发表机构
University of Passau; University of Amsterdam（帕绍大学; 阿姆斯特丹大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对整数优化中弱反事实解释计算困难的问题，本文提出用决策树近似可行区域的快速启发式算法，并在背包和设施选址问题上验证了其有效性。
AI 中文摘要
反事实解释（CEs）的概念近年来在数学优化问题的解释推导中日益受到关注。对于给定问题，反事实是对可变问题参数的理想最小改变，使得改变后问题的最优解存在并满足某个期望标准。已有研究表明，所谓的弱CE可以通过求解一个计算要求高的双层优化问题来计算，当决策变量和可变参数限制为整数时，该问题是$\Sigma_2^p$-完全的。因此，已知的精确求解方法预计在实际相关的问题规模上会失效。在本工作中，我们通过用决策树近似CE问题的可行区域，推导出一种快速启发式算法，使得CE可以更快地计算。为此，我们分析了可行区域的数学结构，并开发了一种手工设计的决策树，其分裂方式模仿该结构。此外，我们开发了几种技术来提高我们方法的性能。我们方法的实用性通过背包问题和设施选址问题的计算实验得到支持。
英文摘要
The concept of counterfactual explanations (CEs) has recently gained increasing attention for deriving explanations of mathematical optimization problems. For a given problem, a counterfactual is an ideally minimal change in the mutable problem parameters such that an optimal solution of the changed problem exists fulfilling some desired criterion. It was shown that so-called weak CEs can be calculated by solving a computationally demanding bilevel optimization problem, which is $Σ_2^p$-complete if decision variables and mutable parameters are restricted to integers. Hence, the known exact solution methods are expected to fail on practically relevant problem sizes. In this work we derive a fast heuristic algorithm by approximating the feasible region of the CE problem with a decision tree for which CEs can be calculated more quickly. To this end we analyze the mathematical structure of the feasible region and develop a hand-crafted decision tree which applies splits imitating this structure. Additionally, we develop several techniques to increase the performance of our method. The practicability of our methods is supported by computational experiments on the knapsack problem and the facility location problem.
