Evolution strategies with exclusion-based selection operators and a Fourier series auxiliary function

Abstract

To improve the efficiencies of evolutionary algorithms (EAs), we have proposed a highly efficient speed-up strategy in our previous research work: the exclusion-based selection operators. These operators could efficiently prevent the individuals of EAs from getting into the attractions of local optima through the search space shrinking method. However, when a global optimum of a minimization problem is located in a very narrow attraction, the exclusion-based selection operators may not be able to find this narrow attraction and delete this global optimum mistakenly, making the algorithm unreliable. In this paper, we propose a new complementary efficient speed-up strategy—the Fourier series auxiliary function. This strategy could guide an algorithm to search for optima with narrow attractions efficiently and effectively, and compensate the deficiency of the exclusion-based selection operators on the algorithm’s reliability. We combine these two strategies together to search the global optima in parallel, one for optima in normal attractions and the other for optima in very narrow attractions respectively. Incorporation of these two strategies with any known evolutionary algorithm leads to an accelerated version of the algorithm. As a case study, the new strategies have been incorporated into evolution strategies (ES), yielding an accelerated exclusion and Fourier series auxiliary function ES: the EFES. The EFES is experimentally tested with a test suite containing 10 complex multimodal function optimization problems and compared against the standard ES (SES) and the fast ES (FES). The experiments all demonstrate that the EFES consistently and significantly outperforms other two ES in efficiency and solution quality.