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.
Nature-inspired algorithms attract many researchers worldwide for solving the hardest optimization problems. One of the well-known members of this extensive family is the evolutionary strategy ES algorithm. To date, many variants of this algorithm have emerged for solving continuous as well as combinatorial problems. One of the more promising variants, a self-adaptive evolutionary algorithm, has recently been proposed that enables a self-adaptation of its control parameters. In this paper, we discuss and evaluate popular common and self-adaptive evolutionary strategy (ES) algorithms. In particular, we present an empirical comparison between three self-adaptive ES variants and common ES methods. In order to assure a fair comparison, we test the methods by using a number of well-known unimodal and multimodal, separable and non-separable, benchmark optimization problems for different dimensions and population size. The results of this experiments study were promising and have encouraged us to invest more efforts into developing in this direction.
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.
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