Generalized Lehmer Mean for Success History based Adaptive Differential Evolution

Vladimir Stanovov, Shakhnaz Akhmedova, Eugene Semenkin, Mariia Semenkina

Abstract

The Differential Evolution (DE) is a highly competitive numerical optimization algorithm, with a small number of control parameters. However, it is highly sensitive to the setting of these parameters, which inspired many researchers to develop adaptation strategies. One of them is the popular Success-History based Adaptation (SHA) mechanism, which significantly improves the DE performance. In this study, the focus is on the choice of the metaparameters of the SHA, namely the settings of the Lehmer mean coefficients for scaling factor and crossover rate memory cells update. The experiments are performed on the LSHADE algorithm and the Congress on Evolutionary Computation competition on numerical optimization functions set. The results demonstrate that for larger dimensions the SHA mechanism with modified Lehmer mean allows a significant improvement of the algorithm efficiency. The theoretical considerations of the generalized Lehmer mean could be also applied to other adaptive mechanisms.

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