Self-adaptive differential evolution for dynamic environments with fluctuating numbers of optima

Abstract

Despite the fact that evolutionary algorithms often solve static problems successfully, dynamic optimization problems tend to pose a challenge to evolutionary algorithms [21]. Differential evolution (DE) is one of the evolutionary algorithms that does not scale well to dynamic environments due to lack of diversity [35]. A significant body of work exists on algorithms for optimizing dynamic problems (see Section 1.3). Recently, several algorithms based on DE have been proposed [19][26][28][27][10]. Benchmarks used to evaluate algorithms aimed at dynamic optimization (like the moving peaks benchmark [5] and the generalized benchmark generator [17] [16]), typically focus on problems where a constant number of optima moves around a multi-dimensional search space. While some of these optima may be obscured by others, these benchmarks do not simulate problems where new optima are introduced, or current optima are removed from the search space. Dynamic Population DE (DynPopDE) [27] is a DE-based algorithm aimed at dynamic optimization problems where the number of optima fluctuates over time. This chapter describes the subcomponents of DynPopDE and then investigates the effect of hybridizing DynPopDE with the self-adaptive component of jDE [10] to form a new algorithm, Self-Adaptive DynPopDE (SADynPopDE). The following sections describe dynamic environments and the benchmark function used in this study. Related work by other researchers is presented in Section 1.3. Differential evolution is described in Section 1.4. The components of DynPopDE, the base algorithm used in this study, are described and motivated in Section 1.5. The incorporation of self-adaptive control parameters into DynPopDE to form SA- DynPopDE and the experimental comparison of these algorithms are described in Section 1.6. The main conclusions of this study are summarized in Section 1.7.