The Effects of CMA-ES Style Selection and Restart Criteria on DE

Abstract

Over the years, a lot of research has gone into the creation of different mutation operators and adaptive parameters for differential evolution (DE). However, the literature is fairly quiet about automatically setting population size and completely silent about varying the selection operator used within DE. In this paper, we steal a page from CMA-ES/IPOP: using ES-style µ+λ selection, which selects across the entire population, in place of more individualistic DE selection with its use of local selection on the target and its child. We find that the most effective choice of selection can depend on the function being optimized, although for most of the functions we tested, the original DE selection was preferable. When adding IPOP style restarting, EqualFunValHist is the most applicable of the stagnation criteria, and it is used to trigger the doubling of the population size upon restart. The initial population size is set to the same as CMA-ES. Here we find, that the restartable DE behave as well and better as regular DE with population size set as lower than the default settings used.