A hybrid evolutionary-simplex search method to solve nonlinear constrained optimization problems

This research article presents a novel design of a hybrid evolutionary-simplex search method to solve the class of general nonlinear constrained optimization problems. In this article, the particle swarm optimization (PSO) method and the Nelder–Mead (NM) simplex search algorithm are utilized in a unified way to enhance the overall performance of the proposed solution method. The NM algorithm is used as an integrative step in the PSO method to reinforce the convergence of the PSO method and overcome the global search weakness in the NM algorithm. On the other hand, a penalty function technique is embedded in the proposed method to solve constrained optimization problems. Two levels of numerical experiments were conducted to evaluate the proposed method. First, a comparison is conducted with well-known benchmark problems. Second, the proposed method is tested in solving three engineering design optimization problems. In addition, the results of the proposed method were compared to optimization methods published in the literature in three main criteria: effectiveness, efficiency and robustness. The results show the competitive performance of the proposed method in this article.