Finding multiple solutions of multimodal optimization using spiral optimization algorithm with clustering

Abstract

A Multimodal optimization is one of the interesting problems in optimization which arises frequently in a wide range of engineering and practical applications. The goal of this problem is to find all of optimum solutions in a single run. Some algorithms fail to find all solutions that have been proven their existence analytically. In our paper [1], a method is proposed to find the roots of a system of non-linear equations using a clustering technique that combine with Spiral Optimization algorithm and Sobol sequence of points. An interesting benefit using this method is that the same inputs will give the same results. Most of the time this does not happen in meta-heuristic algorithms using random factors. Now the method is modified to find solutions of multimodal optimization problems. Generally in an optimization problem, the differential form of the objective function is needed. In this paper, the proposed method is to find optimum points of general multimodal functions that its differential form is not required. Several problems with benchmark functions have been examined using our method and they give good result.