ReVEL: Multi-Turn Reflective LLM-Guided Heuristic Evolution via Structured Performance Feedback

TL;DR

ReVEL introduces a hybrid framework embedding multi-turn LLM reasoning within an evolutionary algorithm to generate robust, diverse heuristics for NP-hard combinatorial problems, outperforming existing methods.

Contribution

It presents a novel multi-turn, feedback-driven LLM-guided heuristic evolution framework with structured performance feedback and adaptive meta-control.

Findings

ReVEL produces heuristics that outperform strong baselines on standard benchmarks.

The framework achieves statistically significant improvements in robustness and diversity.

Multi-turn reasoning with structured grouping enhances automated heuristic design.

Abstract

Designing effective heuristics for NP-hard combinatorial optimization problems remains a challenging and expertise-intensive task. Existing applications of large language models (LLMs) primarily rely on one-shot code synthesis, yielding brittle heuristics that underutilize the models' capacity for iterative reasoning. We propose ReVEL: Multi-Turn Reflective LLM-Guided Heuristic Evolution via Structured Performance Feedback, a hybrid framework that embeds LLMs as interactive, multi-turn reasoners within an evolutionary algorithm (EA). The core of ReVEL lies in two mechanisms: (i) performance-profile grouping, which clusters candidate heuristics into behaviorally coherent groups to provide compact and informative feedback to the LLM; and (ii) multi-turn, feedback-driven reflection, through which the LLM analyzes group-level behaviors and generates targeted heuristic refinements. These refinements are selectively integrated and validated by an EA-based meta-controller that adaptively balances exploration and exploitation. Experiments on standard combinatorial optimization benchmarks show that ReVEL consistently produces heuristics that are more robust and diverse, achieving statistically significant improvements over strong baselines. Our results highlight multi-turn reasoning with structured grouping as a principled paradigm for automated heuristic design.