Not Just for Archiving: Provable Benefits of Reusing the Archive in Evolutionary Multi-objective Optimization

TL;DR

This paper demonstrates that reusing archived solutions in evolutionary multi-objective optimization algorithms can significantly improve performance and speed, especially on complex problems, by providing theoretical proofs and practical experiments.

Contribution

It provides the first analytical proof that reusing archive solutions in MOEAs offers polynomial speedup and overcomes limitations of small populations, validated through experiments.

Findings

Reusing archive solutions can outperform large population approaches.

Small populations without archive reuse may fail on certain problems.

Theoretical analysis shows polynomial speedup from archive reuse.

Abstract

Evolutionary Algorithms (EAs) have become the most popular tool for solving widely-existed multi-objective optimization problems. In Multi-Objective EAs (MOEAs), there is increasing interest in using an archive to store non-dominated solutions generated during the search. This approach can 1) mitigate the effects of population oscillation, a common issue in many MOEAs, and 2) allow for the use of smaller, more practical population sizes. In this paper, we analytically show that the archive can even further help MOEAs through reusing its solutions during the process of new solution generation. We first prove that using a small population size alongside an archive (without incorporating archived solutions in the generation process) may fail on certain problems, as the population may remove previously discovered but promising solutions. We then prove that reusing archive solutions can overcome this limitation, resulting in at least a polynomial speedup on the expected running time. Our analysis focuses on the well-established SMS-EMOA algorithm applied to the commonly studied OneJumpZeroJump problem as well as one of its variants. We also show that reusing archive solutions can be better than using a large population size directly. Finally, we show that our theoretical findings can generally hold in practice by experiments on well-known practical optimization problems -- multi-objective 0-1 Knapsack, TSP, QAP and NK-landscape problems -- with realistic settings.