Design and Analysis of Diversity-Based Parent Selection Schemes for Speeding Up Evolutionary Multi-objective Optimisation

TL;DR

This paper introduces diversity-based parent selection strategies in evolutionary multi-objective optimization, demonstrating through theoretical analysis and experiments that these methods improve performance by focusing on less explored regions.

Contribution

It proposes and analyzes diversity-based parent selection mechanisms for evolutionary algorithms, showing their effectiveness in speeding up convergence on benchmark problems.

Findings

Diversity-based parent selection improves optimization speed.

Theoretical analysis confirms benefits on benchmark functions.

Experimental results align with theoretical predictions.

Abstract

Parent selection in evolutionary algorithms for multi-objective optimisation is usually performed by dominance mechanisms or indicator functions that prefer non-dominated points. We propose to refine the parent selection on evolutionary multi-objective optimisation with diversity-based metrics. The aim is to focus on individuals with a high diversity contribution located in poorly explored areas of the search space, so the chances of creating new non-dominated individuals are better than in highly populated areas. We show by means of rigorous runtime analysis that the use of diversity-based parent selection mechanisms in the Simple Evolutionary Multi-objective Optimiser (SEMO) and Global SEMO for the well known bi-objective functions ${\rm O{\small NE}M{\small IN}M{\small AX}}$ and ${\rm LOTZ}$ can significantly improve their performance. Our theoretical results are accompanied by experimental studies that show a correspondence between theory and empirical results and motivate further theoretical investigations in terms of stagnation. We show that stagnation might occur when favouring individuals with a high diversity contribution in the parent selection step and provide a discussion on which scheme to use for more complex problems based on our theoretical and experimental results.