On the Unbounded External Archive and Population Size in Preference-based Evolutionary Multi-objective Optimization Using a Reference Point

Abstract: Although the population size is an important parameter in evolutionary multi-objective optimization (EMO), little is known about its influence on preference-based EMO (PBEMO). The effectiveness of an unbounded external archive (UA) in PBEMO is also poorly understood, where the UA maintains all non-dominated solutions found so far. In addition, existing methods for postprocessing the UA cannot handle the decision maker's preference information. In this context, first, this paper proposes a preference-based postprocessing method for selecting representative solutions from the UA. Then, we investigate the influence of the UA and population size on the performance of PBEMO algorithms. Our results show that the performance of PBEMO algorithms (e.g., R-NSGA-II) can be significantly improved by using the UA and the proposed method. We demonstrate that a smaller population size than commonly used is effective in most PBEMO algorithms for a small budget of function evaluations, even for many objectives. We found that the size of the region of interest is a less important factor in selecting the population size of the PBEMO algorithms on real-world problems.