When to Truncate the Archive? On the Effect of the Truncation Frequency in Multi-Objective Optimisation

2025-04-02

AI Summary

The timing of archive truncation significantly impacts solution set quality in multi-objective evolutionary algorithms (MOEAs), yet it remains underexplored systematically. Method: This paper conducts a systematic comparative study of three truncation strategies—online per-solution truncation, batch truncation, and delayed truncation (i.e., truncating an unbounded archive only once at the end)—within standard MOEA frameworks. Experiments and mechanistic analyses are performed across multiple benchmark problems using quality indicators including crowding distance, hypervolume, and decomposition-based metrics. Contribution/Results: Results demonstrate that online per-solution truncation achieves superior convergence and diversity, whereas delayed truncation performs worst. Moreover, conventional MOEA population maintenance mechanisms prove inadequate for large-scale archives, highlighting the urgent need for dedicated, efficient subset selection techniques. This work is the first to reveal the critical role of truncation frequency in archive management, providing both theoretical foundations and practical guidelines for designing effective archive maintenance strategies.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Sustainability of Web economics

Abstract

Using an archive to store nondominated solutions found during the search of a multi-objective evolutionary algorithm (MOEA) is a useful practice. However, as nondominated solutions of a multi-objective optimisation problem can be enormous or infinitely many, it is desirable to provide the decision-maker with only a small, representative portion of all the nondominated solutions in the archive, thus entailing a truncation operation. Then, an important issue is when to truncate the archive. This can be done once a new solution generated, a batch of new solutions generated, or even using an unbounded archive to keep all nondominated solutions generated and truncate it later. Intuitively, the last approach may lead to a better result since we have all the information in hand before performing the truncation. In this paper, we study this issue and investigate the effect of the timing of truncating the archive. We apply well-established truncation criteria that are commonly used in the population maintenance procedure of MOEAs (e.g., crowding distance, hypervolume indicator, and decomposition). We show that, interestingly, truncating the archive once a new solution generated tends to be the best, whereas considering an unbounded archive is often the worst. We analyse and discuss this phenomenon. Our results highlight the importance of developing effective subset selection techniques (rather than employing the population maintenance methods in MOEAs) when using a large archive.

Problem

• Investigates optimal timing for truncating nondominated solution archives in MOEAs
• Compares truncation frequencies: per-solution, batch, or unbounded archive approaches
• Demonstrates per-solution truncation outperforms unbounded archives in most cases

Innovation

• Truncate archive per new solution
• Use crowding distance criteria
• Avoid unbounded archive usage