Differential Evolution with Adaptive Mutation and Parameter Control Using Lévy Probability Distribution

Differential evolution (DE) has become a very popular and effective global optimization algorithm in the area of evolutionary computation. In spite of many advantages such as conceptual simplicity, high e眂iency and ease of use, DE has two main components, i.e., mutation scheme and parameter control, which significantly influence its performance. In this paper we intend to improve the performance of DE by using carefully considered strategies for both of the two components. We first design an adaptive mutation scheme, which adaptively makes use of the bias of superior individuals when generating new solutions. Although introducing such a bias is not a new idea, existing methods often use heuristic rules to control the bias. They can hardly maintain the appropriate balance between exploration and exploitation during the search process, because the preferred bias is often problem and evolution-stage dependent. Instead of using any fixed rule, a novel strategy is adopted in the new adaptive mutation scheme to adjust the bias dynamically based on the identified local fitness landscape captured by the current population. As for the other component, i.e., parameter control, we propose a mechanism by using the Lévy probability distribution to adaptively control the scale factor F of DE. For every mutation in each generation, an F_i is produced from one of four different Lévy distributions according to their historical performance. With the adaptive mutation scheme and parameter control using Lévy distribution as the main components, we present a new DE variant called Lévy DE (LDE). Experimental studies were carried out on a broad range of benchmark functions in global numerical optimization. The results show that LDE is very competitive, and both of the two main components have contributed to its overall performance. The scalability of LDE is also discussed by conducting experiments on some selected benchmark functions with dimensions from 30 to 200.