Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design

Handcrafting heuristics for solving complex optimization tasks (e.g., route planning and task allocation) is a common practice but requires extensive domain knowledge. Recently, Large Language Model (LLM)-based automatic heuristic design (AHD) methods have shown promise in generating high-quality heuristics without manual interventions. Existing LLM-based AHD methods employ a population to maintain a fixed number of top-performing LLM-generated heuristics and introduce evolutionary computation (EC) to iteratively enhance the population. However, these population-based procedures cannot fully develop the potential of each heuristic and are prone to converge into local optima. To more comprehensively explore the space of heuristics, this paper proposes to use Monte Carlo Tree Search (MCTS) for LLM-based heuristic evolution. The proposed MCTS-AHD method organizes all LLM-generated heuristics in a tree structure and can better develop the potential of temporarily underperforming heuristics. In experiments, MCTS-AHD delivers significantly higher-quality heuristics on various complex tasks. Our code is available.

(1) Optimization problems (e.g., combinatorial optimization) play an essential role in real life but are NP-hard. (2) We extend the existing LLM-based Automatic Heuristic Design method and propose a more effective MCTS-AHD method, which contributes to a comprehensive exploration of LLM-based Automatic Heuristic Design. (3) It has a significant improvement in effectiveness, being beneficial for optimizing algorithms in practical application scenarios.