Title: Generalizing the Min-Max Regret Criterion using Ordered Weighted Averaging Show Chinese title

Title: 使用有序加权平均推广最小最大遗憾准则

Abstract: In decision making under uncertainty, several criteria have been studied to aggregate the performance of a solution over multiple possible scenarios, including the ordered weighted averaging (OWA) criterion and min-max regret. This paper introduces a novel generalization of min-max regret, leveraging the modeling power of OWA to enable a more nuanced expression of preferences in handling regret values. This new OWA regret approach is studied both theoretically and numerically. We derive several properties, including polynomially solvable and hard cases, and introduce an approximation algorithm. Through computational experiments using artificial and real-world data, we demonstrate the advantages of our OWAR method over the conventional min-max regret approach, alongside the effectiveness of the proposed clustering heuristics. Show Chinese abstract

Abstract: 在不确定性下的决策中，已经研究了几种准则来汇总解决方案在多个可能情景下的表现，包括有序加权平均（OWA）准则和最小最大后悔准则。 本文引入了最小最大后悔的一种新泛化方法，利用OWA的建模能力，以更细致的方式表达在处理后悔值时的偏好。 这种新的OWA后悔方法从理论和数值两个方面进行了研究。 我们推导了几个性质，包括多项式可解和困难的情况，并引入了一个近似算法。 通过使用人工和现实数据的计算实验，我们展示了我们的OWAR方法相对于传统最小最大后悔方法的优势，同时证明了所提出的聚类启发式方法的有效性。