Most multi-objective optimisation algorithms maintain an archive explicitly or implicitly during their search. Such an archive can be solely used to store high-quality solutions presented to the decision maker, but in many cases may participate in the search process (e.g., as the population in evolutionary computation). Over the last two decades, archiving, the process of comparing new solutions with previous ones and deciding how to update the archive/population, stands as an important issue in evolutionary multi-objective optimisation (EMO). This is evidenced by constant efforts from the community on developing various effective archiving methods, ranging from conventional Pareto-based methods to more recent indicator-based and decomposition-based ones. However, the focus of these efforts is on empirical performance comparison in terms of specific quality indicators; there is lack of systematic study of archiving methods from a general theoretical perspective. In this paper, we attempt to conduct a systematic overview of multi-objective archiving, in the hope of paving the way to understand archiving algorithms from a holistic perspective of theory and practice, and more importantly providing a guidance on how to design theoretically desirable and practically useful archiving algorithms. In doing so, we also present that archiving algorithms based on weakly Pareto compliant indicators (e.g., epsilon-indicator), as long as designed properly, can achieve the same theoretical desirables as archivers based on Pareto compliant indicators (e.g., hypervolume indicator). Such desirables include the property limit-optimal, the limit form of the possible optimal property that a bounded archiving algorithm can have with respect to the most general form of superiority between solution sets.

翻译：大多数多目标优化算法在搜索过程中会显式或隐式地维护一个归档。该归档不仅可用于存储向决策者呈现的高质量解，在许多情况下还可能参与搜索过程（例如，作为进化计算中的种群）。过去二十年，归档——即比较新解与旧解并决定如何更新归档/种群的过程——已成为进化多目标优化中的一个重要议题。这体现在学界持续努力开发各种有效的归档方法，从传统的基于帕累托的方法到近期基于指标和基于分解的方法。然而，这些努力的重点在于特定质量指标的实证性能比较；从一般理论角度对归档方法进行系统研究仍显匮乏。本文尝试系统概述多目标归档，旨在从理论与实践的整体视角理解归档算法，更重要的是为设计兼具理论理想性和实践实用性的归档算法提供指导。基于此，我们还表明：基于弱帕累托合规指标（如ε-指标）的归档算法，只要设计得当，能够达到与基于帕累托合规指标（如超体积指标）的归档算法相同的理论理想特性。这些特性包括极限最优属性——即有界归档算法在解集间最一般优越性形式下可能具备的最优属性的极限形式。