Effects of Pareto Set on the Performance of Problem Reformulation-Based Large-Scale Multiobjective Optimization Algorithms

Recently, a number of evolutionary algorithms (EAs) have been proposed for large-scale multiobjective optimization. Among them, due to the high efficiency, the problem reformulation-based large-scale multiobjective optimization framework (LSMOF) has shown to be promising. By associating the weight variables with a set of specific bi-directional vectors representing search directions, LSMOF reformulates the original large-scale multiobjective optimization problem (LSMOP) into a low-dimensional single-objective optimization problem (SOP). For the reformulated SOP, the weight variables are as the decision vector and the hypervolume is as the objective. In many recently proposed competitive EAs for large-scale multiobjective optimization, the promising search directions are also specified similar to the bi-directional vectors of LSMOF. The aim of this paper is to point out some challenges in the construction of bi-directional vectors in LSMOF. We first verify that the lower and upper boundary points from which the bi-directional vectors are generated are crucial to the good performance of LSMOF on the LSMOP test suite. Then, for demonstrating how LSMOF performs when the Pareto set (PS) is changed, a new test suite is designed. The experimental results show that the performance of LSMOF will deteriorate rapidly on the problems with the new PS.