AI 中文总结
本文针对上下文分布鲁棒机会约束规划提出精确MIP重构与有效不等式，利用Wasserstein距离和运输预算耦合特征，生成增强分位数割与秩不等式，显著缩小松弛间隙并加速求解。
AI 中文摘要
我们研究了一种上下文分布鲁棒机会约束规划（C-DRCCP）模型，该模型控制目标上下文邻域内条件违规概率。模糊集基于Wasserstein距离定义在上下文和结果的联合分布上。对于具有右侧不确定性的仿射安全系统，我们推导出精确的混合整数规划（MIP）重构。该重构揭示，最坏情况下的条件风险由运输预算的两种耦合使用决定：将经验质量移入条件邻域，以及将条件质量移入失效区域。等价地，当达到条件风险边界所需的最小运输成本至少为可用预算时，鲁棒可行性成立。校准模糊集为真实条件违规概率提供了有限样本保证。这一特征导致了利用上下文运输的强有效不等式。每个上下文质量分配同时决定条件情景权重和将结果移入失效的可用预算，而传统分位数割仅利用诱导权重。考虑剩余预算产生增强的分位数割，严格优于标准分位数界限，并产生更紧的MIP系数。我们还从上下文运输成本的交换性质推导出秩不等式，将跨上下文分配的可行失效模式联系起来。大量数值实验表明，这些不等式缩小了大部分线性松弛间隙，加速了求解过程，并使基线公式无法处理的大样本实例变得可行。
英文摘要
We study a contextual distributionally robust chance-constrained programming (C-DRCCP) model that controls violation probabilities conditional on a neighborhood of a target context. The ambiguity set is defined over the joint distribution of contexts and outcomes using the Wasserstein distance. For affine safety systems with right-hand-side uncertainty, we derive an exact mixed-integer programming (MIP) reformulation. The reformulation reveals that worst-case conditional risk is determined by two coupled uses of the transportation budget: moving empirical mass into the conditioning neighborhood and moving conditioned mass into the failure region. Equivalently, robust feasibility holds when the minimum transportation cost needed to reach the conditional risk boundary is at least the available budget. Calibrating the ambiguity set gives a finite-sample guarantee for the true conditional violation probability. This characterization leads to strong valid inequalities that exploit the contextual transport. Each contextual mass allocation determines both the conditional scenario weights and the budget available to move outcomes into failure, whereas conventional quantile cuts utilize only the induced weights. Accounting for the remaining budget generates strengthened quantile cuts that strictly dominate standard quantile bounds and yield tighter MIP coefficients. We also derive rank inequalities from an exchange property of contextual transportation costs, linking feasible failure patterns across contextual allocations. Extensive numerical experiments demonstrate that these inequalities close much of the linear-relaxation gap, speed up the solution process, and enable large-sample instances that are intractable for the baseline formulation.
Comments42 pages, 5 figures
