Leveraging Large Language Models to Develop Heuristics for Emerging Optimization Problems

Abstract: Combinatorial optimization problems often rely on heuristic algorithms to generate efficient solutions. However, the manual design of heuristics is resource-intensive and constrained by the designer's expertise. Recent advances in artificial intelligence, particularly LLMs, have demonstrated the potential to automate heuristic generation through evolutionary frameworks. Recent works focus only on well-known combinatorial optimization problems like the traveling salesman problem and online bin packing problem when designing constructive heuristics. This study investigates whether LLMs can effectively generate heuristics for niche, not yet broadly researched optimization problems, using the unit-load pre-marshalling problem as an example case. We propose the Contextual Evolution of Heuristics (CEoH) framework, an extension of the Evolution of Heuristics (EoH) framework, which incorporates problem-specific descriptions to enhance in-context learning during heuristic generation. Through computational experiments, we evaluate CEoH and EoH and compare the results. Results indicate that CEoH enables smaller LLMs to generate high-quality heuristics more consistently and even outperform larger models. Larger models demonstrate robust performance with or without contextualized prompts. The generated heuristics exhibit scalability to diverse instance configurations.