Some quality indicators have been proposed for benchmarking preference-based evolutionary multi-objective optimization algorithms using a reference point. Although a systematic review and analysis of the quality indicators are helpful for both benchmarking and practical decision-making, neither has been conducted. In this context, first, this paper reviews existing regions of interest and quality indicators for preference-based evolutionary multi-objective optimization using the reference point. We point out that each quality indicator was designed for a different region of interest. Then, this paper investigates the properties of the quality indicators. We demonstrate that an achievement scalarizing function value is not always consistent with the distance from a solution to the reference point in the objective space. We observe that the regions of interest can be significantly different depending on the position of the reference point and the shape of the Pareto front. We identify undesirable properties of some quality indicators. We also show that the ranking of preference-based evolutionary multi-objective optimization algorithms significantly depends on the choice of quality indicators.

翻译：针对基于参考点的偏好演化多目标优化算法，已有若干质量指标被提出用于基准测试。尽管对质量指标的系统性综述与分析有助于基准测试和实际决策，但目前尚无相关研究开展。在此背景下，本文首先回顾了现有基于参考点的偏好演化多目标优化中的感兴趣区域与质量指标，指出每个质量指标均针对不同感兴趣区域设计。随后，本文探究了质量指标的性质，证明成就标量化函数值并不总是与目标空间中解至参考点的距离一致。我们观察到，感兴趣区域可能因参考点位置及帕累托前沿形状的差异而显著不同。研究识别出部分质量指标存在不良性质，并表明偏好演化多目标优化算法的排序结果高度依赖于所选质量指标。