Counterfactual explanations (CEs) offer a human-understandable way to explain decisions by identifying specific changes to the input parameters of a base or present model that would lead to a desired change in the outcome. For optimization models, CEs have primarily been studied in limited contexts and little research has been done on CEs for general integer optimization problems. In this work, we address this gap. We first show that the general problem of constructing a CE is $Σ_2^p$-complete even for binary integer programs with just a single mutable constraint. Second, we propose solution algorithms for several of the most tractable special cases: (i) mutable objective parameters, (ii) a single mutable constraint, (iii) mutable right-hand-side, and (iv) all input parameters can be modified. We evaluate our approach using classical knapsack problem instances, focusing on cases with mutable constraint parameters. Additionally, we present experiments on the resource constrained shortest path problem.

翻译：反事实解释通过识别对基础或现有模型输入参数的具体更改（这些更改将导致期望的结果变化），提供了一种人类可理解的方式来解释决策。对于优化模型，反事实解释的研究主要局限于特定情境，针对通用整数优化问题的反事实解释研究尚不充分。本研究旨在填补这一空白。首先，我们证明即使对于仅包含单个可变约束的二元整数规划，构建反事实解释的通用问题也是$Σ_2^p$完全的。其次，我们针对若干最易处理的特殊情况提出了求解算法：（i）可变目标参数，（ii）单个可变约束，（iii）可变右端项，以及（iv）所有输入参数可修改。我们使用经典背包问题实例评估所提出的方法，重点关注约束参数可变的情况。此外，我们还对资源约束最短路径问题进行了实验分析。