The Nelder-Mead Simplex Method with Variables Partitioning for Solving Large Scale Optimization Problems

Abstract

This paper presents a novel method to solve unconstrained continuous optimization problems. The proposed method is called SVP (simplex variables partitioning). The SVP method uses three main processes to solve large scale optimization problems. The first process is a variable partitioning process which helps our method to achieve high performance with large scale and high dimensional optimization problems. The second process is an exploration process which generates a trail solution around a current iterate solution by applying the Nelder-Mead method in a random selected partitions. The last process is an intensification process which applies a local search method in order to refine the the best solution so far. The SVP method starts with a random initial solution, then it is divided into partitions. In order to generate a trail solution, the simplex Nelder-Mead method is applied in each partition by exploring neighborhood regions around a current iterate solution. Finally the intensification process is used to accelerate the convergence in the final stage. The performance of the SVP method is tested by using 38 benchmark functions and is compared with 2 scatter search methods from the literature. The results show that the SVP method is promising and producing good solutions with low computational costs comparing to other competing methods.

This work was partially supported by Grant of SGS No. SP2013/70, VSB - Technical University of Ostrava, Czech Republic., and was supported by the European Regional Development Fund in the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070) and by the Bio-Inspired Methods: research, development and knowledge transfer project, reg. no. CZ.1.07/2.3.00/20.0073 funded by Operational Programme Education for Competitiveness, co-financed by ESF and state budget of the Czech Republic.