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

2025-07-17

AI Summary

Mixed-integer linear programming (MILP) solutions often lack interpretability, hindering user trust and decision-making transparency. Method: This paper introduces X-MILP, the first approach to integrate constraint reasoning with graphical contrastive explanation for MILP. It models user queries as additional constraints, identifies critical infeasibility sources via irreducible inconsistent subsystems (IIS), and constructs a structured “reasoning graph” that explicitly encodes causal and dependency relations among constraints. Contribution/Results: X-MILP is domain-agnostic and requires no domain-specific knowledge, enabling structured, contrastive explanations across diverse problem instances. Experiments on canonical MILP benchmarks demonstrate that X-MILP efficiently generates semantically clear, traceable graphical explanations. These explanations significantly enhance solution transparency, user comprehension, and decision-making credibility—thereby advancing explainable optimization.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Humans and AI: Explainable AI (XAI) for Human Understanding
• Machine Learning: Transparent, Interpretable, Explainable ML

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• Develop contrastive explanations for Mixed-Integer Linear Programming (MILP)
• Encode user queries as constraints to explain MILP solutions
• Construct graph-based explanations using Irreducible Infeasible Subsystems (IIS)

Innovation

• Uses constraint reasoning for MILP explanations
• Encodes user queries as additional constraints
• Constructs graph of reasons from IIS