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An unbounded external archive has been used to store all nondominatedsolutions found by an evolutionary multi-objective optimization algorithm insome studies. It has been shown that a selected solution subset from the storedsolutions is often better than the final population. However, the use of theunbounded archive is not always realistic. When the number of examinedsolutions is huge, we must pre-specify the archive size. In this study, weexamine the effects of the archive size on three aspects: (i) the quality ofthe selected final solution set, (ii) the total computation time for thearchive maintenance and the final solution set selection, and (iii) therequired memory size. Unsurprisingly, the increase of the archive size improvesthe final solution set quality. Interestingly, the total computation time of amedium-size archive is much larger than that of a small-size archive and ahuge-size archive (e.g., an unbounded archive). To decrease the computationtime, we examine two ideas: periodical archive update and archiving only inlater generations. Compared with updating the archive at every generation, thefirst idea can obtain almost the same final solution set quality using a muchshorter computation time at the cost of a slight increase of the memory size.The second idea drastically decreases the computation time at the cost of aslight deterioration of the final solution set quality. Based on ourexperimental results, some suggestions are given about how to appropriatelychoose an archiving strategy and an archive size.

Effects of Archive Size on Computation Time and Solution Quality for Multi-Objective Optimization