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

Automatic Heuristic Design (AHD) has emerged as a transformative approach for solving combinatorial optimization problems. While recent Large Language Model (LLM)-based methods have shown promise, they predominantly rely on fixed evolutionary operators and struggle to effectively accumulate and reuse historical search experience. This paper proposes RefineEvo, a novel evolutionary framework that transforms AHD from a static trial-and-error process into a planning-guided, experience-driven system. RefineEvo introduces a Planner to dynamically schedule evolutionary operators and trigger refinement based on the current search state, and a Reflector to distill valuable lessons into a Bidirectional Experience Pool containing both positive insights and negative pitfalls. This synergistic framework enables the system to adapt its search tools to the evolving complexity of the problem and leverage trajectory-aware, situation-conditioned insights to guide generation. Experiments on several classic combinatorial optimization benchmarks demonstrate that RefineEvo consistently outperforms strong baselines. In particular, RefineEvo delivers superior solution quality while improving token efficiency, enabling more efficient and autonomous heuristic design.

Large language model-based automated heuristic design (LLM-AHD) has shown strong potential in discovering effective heuristics for combinatorial optimization problems. However, existing methods primarily optimize a single heuristic, whereas practical optimization frameworks often rely on multiple interacting components. Directly extending single-heuristic methods is challenging because early component selection can overlook components with late potential, while independent evolution ignores inter-component dependencies. We propose MuEvo, an LLM-driven framework for evolving heuristic ensembles under ensemble-level feedback. MuEvo combines Dynamic Component Management, which uses short-budget probing and a reversible lifecycle to revise component priorities throughout the search, with LLM-Driven Co-Evolution, which coordinates component populations through Multi-Ensemble Evaluation, Cross-Component Information Sharing, Relation-Guided Pair Evolution, and Adaptive Budget Allocation. We evaluate MuEvo on selection hyper-heuristics and componentized ant colony optimization across four combinatorial optimization domains. Results show that MuEvo consistently improves human-designed frameworks and outperforms representative multi-component extensions of state-of-the-art LLM-AHD methods, demonstrating its effectiveness across both controller-mediated heuristic pools and functionally differentiated algorithmic components.

LLM-based automated heuristic design (AHD) discovers heuristics for combinatorial optimization problems (COPs), where an LLM generates candidates in an evolutionary search. Existing frameworks freeze the generator or fine-tune it on a scalar fitness signal hiding which instances each heuristic covers. Reflection-based frameworks improve heuristics with natural-language feedback, but it stays in the prompt and never reaches the generator's weights. We propose EPOCH, which makes instance coverage the objective of the evolutionary search and fine-tunes the generator to internalize reflection. Parent selection, operator allocation, and stagnation recovery all optimize how well the heuristics jointly cover the training instances, so the search returns a complementary heuristic ensemble. The generator learns from its own search by experiential preference optimization. A teacher LLM returns a natural-language insight on the generated heuristics, and the generator produces new heuristics with this insight. These improvements join the preference pairs for direct preference optimization (DPO). Since DPO only teaches the generator to rank these improvements, a reflective self-distillation (RSD) term makes it more likely to generate them on its own, and the gains accumulate over the long horizon of the search. Across COPs and open-source LLM backbones, EPOCH's heuristic ensembles outperform inference-only and fine-tuned baselines and generalize across problem scales.