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

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


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.


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How to Cite
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:
Research articles