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.

翻译：尽管种群规模是多目标进化优化（EMO）中的一个重要参数，但关于其对偏好驱动多目标进化优化（PBEMO）影响的研究仍十分有限。同样，无界外部存档（UA）在PBEMO中的有效性也尚未得到充分理解，该存档保留了迄今发现的所有非支配解。此外，现有用于后处理UA的方法无法处理决策者的偏好信息。基于此，本文首先提出一种基于偏好的后处理方法，用于从UA中选择代表性解。随后，我们研究了UA和种群规模对PBEMO算法性能的影响。结果表明，结合UA及所提方法可显著提升PBEMO算法（如R-NSGA-II）的性能。我们证明，在函数评估预算有限的情况下，即使面对多目标问题，大多数PBEMO算法采用比常用值更小的种群规模仍是有效的。此外，研究发现感兴趣区域的大小对实际问题上PBEMO算法种群规模选择的影响较小。