An Efficient Hybrid Evolution Strategy Algorithm with Direct Search Method for Global Optimization

Abstract

The main purpose of this article is to demonstrate how evolution strategy optimizers can be improved by incorporating an efficient hybridization scheme with restart strategy in order to jump out of local solution regions. The authors propose a hybrid (μ, λ)ES-NM algorithm based on the Nelder-Mead (NM) simplex search method and evolution strategy algorithm (ES) for unconstrained optimization. At first, a modified NM, called Adaptive Nelder-Mead (ANM) is used that exhibits better properties than standard NM and self-adaptive evolution strategy algorithm is applied for better performance, in addition to a new contraction criterion is proposed in this work. (μ, λ)ES-NM is balancing between the global exploration of the evolution strategy algorithm and the deep exploitation of the Nelder-Mead method. The experiment results show the efficiency of the new algorithm and its ability to solve optimization problems in the performance of accuracy, robustness, and adaptability.