Γ-鲁棒极大极小问题的精确与启发式方法
Exact and Heuristic Methods for $Γ$-Robust Min-Max Problems
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中文总结 AI 辅助
本文研究带Γ-鲁棒不确定数据的混合整数线性极大极小问题，提出精确与启发式求解方法，经560个背包拦截问题实例测试，该启发式方法能缩小最优性间隙且性能优于基准方法。
中文摘要 AI 辅助
双层优化是用于建模分层决策过程的有力工具，这类过程出现在各类实际应用中。然而，由于其嵌套结构，即使所有变量均为连续型且问题的所有参数完全已知，双层问题本质上也难以求解。若考虑混合整数方面及不确定性下的问题，还会出现进一步的挑战。本文总结了作者博士论文中的部分研究成果，研究带有Γ-鲁棒不确定数据处理的混合整数线性极大极小问题，针对该问题提出了精确与启发式求解方法。通过对560个背包拦截问题实例的计算研究评估了方法的性能，结果表明，该启发式方法能针对所考虑实例的很大一部分缩小最优性间隙，且在实际应用中通常优于启发式和精确基准方法。
英文摘要
Bilevel optimization is a powerful tool for modeling hierarchical decision-making processes, which arise in various real-world applications. Due to their nested structure, however, bilevel problems are intrinsically hard to solve, even if all variables are continuous and all parameters of the problem are exactly known. Further challenges arise if mixed-integer aspects and problems under uncertainty are considered. In this article, we summarize selected results from the author's dissertation. We study mixed-integer linear min-max problems with a $Γ$-robust treatment of uncertain data, for which we present exact and heuristic solution approaches. The performance of the methods is assessed in a computational study on 560 instances of the knapsack interdiction problem. Our results show that the heuristic closes the optimality gap for a significant portion of the considered instances and often practically outperforms both heuristic and exact benchmark approaches.
