揭示异质群体中的潜在共识：混合线性排序问题
Uncovering latent consensus in heterogeneous populations: The Mixture Linear Ordering Problem
AI总结：
本文提出混合线性排序问题，通过将群体分为潜在组并考虑其排序模式，解决传统线性排序在异质群体中的不足，采用混合整数规划和启发式方法实现高效求解。
摘要：
经典的线性排序问题旨在寻找一个单一的排序来表示给定的偏好矩阵。尽管适用于同质群体，但当观察到的偏好来自多个潜在群体且具有不同的排序模式时，它会失效。为此，我们引入一个扩展方法，将人口划分为潜在群体，每个群体有自己的线性顺序、相对大小和偏好结构。然后，观察到的矩阵被解释为这些群体特定偏好的汇总结果。我们开发了混合整数规划公式，包括一个紧凑的重新公式，该公式在线性排序多面体内提供几何解释。由于精确解在较大实例中计算成本高，我们提出了一种多起点交替方向数学启发式方法，逐步更新群体排序和权重。在合成生成的实例上的计算实验，匹配偏好聚合场景中典型大小，证明了精确方法在成功恢复潜在群体方面的有效性。此外，所提出的启发式方法在更短的时间内提供了高质量的解，偶尔在限定时间内改进了精确方法的最佳候选解。
英文摘要：
The classical linear ordering problem seeks a single ranking representing a given preference matrix. While suitable for homogeneous populations, it fails when observed preferences arise from several latent groups with distinct ranking patterns. To address this limitation, we introduce an extension partitioning the population into latent groups, each characterized by its own linear order, relative size, and preference structure. The observed matrix is then explained as the aggregate outcome of these group-specific preferences. We develop mixed-integer programming formulations, including a compact reformulation yielding a geometric interpretation within the linear ordering polytope. Because exact solutions become computationally demanding for larger instances, we propose a multi-start alternating-direction matheuristic iteratively updating group rankings and weights. Computational experiments on synthetically generated instances, matching sizes typical in preference aggregation scenarios, demonstrate the effectiveness of the exact approach in successfully recovering the underlying groups. Furthermore, the proposed heuristic delivers high-quality solutions in substantially shorter times, occasionally improving upon the exact method's best incumbent in difficult instances within the imposed time limit.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
