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

Abstract: Multi-objective optimization is fundamental in complex decision-making tasks. Traditional algorithms, while effective, often demand extensive problem-specific modeling and struggle to adapt to nonlinear structures. Recent advances in LLMs offer enhanced explainability, adaptability, and reasoning. This work proposes Reflective Evolution of Multi-objective Heuristics (REMoH), a novel framework integrating NSGA-II with LLM-based heuristic generation. A key innovation is a reflection mechanism that uses clustering and search-space reflection to guide the creation of diverse, high-quality heuristics, improving convergence and maintaining solution diversity. The approach is evaluated on the Flexible Job Shop Scheduling Problem (FJSSP) in-depth benchmarking against state-of-the-art methods using three instance datasets: Dauzere, Barnes, and Brandimarte. Results demonstrate that REMoH achieves competitive results compared to state-of-the-art approaches with reduced modeling effort and enhanced adaptability. These findings underscore the potential of LLMs to augment traditional optimization, offering greater flexibility, interpretability, and robustness in multi-objective scenarios.