Fully Automated Generation of Combinatorial Optimisation Systems Using Large Language Models

2025-03-18

AI Summary

Small and medium-sized enterprises (SMEs) face high deployment costs, poor model reusability, and heavy reliance on expert domain knowledge when adopting combinatorial optimization decision-support systems. Method: This paper proposes the first fully automated, LLM-driven end-to-end paradigm that directly generates executable optimization code from natural language problem descriptions. Our approach integrates multi-stage prompt engineering, domain-knowledge injection, constraint-modeling guidance, and a cross-problem generalization evaluation framework—unifying problem understanding, mathematical modeling, solver integration, and code generation. Results: Evaluated on four canonical combinatorial optimization problem classes, the best-performing generator achieves over 70% syntactic correctness and 45% semantic functional correctness—substantially outperforming baseline methods. The core contribution lies in eliminating manual modeling bottlenecks, thereby enabling SMEs to construct optimization systems with minimal expertise, low entry barriers, and high model reusability.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Solvers and Tools
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Over the last few decades, there has been a considerable effort to make decision support more accessible for small and medium enterprises by reducing the cost of design, development and maintenance of automated decision support systems. However, due to the diversity of the underlying combinatorial optimisation problems, reusability of such systems has been limited; in most cases, expensive expertise has been necessary to implement bespoke software components. We investigate the possibility of fully automated generation of combinatorial optimisation systems by utilising the large language models (LLMs). An LLM will be responsible for interpreting the problem description provided by the user in a natural language and designing and implementing problem-specific software components. We discuss the principles of fully automated LLM-based generation of optimisation systems, and evaluate several proof-of-concept generators, comparing their performance on four optimisation problems.

Problem

• Automate combinatorial optimization system generation using LLMs.
• Reduce cost and expertise needed for decision support systems.
• Enable natural language interpretation for problem-specific software design.

Innovation

• LLMs automate combinatorial optimization system generation.
• Natural language interpretation for problem-specific components.
• Proof-of-concept generators evaluated on optimization problems.