Towards Enhancing Solution Space Diversity in Multi-Objective Optimization: a Hypervolume-Based Approach

Abstract

Diversity is an important notion in multi-objective evolutionary algorithms (MOEAs) and a lot of researchers have investigated this issue by means of appropriate methods. However most of evolutionary multi-objective algorithms have attempted to take control on diversity in the objective space only and maximized diversity of solutions (population) on Pareto-front. Nowadays due to importance of Multi-objective optimization in industry and engineering, most of the designers want to find a diverse set of Pareto-optimal solutions which cover as much as space in its feasible regain of the solution space. This paper addresses this issue and attempt to introduce a method for preserving diversity of non-dominated solution (i.e. Pareto-set) in the solution space. This paper introduces the novel diversity measure as a first time, and then this new diversity measure is integrated efficiently into the hypervolume based Multi-objective method. At end of this paper we compare the proposed method with other state-of-the-art algorithms on well-established test problems. Experimental results show that the proposed method outperforms its competitive MOEAs respect to the quality of solution space criteria and Pareto-set approximation.