Hierarchical Representations for Cross-task Automated Heuristic Design using LLMs

Designing heuristic algorithms for complex optimization problems is a time-consuming and expert-driven process. Recently, Automated Heuristic Design (AHD) using Large Language Models (LLMs) has shown significant promise for automating algorithm development. However, existing works mainly rely on programs to represent heuristics, which are inherently taskspecific and fail to generalize as effectively as established metaheuristics like tabu search or guided local search. To bridge this gap, we introduce Multi-Task Hierarchical Search (MTHS), an LLM-guided evolutionary method that co-designs general-purpose metaheuristics and task-specific programs. MTHS employs a hierarchical representation and adopts a two-level evolution framework to evolve task-agnostic metaheuristics and task-specific program implementations simultaneously across multiple heuristic design tasks. During this evolution, a knowledge transfer mechanism allows learning from elite programs designed for other tasks. We evaluated MTHS on distinct combinatorial optimization problems, where it outperforms both commonly-used heuristics and existing LLM-driven AHD approaches. Our results demonstrate that the hierarchical representations facilitate effective multi-task AHD, and the evolved metaheuristics exhibit strong generalization to related tasks.