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

2025-08-23

AI Summary

Evolutionary multi-objective optimization (EMO) suffers from loss of high-quality solutions and slow convergence due to population oscillation and small population sizes. Method: This paper proposes an archive solution reutilization mechanism, which strategically reintegrates non-dominated solutions from the external archive into the evolutionary process. Contribution/Results: Theoretically, we provide the first rigorous analysis showing that, within the SMS-EMOA framework, archive reutilization breaks the runtime bottleneck of conventional approaches—achieving polynomial expected speedup, outperforming mere population expansion—on benchmark problems including OneJumpZeroJump and its variants. Empirically, the mechanism significantly improves convergence speed and solution set quality across canonical multi-objective benchmarks: 0–1 knapsack, TSP, QAP, and NK-landscape. These results demonstrate that archive reutilization offers both theoretical guarantees and practical efficacy, establishing a novel paradigm for knowledge transfer in EMO.

Technology Category

• Search and Optimization: Evolutionary Computation
• Multiagent Systems: Mechanism Design
• Data Mining & Knowledge Management: Data Compression

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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 four well-known practical optimization problems -- multi-objective 0-1 Knapsack, TSP, QAP and NK-landscape problems -- with realistic settings.

Problem

• Reusing archive solutions improves evolutionary multi-objective optimization efficiency
• Addresses population oscillation and solution loss in small population MOEAs
• Achieves polynomial speedup in expected running time through archive reuse

Innovation

• Reusing archive solutions for polynomial speedup
• Overcoming limitations of small population sizes
• Enhancing MOEAs through archived solution integration