Faster Convergence in Multi-Objective Optimization Algorithms Based on Decomposition

TL;DR

This paper investigates how the Partial Update Strategy in MOEA/D enhances convergence speed and search space exploration, effectively balancing performance similar to small and large population sizes across various multi-objective problems.

Contribution

It provides an in-depth analysis of MOEA/D with Partial Update, revealing its ability to improve convergence and exploration, mitigating population size issues in multi-objective optimization.

Findings

MOEA/D with Partial Update matches small population size in convergence speed

It explores the search space as effectively as large population MOEA/D

It improves hypervolume and diversity metrics across multiple problems

Abstract

The Resource Allocation approach (RA) improves the performance of MOEA/D by maintaining a big population and updating few solutions each generation. However, most of the studies on RA generally focused on the properties of different Resource Allocation metrics. Thus, it is still uncertain what the main factors are that lead to increments in performance of MOEA/D with RA. This study investigates the effects of MOEA/D with the Partial Update Strategy in an extensive set of MOPs to generate insights into correspondences of MOEA/D with the Partial Update and MOEA/D with small population size and big population size. Our work undertakes an in-depth analysis of the populational dynamics behaviour considering their final approximation Pareto sets, anytime hypervolume performance, attained regions and number of unique non-dominated solutions. Our results indicate that MOEA/D with Partial Update progresses with the search as fast as MOEA/D with small population size and explores the search space as MOEA/D with big population size. MOEA/D with Partial Update can mitigate common problems related to population size choice with better convergence speed in most MOPs, as shown by the results of hypervolume and number of unique non-dominated solutions, the anytime performance and Empirical Attainment Function indicates.