Analysis of inter and intra-front operations in multi-modal multi-objective optimization problems

Abstract

Many real-world multi-objective optimization problems inherently have multiple multi-modal solutions and it is in fact very important to capture as many of these solutions as possible. Several crowding distance methods have been developed in the past few years to approximate the optimal solution in the search space. In this paper, we discuss some of the shortcomings of the crowding distance-based methods such as inaccurate estimates of the density of neighboring solutions in the search space. We propose a new classification for the selection operations of Pareto-based multi-modal multi-objective optimization algorithms. This classification is based on utilizing nearby solutions from other fronts to calculate the crowding values. Moreover, to address some of the drawbacks of existing crowding methods, we propose two algorithms whose selection mechanisms are based on each of the introduced types of selection operations. These algorithms are called NxEMMO and ES-EMMO. Our proposed algorithms are evaluated on 14 test problems of various complexity levels. According to our results, in most cases, the NxEMMO algorithm with the proposed selection mechanism produces more diverse solutions in the search space in comparison to other competitive algorithms.