Techniques for Highly Multiobjective Optimisation: Some Nondominated Points are Better than Others

TL;DR

This paper investigates ranking methods for nondominated solutions in many-objective evolutionary optimization, finding that simple average ranking variants often outperform other approaches across diverse problem settings.

Contribution

It introduces and compares various ranking methods for nondominated points, highlighting the effectiveness of simple average ranking strategies in many-objective EMO.

Findings

Simple average ranking variants outperform other methods.

Ranking methods improve selection in many-objective EMO.

Performance is consistent across problems with 5-20 objectives.

Abstract

The research area of evolutionary multiobjective optimization (EMO) is reaching better understandings of the properties and capabilities of EMO algorithms, and accumulating much evidence of their worth in practical scenarios. An urgent emerging issue is that the favoured EMO algorithms scale poorly when problems have many (e.g. five or more) objectives. One of the chief reasons for this is believed to be that, in many-objective EMO search, populations are likely to be largely composed of nondominated solutions. In turn, this means that the commonly-used algorithms cannot distinguish between these for selective purposes. However, there are methods that can be used validly to rank points in a nondominated set, and may therefore usefully underpin selection in EMO search. Here we discuss and compare several such methods. Our main finding is that simple variants of the often-overlooked Average Ranking strategy usually outperform other methods tested, covering problems with 5-20 objectives and differing amounts of inter-objective correlation.