Title: Cognitively Inspired Reflective Evolution: Interactive Multi-Turn LLM–EA Synthesis of Heuristics for Combinatorial Optimization
Primary area: optimization
Keywords: Combinatorial Optimization, Heuristic Evolution, Large Language Models, Multi-turn Strategy Generation, Reflective Mechanism

Abstract: Designing effective heuristics for NP-hard combinatorial optimization problems remains a challenging, expertise-driven task. Recent uses of large language models (LLMs) primarily rely on one-shot code synthesis, producing fragile, unvalidated heuristics and under-utilizing LLMs' capacity for iterative reasoning and structured reflection. In this paper, we introduce Cognitively Inspired Reflective Evolution - CIRE, a hybrid framework that embeds LLMs as interactive, multi-turn reasoners within an evolutionary algorithm (EA). CIRE (i) constructs performance-profile clusters of candidate heuristics to give the LLM compact, behaviorally coherent context; (ii) engages the model in multi-turn, feedback-driven reflection tasks that produce explainable performance analyses and targeted heuristic refinements to broaden the exploration--exploitation frontier; and (iii) integrates and selectively validates these proposals via an EA meta-controller that adaptively balances search. Extensive experiments on benchmark combinatorial optimization show that CIRE yields heuristics that are both more robust and more diverse, achieving consistent, statistically significant gains over one-shot LLM generation, genetic programming baselines, and population-based EAs without LLM feedback. These findings suggest that interactive, cognitively inspired multi-turn reasoning is a promising paradigm for automated heuristic design.