Differential evolution with dynamic strategy and parameter selection by detecting landscape modality

Differential Evolution (DE) is an evolutionary algorithm. DE has been successfully applied to optimization problems including non-linear, non-differentiable, non-convex and multimodal functions. There are several mutation strategies such as the best and the rand strategy in DE. It is known that the best strategy is suitable for unimodal problems and the rand strategy is suitable for multimodal problems. However, the landscape of a problem to be optimized is often unknown and the landscape is changing dynamically while the search process proceeds. In this study, we propose a new and simple method that detects the modality of landscape being searched: unimodal or not unimodal. In the method, some points on the line connecting the centroid of search points and the best search point are sampled. When the objective values of the sampled points are changed decreasingly and then increasingly, it is thought that one valley exists. If there exists only one valley, the landscape is unimodal and a greedy strategy like the best strategy is adopted. Otherwise, the rand strategy is adopted. Also, the sampled points realize global search in the region spanned by all search points and realize local search near the best search point. The effect of the proposed method is shown by solving some benchmark problems.