A Framework for Data-Driven Explainability in Mathematical Optimization
This addresses the issue of acceptance of optimal solutions by practitioners in mathematical optimization, though it is incremental as it builds on existing optimization methods.
The paper tackles the problem of optimization solutions being perceived as black boxes by practitioners, proposing a framework that introduces explainability as an evaluation criterion alongside objective value, and finds that the cost of enforcing explainability can be very small in experiments on road networks.
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.