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存档。该存档既可仅用于存储呈现给决策者的高质量解，也可参与搜索过程（例如，作为进化计算中的种群）。近二十年来，存档——即比较新解与旧解并决定如何更新存档/种群的过程——已成为进化多目标优化中的一个重要议题。这一点体现在学术界不断努力开发各种有效的存档方法上，从传统的基于Pareto的方法到近年兴起的基于指标和基于分解的方法。然而，这些努力的焦点在于特定质量指标上的实证性能比较；从一般理论角度对存档方法进行系统研究仍显不足。本文试图对多目标存档进行系统性综述，以期从理论与实践的整体视角理解存档算法，更重要的是为设计兼具理论理想性与实践实用性的存档算法提供指导。在此过程中，我们还指出，基于弱Pareto合规指标（如ε-指标）的存档算法，若设计得当，能够达到与基于Pareto合规指标（如超体积指标）的存档算法相同的理论理想性。这些理想性包括极限最优性——即有界存档算法在解集最一般优越性形式下可能具备的最优性质的极限形式。