Solving Mono- and Multi-Objective Problems Using Hybrid Evolutionary Algorithms and Nelder-Mead Method

Abstract

Evolution strategies (ES) are a family of strong stochastic methods for global optimization and have proved their capability in avoiding local optima more than other optimization methods. Many researchers have investigated different versions of the original evolution strategy with good results in a variety of optimization problems. However, the convergence rate of the algorithm to the global optimum stays asymptotic. In order to accelerate the convergence rate, a hybrid approach is proposed using the nonlinear simplex method (Nelder-Mead) and an adaptive scheme to control the local search application, and the authors demonstrate that such combination yields significantly better convergence. The new proposed method has been tested on 15 complex benchmark functions and applied to the bi-objective portfolio optimization problem and compared with other state-of-the-art techniques. Experimental results show that the performance is improved by this hybridization in terms of solution eminence and strong convergence.

Application of Evolutionary Artificial Intelligence. An Exploratory Literature Review

“…For the distribution of various unmanned aircraft tasks, a multi-objective evolutionary algorithm named D-NAGA-III was proposed, which effectively optimizes military tasks. Boukhari et al [16] improved the hybrid approach of evolutionary strategies and multi-objective optimization to accelerate the speed of convergence and applied it to two-objective portfolio optimization.…”