Benchmarking Stopping Criteria for Evolutionary Multi-objective Optimization

2026-04-28

AI Summary

This work addresses the lack of effective evaluation methodologies for stopping criteria in evolutionary multi-objective optimization, a limitation that has hindered progress in the field. To this end, it proposes the first comprehensive benchmarking framework specifically designed for assessing stopping criteria. The framework introduces several innovations, including a scalar performance metric, standardized encoding of population states, and a file-based reproducible testing protocol. These components collectively enable unified, efficient, and reproducible evaluation of stopping criteria while significantly reducing storage overhead and enhancing comparative efficiency. The authors conduct systematic experiments evaluating five representative stopping criteria, demonstrating the effectiveness and practical utility of the proposed framework.

Abstract

Stopping criteria automatically determine when to stop an evolutionary algorithm, so as not to waste function evaluations on a stagnant population. Although stopping criteria play an important role in real-world applications, they have attracted little attention in the evolutionary multi-objective optimization (EMO) community. In fact, new stopping criteria for EMO have been rarely developed in recent years. One reason for the stagnation in developing stopping criteria for EMO is a lack of effective benchmarking methodologies. To address this issue, this paper proposes (i) a performance measure of stopping criteria for EMO and (ii) a file-based benchmarking approach. This paper also proposes (iii) a data representation method that effectively stores population states in text files. (i) The proposed measure represents the performance of stopping criteria as a single scalar value, making comparison easy. (ii) The proposed file-based approach not only simplifies the benchmarking process but also facilitates reproducibility. (iii) The proposed data representation method addresses the issue of file size in (ii). We demonstrate the effectiveness of our three contributions (i)--(iii) by benchmarking five representative stopping criteria for EMO.

Problem

• stopping criteria
• evolutionary multi-objective optimization
• benchmarking
• performance evaluation

Innovation

• stopping criteria
• evolutionary multi-objective optimization
• benchmarking
• performance measure
• file-based evaluation