), 1–28 (2007)

Igel, C., Suttorp, T., Hansen, N.: A computational efficient covariance matrix update and a (1+ 1)-cma forevolution strategies. In: Proceedings of the 8th annual conference on Genetic and evolutionary computation,pp. 453–460. ACM (2006)

van Rijn, S., Wang, H., van Leeuwen, M., B ̈ack, T.: Evolving the structure of evolution strategies. In:Computational Intelligence (SSCI), 2016 IEEE Symposium Series on, pp. 1–8. IEEE (2016)

van Rijn, S., Wang, H., van Stein, B., B ̈ack, T.: Algorithm configuration data mining for cma evolutionstrategies. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 737–744. ACM(2017)

Wineberg, L.: Reexpressing problematic optimization data. In: Proceedings of the 2017 Annual Conferenceon Genetic and Evolutionary Computation, pp. 897–904. ACM (2017)

Published
2018-06-01
How to Cite
[1]
Wineberg, M. and Opawale, S. 2018. Increasing Population (μ + λ)-CMA-ES with Centre and Elitism (IPOP!+). MENDEL. 24, 1 (Jun. 2018), 1-8. DOI:https://doi.org/10.13164/mendel.2018.1.001.
Section
Research articles