Multi-Agent AI System for Generating Optimization Procedures and Solutions : Leveraging autonomous agents for generating optimization algorithms using exact methods and heuristics

Abstract

This thesis examines how effective optimization algorithms for complex combinatorial optimization problems can be developed using a multi-agent system based on large language models. The work presents a fully automated system in which specialized agents collaborate to interpret user-defined problems, generate optimization code, and iteratively improve solutions through feedback. The system was evaluated on established benchmarks, such as the vehicle routing problem and the cutting stock problem, and was able to produce solutions that achieved optimal or near-optimal results.

The findings show that composing the system into separate agents with clear roles is essential for handling complexity and ensuring that the end-to-end code generation process can correct itself. The performance of the system depends strongly on giving the agents precise, problem-specific instructions and enabling smooth cooperation between agents focused on analysis, code generation, execution, and error correction. This approach offers a good alternative to the time-consuming manual design of algorithms and allows domain experts to focus more on defining the problem, rather than writing detailed implementation.

This research provides a validated example of how solving optimization tasks can be automated by distributing work between language model-based agents. The results give clear evidence that this approach is effective for tackling challenging computational problems. The contribution is relevant for both industry and academia, as it can help speed up development in operations research and support new applications of artificial intelligence in practice.