MuEvo: LLM-Driven Evolution of Multi-Heuristic Ensemble

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.

Beyond Static Priors: Dynamic Neural Guidance for Large-Scale Ant Colony Optimization

Neural-guided Ant Colony Optimization (ACO) suffers from a fundamental training-inference misalignment: policies are typically trained to generate static priors (e.g., heatmaps), yet deployed to guide iterative, long-horizon search processes. In this paper, we present DyNACO, a novel framework that achieves dynamic neural guidance by periodically observing the pheromone distribution and the incumbent solution. To make DyNACO tractable at scale, we pair the policy with a perturbation-based ACO backend and a scope-restricted refinement mechanism that jointly ensure efficacy and stable credit assignment. On TSP, DyNACO scales to 100,000-node instances and outperforms neural baselines while often reducing total runtime compared to the unguided solver. We extend DyNACO to CVRP via a capacity-aware backend, consistently improving the unguided baseline with less than 1% neural overhead. We further provide in-depth analysis validating the model's generalization capabilities and elucidating why dynamic guidance outperforms static priors. Our work underscores the necessity of aligning neural training with iterative search dynamics in learning-guided optimization. The code is available at https://github.com/shoraaa/DyNACO.