MeEvo: Metacognitive Evolution Combined with Natural Evolution for Automatic Heuristic Design

Automated heuristic design (AHD) with large language models (LLMs) has produced strong heuristics for combinatorial optimization problems (COPs). Yet existing frameworks optimize for average performance on a small fixed dataset and steer the search with "verbal gradients" distilled from scalar better/worse feedback. No single heuristic dominates across instance distributions, and scalar feedback tells the LLM whether a heuristic improved, but not where in the instance space or why. We propose MOSAIC, a grid-based framework that adversarially co-evolves problem instances and specialist heuristics inside a Quality-Diversity (QD) archive indexed by structural instance features. Instances evolve to expose weaknesses of the current heuristics, and heuristics evolve to eliminate them by specializing to the newly exposed regions. Each archive cell keeps a specialist heuristic, representative instances, and insights explaining what works in its region, forming a persistent memory that accumulates over the evolutionary search. For each heuristic pair sampled from distant grid regions, an LLM-guided evolutionary loop generates discriminative instances, and a decision tree identifies the feature-space regions where each heuristic wins. A reflection LLM then contrasts the two heuristics to produce multi-directional insights that persist in those regions and guide crossover and mutation. The archive is simultaneously a co-evolved benchmark of discriminative instances and a pool of region specialist heuristics, from which greedy selection extracts a compact complementary portfolio. Across COPs, test sizes, and LLM backbones, the portfolio consistently outperforms state-of-the-art LLM-based AHD methods, and the co-evolved instances attain higher feature-space coverage and stronger heuristic discrimination than evolutionary instance-generation baselines.

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.

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.