The distribution of objective vectors in a Pareto Front Approximation (PFA) is crucial for representing the associated manifold accurately. Distribution Indicators (DIs) assess the distribution of a PFA numerically, utilizing concepts like distance calculation, Biodiversity, Entropy, Potential Energy, or Clustering. Despite the diversity of DIs, their strengths and weaknesses across assessment scenarios are not well-understood. This paper introduces a taxonomy for classifying DIs, followed by a preference analysis of nine DIs, each representing a category in the taxonomy. Experimental results, considering various PFAs under controlled scenarios (loss of coverage, loss of uniformity, pathological distributions), reveal that some DIs can be misleading and need cautious use. Additionally, DIs based on Biodiversity and Potential Energy show promise for PFA evaluation and comparison of Multi-Objective Evolutionary Algorithms.

翻译：帕累托前沿近似（PFA）中目标向量的分布对于准确表征相关流形至关重要。分布指标（DI）通过距离计算、生物多样性、熵、势能或聚类等概念对PFA的分布进行数值评估。尽管分布指标种类繁多，但其在不同评估场景中的优势与局限性尚未被充分理解。本文提出了一种分布指标的分类体系，进而对九种分别代表该分类体系中各类型的分布指标进行偏好分析。在受控场景（覆盖性缺失、均匀性缺失、病态分布）下针对不同PFA的实验结果表明，部分分布指标可能产生误导，需谨慎使用。此外，基于生物多样性和势能的分布指标在PFA评估及多目标进化算法比较中展现出良好的应用前景。