Automated Priority Rule Design for the Resource-Constrained Project Scheduling Problem: A Large Language Model-Guided Population-Based Search
The objective of the resource-constrained project scheduling problem (RCPSP) is to minimize makespan while satisfying precedence and renewable-resource constraints. Priority-rule heuristics construct feasible schedules with low computational cost and explicit decision logic, making them widely used in practice and an attractive alternative to more computationally intensive methods. However, no traditional rule performs consistently well across projects, and researchers have therefore investigated automated priority-rule design. Genetic programming (GP) hyper-heuristics have been the predominant approach to this task, but evolving a high-performing rule may require evaluating many candidate rules on the training projects. Recent advances in large language models (LLMs) make it possible to generate and iteratively revise priority rules using performance feedback. This paper presents an LLM-guided population-based framework for automated priority-rule design. During the offline search, an LLM generates and revises candidate rules, while schedule quality on training projects determines candidate fitness and guides subsequent revisions. At the end of the search, the best rule is returned and applied directly to unseen projects without further search or LLM calls. Experiments show that the LLM-designed rules outperform traditional single rules across the test sets and outperform GP-designed rules obtained under comparable search effort, while remaining competitive with rules obtained from a substantially larger GP search. On large projects, selected LLM-designed rules outperform all considered traditional rules and two genetic algorithm configurations on highly parallel projects. An ablation study examines how changes to the main search components affect performance, while rule analyses describe the structure and decision behavior of the LLM-designed rules.