Incorporating Nelder-Mead Simplex as an Accelerating Operator to Improve the Performance of Metaheuristics in Nonlinear System Identification

This chapter explores the use of Nelder-Mead simplex (NMS) as an accelerating operator to improve the performance of metaheuristic algorithms, which are commonly used for solving complex optimization problems. NMS is a search method that forms a simplex of points, iteratively transforming it to find the optimal solution. The incorporation of NMS in metaheuristic algorithms can significantly enhance the convergence speed and solution quality. The solutions in each iteration are modified by several operations of reflection, contraction, and expansion to enhance the algorithm. A case study of nonlinear system identification in structural dynamics is presented. The problem is defined to estimate the parameters of the modified Bouc-Wen model of a magnetorheological damper (MRD). The results demonstrate that the incorporation of NMS accelerates and improves the performance of each algorithm. The proposed methods offer a promising solution for enhancing the performance of metaheuristic algorithms in solving complex optimization problems.