# A Framework for Data-Driven Explainability in Mathematical Optimization

arXiv: https://arxiv.org/abs/2308.08309 · HTML: https://mlsanity.com/paper/2308.08309/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 32 references that are in the map.
- First posted on arXiv 16 Aug 2023.

## Builds on (most cited first, 9 of 9)

- [Towards Explainable Artificial Intelligence](https://mlsanity.com/paper/1909.12072/) (2019)
- [Explainable k-Means and k-Medians Clustering](https://mlsanity.com/paper/2002.12538/) (2020)
- [Contrastive Explanation: A Structural-Model Approach](https://mlsanity.com/paper/1811.03163/) (2018)
- [Fairness and Explainability: Bridging the Gap Towards Fair Model Explanations](https://mlsanity.com/paper/2212.03840/) (2022)
- [A Framework for Inherently Interpretable Optimization Models](https://mlsanity.com/paper/2208.12570/) (2022)
- [Explainable Data-Driven Optimization: From Context to Decision and Back Again](https://mlsanity.com/paper/2301.10074/) (2023)
- [Algorithms and Uncertainty Sets for Data-Driven Robust Shortest Path Problems](https://mlsanity.com/paper/1802.04149/) (2018)
- [The Price of Explainability for Clustering](https://mlsanity.com/paper/2304.09743/) (2023)
- [Fairness over time in dynamic resource allocation with an application in Healthcare](https://mlsanity.com/paper/2101.03716/) (2021)

## Built on by (most cited first, 2 of 2)

- [Counterfactual Explanations for Linear Optimization](https://mlsanity.com/paper/2405.15431/) (2024)
- [Coherent Local Explanations for Mathematical Optimization](https://mlsanity.com/paper/2502.04840/) (2025)

## Abstract (arXiv)

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.