SM2-AHD: Search Experience Memory and Meta-Cognitive Reflection for LLM-Based Automatic Heuristic Design

Automatic Heuristic Design (AHD) aims to construct high-quality heuristics with as little human intervention as possible; LLM-based AHD, which uses LLMs as code generators, has already produced heuristics that surpass hand-crafted ones through iterative search. Existing evolutionary methods, however, rely on a relatively fixed evolutionary framework and remain sensitive to the initial population and to the hyperparameters. We therefore propose SM2-AHD, a meta-level AHD framework in which the code population and the outer framework co-evolve throughout the search with two independent components. At the code level, Search Experience Memory (SEM) encodes each trajectory into a memory unit that carries its code lineage and failure attribution, and injects retrieved historical cases into the mutation prompt. At the level of the outer framework, Meta-Reflection periodically diagnoses verifiable search statistics and, under safety constraints, adjusts the exploration strength and the operator weights online. Experiments show that SM2-AHD outperforms several existing state-of-the-art methods across a range of heuristic design problems.