Constraint Reasoning and Large Language Models Join Forces: Providing Contrastive Explanations for Real-World Optimisation-Based Applications

Roger X. Lera-Leri, Filippo Bistaffa, Athina Georgara, Juan A. Rodríguez-Aguilar

We focus on optimisation-based Decision Support Systems in real-world applications. In this context, we aim to provide contrastive explanations that answer users' questions about recommendations based on the solution of an optimisation problem, specifically a Mixed-Integer Program (MIP). Addressing this endeavour is crucial to ensure human oversight of the decisions implemented, as required by international guidelines on trustworthy and responsible automated decision-making systems. We propose a novel methodology that combines constraint reasoning techniques and Large Language Models (LLMs) to generate contrastive explanations for optimisation problems encoded as MIPs. Although LLMs have shown impressive capabilities in Natural Language processing, they can produce incorrect answers due to reasoning limitations. To overcome these limitations, we leverage constraint reasoning techniques to distil the information necessary to produce an explanation, which is then passed as input to an LLM as the so-called graph of reasons. Such a graph captures the semantics and the relationships among constraints of the optimisation problem. Results on real-world scheduling domains show that…