When to Truncate the Archive? On the Effect of the Truncation Frequency in Multi-Objective Optimisation
Zhiji Cui, Zimin Liang, Lie Meng Pang, Hisao Ishibuchi, Miqing Li
TL;DR
The work addresses when to truncate an archive of nondominated solutions in MOEAs by comparing immediate, batch, and unbounded truncation across five representative MOEAs. It demonstrates that immediate truncation frequently yields the best trade-off between quality and diversity, while unbounded archiving can incur substantial loss due to cumulative truncation error, especially with one-by-one removal strategies. The findings highlight the need for effective subset-selection techniques for large archives and suggest that standard population-maintenance truncation methods may be ill-suited for unbounded archiving. Collectively, the results inform practical archiving strategies and point to directions for developing truncation methods tailored to large or unbounded archives.
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.