Advancements in mathematical programming have made it possible to efficiently tackle large-scale real-world problems that were deemed intractable just a few decades ago. However, provably optimal solutions may not be accepted due to the perception of optimization software as a black box. Although well understood by scientists, this lacks easy accessibility for practitioners. Hence, we advocate for introducing the explainability of a solution as another evaluation criterion, next to its objective value, which enables us to find trade-off solutions between these two criteria. Explainability is attained by comparing against (not necessarily optimal) solutions that were implemented in similar situations in the past. Thus, solutions are preferred that exhibit similar features. Although we prove that already in simple cases the explainable model is NP-hard, we characterize relevant polynomially solvable cases such as the explainable shortest-path problem. Our numerical experiments on both artificial as well as real-world road networks show the resulting Pareto front. It turns out that the cost of enforcing explainability can be very small.

翻译：数学规划技术的进步使得高效解决数十年前仍被视为棘手的规模化现实问题成为可能。然而，由于优化软件常被视为黑箱模型，即使理论上最优的解也可能不被采纳。尽管科学家对此有充分理解，但从业者难以直观把握。为此，我们主张将解的可解释性作为除目标函数值外的另一评估准则，从而能够在两个准则间寻找折衷方案。可解释性通过将解与过去类似情境中实施的（未必最优的）解进行对比实现。具体而言，具有相似特征的解更受青睐。尽管我们证明即使在简单情形下可解释模型也属于NP难问题，但成功刻画了如可解释最短路问题等多项式可解案例。基于人工与真实道路网络的数值实验展示了所得帕累托前沿。结果表明，实施可解释性所需付出的代价往往微乎其微。