Title: Experience-Guided Reflective Co-Evolution of Prompts and Heuristics for Automatic Algorithm Design
Primary area: applications to computer vision, audio, language, and other modalities
Keywords: Large Language Model;Auto Heuristic Design;Heuristic Evolution

Abstract: Combinatorial optimization problems are traditionally tackled with handcrafted heuristic algorithms, which demand extensive domain expertise and significant implementation effort. Recent progress has highlighted the potential of automatic heuristic design powered by large language models (LLMs), enabling the automated generation and refinement of heuristics. These approaches typically maintain a population of heuristics and employ LLMs as mutation operators to evolve them across generations. While effective, such methods often risk stagnating in local optima. To address this issue, we propose the Experience-Guided Reflective Co-\textbf{Evo}lution of \textbf{P}rompt and \textbf{H}euristics (\textbf{EvoPH}) for automatic algorithm design, a novel framework that integrates the island migration model with the MAP elites algorithm to simulate diverse heuristic populations. In EvoPH, prompts are co-evolved with heuristic strategies, guided by performance feedback and predefined strategy selection. We evaluate our framework on two problems, i.e., Traveling Salesman Problem and Bin Packing Problem. Experimental results demonstrate that EvoPH achieves the lowest relative error against optimal solutions across both datasets, advancing the field of automatic algorithm design with LLMs.