从多个最优解中选出代表性子集，提升决策效率。
Picking a Representative Set of Solutions in Multiobjective Optimization: Axioms, Algorithms, and Experiments
- 将多目标优化的筛选问题转化为多胜者投票模型，分析现有评估方法。
- 提出新指标‘定向覆盖’，在不同目标结构下表现更优。
- 实验证明选择不同评估标准会显著影响结果，适合需高效决策的场景。
许多现实决策问题需要同时优化多个目标，导致最优解的选择变得复杂：所有帕累托最优解都是可行候选，最终选择取决于决策者的主观偏好。为减轻决策负担，已有研究提出帕累托剪枝问题，即计算一个固定大小的帕累托最优解子集，以最佳代表完整解集，依据特定质量度量。本文将帕累托剪枝重新建模为多胜者投票问题，对现有质量度量进行公理化分析，揭示若干反直觉行为。基于此，提出新的度量——定向覆盖。同时分析各类度量优化的计算复杂性，识别出在目标数量与结构变化下可解与不可解之间的边界。最后通过实验评估表明，质量度量的选择对所选解集特性有决定性影响，所提方法在多种设置下表现竞争力甚至更优。
原文摘要 · Abstract (English)
Many real-world decision-making problems involve optimizing multiple objectives simultaneously, rendering the selection of the most preferred solution a non-trivial problem: All Pareto optimal solutions are viable candidates, and it is typically up to a decision maker to select one for implementation based on their subjective preferences. To reduce the cognitive load on the decision maker, previous work has introduced the Pareto pruning problem, where the goal is to compute a fixed-size subset of Pareto optimal solutions that best represent the full set, as evaluated by a given quality measure. Reframing Pareto pruning as a multiwinner voting problem, we conduct an axiomatic analysis of existing quality measures, uncovering several unintuitive behaviors. Motivated by these findings, we introduce a new measure, directed coverage. We also analyze the computational complexity of optimizing various quality measures, identifying previously unknown boundaries between tractable and intractable cases depending on the number and structure of the objectives. Finally, we present an experimental evaluation, demonstrating that the choice of quality measure has a decisive impact on the characteristics of the selected set of solutions and that our proposed measure performs competitively or even favorably across a range of settings.
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