REMoH: A Reflective Evolution of Multi-objective Heuristics approach via Large Language Models

Multi-objective optimization is a central challenge in complex decision-making problems. Here, solution quality depends on balancing competing performance criteria. Classical exact and heuristic optimization methods have demonstrated strong results. However, they typically require substantial problem-specific mod-eling effort and often face scalability limitations. Recent advances in Large Language Models (LLMs) offer new possibilities for automating the design of heuristics. Yet, their effectiveness relative to established optimization paradigms remains insufficiently benchmarked. This paper introduces Reflective Evolution of Multi-objective Heuristics (REMoH), a hybrid framework that integrates 1 LLM-generated heuristics within an NSGA-II evolutionary process. The primary contribution of this work is a systematic benchmarking of LLM-driven heuristics against exact mathematical programming, classical heuristics, and learning-based methods in a multi-objective scheduling context. Experiments on the Flexible Job Shop Scheduling Problem show that LLM-generated heuristics achieve competitive, well-balanced trade-offs across objectives. They often approach the performance of exact solvers while requiring significantly less modeling effort and computational overhead. A lightweight reflective mechanism is included to guide heuristic evolution. However, it plays a secondary role in the overall framework. The results highlight the potential of LLMs as practical heuristic generators for multi-objective optimization. They offer a flexible and scalable alternative to traditional approaches.