Evolution Strategies with a Fourier Series Auxiliary Function for Difficult Function Optimization

Abstract

Through identifying the main causes of low efficiency of the currently known evolutionary algorithms for difficult function optimization problem, the complementary efficiency speed-up strategy—Fourier series auxiliary function technique is suggested, analyzed, and partially explored. The Fourier series auxiliary function could guide an algorithm to search for optima with small attraction basins efficiently. Incorporation of this technique with any known evolutionary algorithm leads to an accelerated version of the algorithm for the difficult function optimization. As a case study, the developed technique has been incorporated with evolution strategies (ES), yielding accelerated Fourier series auxiliary function evolution strategies: the FES. The experiments demonstrate that the FES consistently outperforms the standard ES in efficiency and solution quality.