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Planning of Heuristics: Strategic Planning on Large Language Models with Monte Carlo Tree Search for Automating Heuristic Optimization

Heuristics have achieved great success in solv- ing combinatorial optimization problems (COPs). However, heuristics designed by humans re- quire too much domain knowledge and testing time. Given the fact that Large Language Mod- els (LLMs) possess strong capabilities to under- stand and generate content, and a knowledge base that covers various domains, which offer a novel way to automatically optimize heuristics. There- fore, we propose Planning of Heuristics (PoH), an optimization method that integrates the self- reflection of LLMs with the Monte Carlo Tree Search (MCTS), a well-known planning algo- rithm. PoH iteratively refines generated heuristics by evaluating their performance and providing im- provement suggestions. Our method enables to it- eratively evaluate the generated heuristics (states) and improve them based on the improvement sug- gestions (actions) and evaluation results (rewards), by effectively simulating future states to search for paths with higher rewards. In this paper, we apply PoH to solve the Traveling Salesman Prob- lem (TSP) and the Flow Shop Scheduling Prob- lem (FSSP). The experimental results show that PoH outperforms other hand-crafted heuristics and Automatic Heuristic Design (AHD) by other LLMs-based methods, and achieves the signifi- cant improvements and the state-of-the-art per- formance of our proposed method in automating heuristic optimization with LLMs to solve COPs.

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