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.

Recently, the Deep Learning community has become interested in evolutionary optimization (EO) as a means to address hard optimization problems, e.g.

Dynamic programming methods have been shown to scale much better because they exploit the tree structure by solving subtrees as independent subproblems.

Solving optimization problems is the key to decision making in many real-life analytics applications. However, the coefficients of the optimization problems are often uncertain and dependent on external factors, such as future demand or energy or stock prices. Machine learning (ML) models, especially neural networks, are increasingly being used to estimate these coefficients in a data-driven way.