求解预算不确定性下k-删除可恢复鲁棒0-1问题的精确方法

中文摘要 AI 辅助

我们研究k-删除可恢复鲁棒0-1问题，其中决策者在目标不确定性下求解组合优化问题。该模型采用两阶段鲁棒设置。决策者首先承诺一个初始方案，并在不确定性揭示后可以撤销该决策中最多k个组件。底层不确定性使用预算不确定性集建模，使得决策者仅对冲不确定参数中的有限数量偏差。我们提出了k-删除可恢复鲁棒问题的四种重构，可通过（i）通用混合整数线性规划求解器，（ii）分支切割方法，或（iii）列与约束生成算法来处理。对于每种重构，我们确定合适的求解方法并证明其正确性。总体而言，我们提出了八种求解k-删除可恢复鲁棒问题的方法，并在分配问题和单源容量设施选址问题的实例上进行广泛的计算研究，评估和比较这些方法。

英文摘要

We study the k-delete recoverable robust 0-1 problem in which a decision-maker solves a combinatorial optimization problem subject to objective uncertainty. The model follows a two-stage robust setup. The decision-maker first commits to an initial plan and may then revoke up to k components of this decision after the uncertainty is revealed. The underlying uncertainty is modeled using a budgeted uncertainty set so that the decision-maker only hedges against a limited number of deviations in the uncertain parameters. We present four reformulations of the k-delete recoverable robust problem, which can be tackled using (i) general-purpose mixed-integer linear programming solvers, (ii) branch-and-cut methods, or (iii) column-and-constraint generation algorithms. For each formulation, we identify suitable solution methods and prove their correctness. Overall, we present eight approaches to solve the k-delete recoverable robust problem, which we assess and compare in an extensive computational study on instances of the assignment problem and the single-source capacitated facility location problem.

发表机构

• Eindhoven University of Technology（埃因霍温理工大学）
• ESSEC Business School（法国高等经济商业学院）
• RWTH Aachen University（亚琛工业大学）

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