Abstract. To improve the efficiency of the currently known evolutionary algorithms, we have proposed two complementary efficiency speed-up strategies in our previous research work respectively: the exclusion-based selection operators and the Fourier series auxiliary function. In this paper, we combine these two strategies together to search the global optima in parallel, one for optima in large attraction basins and the other for optima in very narrow attraction basins respectively. They can compliment each other to improve evolutionary algorithms (EAs) on efficiency and safety. In a case study, the two strategies have been incorporated into evolution strategies (ES), yielding a new type of 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). The experiments all demonstrate that the EFES consistently and sig...