MURKA: Multi-Reward Reinforcement Learning with Knowledge Alignment for Optimization Tasks

Optimization plays a central role in Operations Research (OR) and numerous industrial applications, yet automating the end-to-end process of translating natural language descriptions into executable optimization programs remains a formidable challenge. While recent efforts have applied Large Language Models (LLMs) to this task, existing approaches are hindered by high inference costs, limited robustness across domains, and weak verification mechanisms. In this work, we propose MURKA, a reinforcement learning and knowledge distillationbased framework that enhances LLM-driven optimization modeling via collaborative agent alignment. MURKA orchestrates three specialized agents--Extractor, Solver, and Checker--to achieve accurate problem understanding, robust formulation, and verifiable execution. The Extractor is trained using group relative policy optimization with a composite reward function that incorporates semantic correctness and execution fidelity.