Multi-Objective Archiving

Miqing Li, Manuel López-Ibáñez, Xin Yao

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Abstract

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., ϵ-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.
Original languageEnglish
JournalIEEE Transactions on Evolutionary Computation
DOIs
Publication statusAccepted/In press - 8 Sept 2023

Keywords

  • Multi-objective optimisation
  • evolutionary computation
  • archive
  • archiving methods
  • population update
  • environmental selection

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