Finding multiple solutions for multimodal optimization problems using a multi-objective evolutionary approach

Abstract

In a multimodal optimization task, the main purpose is to find multiple optimal (global and local) solutions associated with a single objective function. Starting with the preselection method suggested in 1970, most of the existing evolutionary algorithms based methodologies employ variants of niching in an existing single-objective evolutionary algorithm framework so that similar solutions in a population are de-emphasized in order to focus and maintain multiple distant yet near-optimal solutions. In this paper, we use a completely different and generic strategy in which a single-objective multimodal optimization problem in converted into a suitable bi-objective optimization problem so that all local and global optimal solutions become members of the resulting weak Pareto-optimal set. We solve up to 16-variable test-problems having as many as 48 optima and also demonstrate successful results on constrained multimodal test-problems, suggested for the first time. The concept of using multi-objective optimization for solving single-objective multimodal problems seems novel and interesting, and importantly opens further avenues for research.