Evaluating the CMA Evolution Strategy on Multimodal Test Functions

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In this paper the performance of the CMA evolution strategy with rank-μ-update and weighted recombination is empirically investigated on eight multimodal test functions. In particular the effect of the population size λ on the performance is investigated. Increasing the population size remarkably improves the performance on six of the eight test functions. The optimal population size takes a wide range of values, but, with one exception, scales sub-linearly with the problem dimension. The global optimum can be located in all but one function. The performance for locating the global optimum scales between linear and cubic with the problem dimension. In a comparison to state-of-the-art global search strategies the CMA evolution strategy achieves superior performance on multimodal, non-separable test functions without intricate parameter tuning.