Pseudo multi-population differential evolution for multimodal optimization

Multimodal optimization aims at locating multiple optima in a run, which has two main advantages over traditional single objective global optimization. First, it would be useful to provide multiple solutions since some solutions may be hard to realize physically. Second, a multimodal algorithm is not so easy to get stuck in a local optimum. In recent years, multi-population evolutionary algorithms have been used for multimodal optimization. However, their ability to locate multiple peaks is limited by the number of populations used. It is difficult to find out all the peaks if the populations are fewer than the peaks. When algorithms increase the number of populations, they have to maintain huge population sizes and hence encounter lower search efficiency. This paper overcomes such deficiencies by proposing a pseudo multi-population differential evolution (p-MPDE). The p-MPDE employs a small exemplar population to conduct normal DE operation. Each other individual uses the differential of two randomly chosen members in the exemplar population to mutate themselves and evolve. Each such individual represents a pseudo population and promises to find a global or local optimum. In the experiment, p-MPDE was compared to other state-of-the-art multimodal algorithms and the result shows that p-MPDE outperforms R3PSO, LIPS and CDE on CEC2013 niching benchmark.