Exploiting Constraint Reasoning to Build Graphical Explanations for Mixed-Integer Linear Programming

TL;DR

This paper introduces X-MILP, a novel, domain-agnostic method for generating contrastive explanations for MILP solutions by encoding user queries as constraints and analyzing infeasible subsystems to build explanatory graphs.

Contribution

The paper presents a new approach that leverages constraint reasoning and IIS computation to produce interpretable explanations for MILPs, enhancing transparency in decision-making.

Findings

Effective encoding of user queries as constraints

Construction of explanation graphs from IIS

Empirical evaluation on standard optimization problems

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.