Multilevel Neider Mead´s simplex method

Nelder-Mead´s simplex (NMS) algorithm has been the work horse for numerous problems in various fields of engineering since its introduction in 1965 [1, 2]. Being a multi dimensional direct search method its performance is commendable for unconstrained local optimization problems. Despite its popularity NMS fails to converge for higher dimensional problems. In this paper a modification to the basic algorithm is proposed using multilevel approach (is named as MNMS). Also modifications to the parameters used in MNMS have been proposed with the help of sensitivity analysis. MNMS is able to capture the optimum for higher dimensional problems with (i) higher success rate and (ii) faster convergence. Numerical experiments with higher dimensional problems have demonstrated the superiority of MNMS over a class of algorithms based on NMS.