An Improvement Evolutionary Algorithm Based on Grid-Based Pareto Dominance for Many-Objective Optimization

Abstract

Pareto dominance based Multi-objective Evolutionary Algorithms (MOEAs) is an effective method for solving multi-objective problems with two or three objectives. However, in many-objective problems, the determination of the solution set scale is a challenge which highly limits the performance of existing MOEAs. The small quantity of solution set in MOEA may lead to large non-dominance area which dramatically reduces the selection pressure, while large scale solution set will inevitably increases the time and memory consumption. In order to solve this problem, in this paper, a grid-based Pareto dominance approach is proposed for many-objective problem. In this approach, one single solution is used to create the non-dominance area which approximates that used to be determined by a set of solutions in MOEA. Moreover, in this approach, both the selection pressure, diversity of solutions and time and memory consumption are taken into consideration by utilizing the smallest number of virtual solutions to determine whether a solution is a non-dominance solution. In this paper, a new MOEA based on the grid-based Pareto dominance is designed for many-objective problems. In the experiment, the well-known algorithms and relaxed forms of Pareto dominance are used to compare with the algorithm and the grid-based Pareto dominance. The experimental results show that the proposed approaches can guide the search for many-objective spaces to converge to the true PF and maintain the diversity of solutions.