Exploiting constraint reasoning to build graphical explanations for mixed-integer linear programming

Lera-Leri, Roger X., Bistaffa, Filippo, Georgara, Athina and Rodríguez-Aguilar, Juan A. (2025) Exploiting constraint reasoning to build graphical explanations for mixed-integer linear programming. Calvaresi, Davide, Najjar, Amro, Omicini, Andrea, Ciatto, Giovanni, Aydogan, Reyhan, Carli, Rachele, Främling, Kary and Tiribelli, Simona (eds.) In Explainable, Trustworthy, and Responsible AI and Multi-Agent Systems - 7th International Workshop, EXTRAAMAS 2025, Revised Selected Papers. vol. 15936 LNCS, Springer Cham. pp. 21-39 . (doi:10.1007/978-3-032-01399-6_2).

Abstract

Following the recent push for trustworthy AI, there has been an increasing interest in developing contrastive explanation techniques for optimisation, especially concerning the solution of specific decision-making processes formalised as MILPs. Along these lines, we propose X-MILP, a domain-agnostic approach for building contrastive explanations for MILPs based on constraint reasoning techniques. First, we show how to encode the queries a user makes about the solution of an MILP problem as additional constraints. Then, we determine the reasons that constitute the answer to the user’s query by computing the Irreducible Infeasible Subsystem (IIS) of the newly obtained set of constraints. Finally, we represent our explanation as a “graph of reasons” constructed from the IIS, which helps the user understand the structure among the reasons that answer their query. We test our method on instances of well-known optimisation problems to evaluate the empirical hardness of computing explanations.

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Contributors

Author: Athina Georgara

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