Pareto Dominance-Based Algorithms With Ranking Methods for Many-Objective Optimization

Abstract

In Pareto dominance-based multi-objective evolutionary algorithms (PDMOEAs), Pareto dominance fails to provide the essential selection pressure required to drive the search toward convergence in many-objective optimization problems (MaOPs). Recently, the idea of using secondary criterion, such as knee points and so on to enhance the convergence, is becoming popular. In this paper, we propose to employ popular ranking methods—average rank (AR) and weighted sum (WS) of objectives, which are capable of accelerating the convergence as secondary criterion. After nondominated sorting, based on the secondary criterion employed (AR or WS) and a niche radius, nondominated solutions are assigned a rank referred to as priority rank (PR). In other words, among a set of nondominated solutions, solutions that are diverse and best within a neighborhood in terms of ranking method (AR or WS) employed are assigned a better PR. During mating and environmental selections, giving preference to solutions with least PR enables the selection of solutions that are diverse and can improve the convergence speed of MOEA without the need for additional diversity maintenance mechanisms. The performances of proposed PDMOEAs with ranking methods are compared with the state-of-the-art methods to demonstrate the significance of ranking methods in accelerating the convergence. PDMOEA with AR as secondary criterion is referred to as PDMOEA-AR while PDMOEA with WS as secondary criterion is referred to as PDMOEA-WS. From the experimental results, it has been observed that PDMOEAs with ranking methods (PDMOEA-AR and PDMOEA-WS) outperform the state-of-the-art algorithms on benchmark MaOPs, such as DTLZ and WFG. In addition, it has been observed that PDMOEA-AR performs better on a wide variety of MaOPs with diverse characteristics whereas PDMOEA-WS is particularly suitable for only a subclass of MaOPs. In other words, the range-independent nature of AR makes PDMOEA-AR a general-purpose algorithm, which performs better on a wide variety of problems.