Diversity Enhancement via Magnitude

TL;DR

This paper introduces a novel approach using the theory of magnitude to systematically enhance diversity in candidate solutions for multi-objective evolutionary algorithms, improving their performance on benchmark problems.

Contribution

It develops a magnitude-based framework to manipulate solution sets, providing a new method for diversity promotion in evolutionary algorithms.

Findings

Effective diversity enhancement on benchmark problems

Framework applicable to leading evolutionary algorithms

Extensions of the approach discussed

Abstract

Promoting and maintaining diversity of candidate solutions is a key requirement of evolutionary algorithms in general and multi-objective evolutionary algorithms in particular. In this paper, we use the recently developed theory of magnitude to construct a gradient flow and similar notions that systematically manipulate finite subsets of Euclidean space to enhance their diversity, and apply the ideas in service of multi-objective evolutionary algorithms. We demonstrate diversity enhancement on benchmark problems using leading algorithms, and discuss extensions of the framework.