From Informal Descriptions to Formal MILP Models Through a Multi-Agent Approach with Structured Knowledge Integration

Constructing Mixed Integer Linear Programming (MILP) models often demands domain expertise and meticulous manual formulation, especially when problem descriptions are informal, incomplete, or expressed in plain language. These challenges make translating user requirements into precise mathematical models difficult and error-prone. This paper presents CaptainMILO, a conversational multi-agent system that empowers non-expert users to formulate MILP models directly from natural language inputs. CaptainMILO provides interactive guidance to structure optimisation problems, identify and clarify missing information, and transform informal descriptions into well-organised problem statements with corresponding mathematical models. The system combines Dynamic Beam Search over purpose-built Mixed Integer Linear Optimisation Graphs with structured information elicitation to enable accurate, stepwise model construction. Specialised agents handle requirement extraction, query refinement, and constraint specification, while Proctor components monitor each stage to ensure logical consistency and correctness. Empirical evaluations demonstrate that CaptainMILO outperforms both raw GPT-4o and a single-agent baseline without Dynamic Beam Search in model accuracy and user satisfaction, as measured through automatic GPT-4o-based assessments. These results show that CaptainMILO advances the integration of structured knowledge with interactive conversational guidance, making MILP formulation more accessible, reliable, and intuitive for non-expert users.