LLM-assisted evolutionary search (LES) has emerged as a promising paradigm for automated algorithm design. However, existing methods usually suffer from two inherent limitations when facing the automated design of real-world complex algorithms that usually consist of multiple components. The first limitation is that they either focus on modifying entire algorithms, making it difficult to reuse high-quality components, or concentrate on component refinement within a limited set of predefined multicomponent configurations. The second limitation is the insufficient explicit modeling and exploitation of algorithm semantics. These limitations severely degrade search efficiency and hinder effective exploration of complex design spaces. Therefore, this paper proposes STABLE (Semantics-Aware Bilevel Co-Evolution), an LES method purpose-built for automated multicomponent algorithm design that introduces structural algorithm formulation and semantics-driven evolution. In STABLE, complex algorithms are organized into hierarchical and modular architectures rooted in domain knowledge, aligning the search space with their intrinsic compositional traits. Based on this structured algorithm formulation, STABLE simultaneously optimizes high-level multicomponent configurations and low-level functional components, enabling coordinated cross-level updates while maintaining suitable granularities for design space exploration. At each level, STABLE establishes a multi-faceted semantic model to assist LLMs in capturing structural correlations, functional compatibilities, and inherent rationalities among algorithm components. This semantic model serves as the core guidance for evolutionary search, enabling principled algorithm generation and algorithm evaluation. Extensive experiments demonstrate that STABLE outperform both human-designed baselines and those from advanced LES methods.
Designing heuristics for combinatorial optimization problems (COPs) is a fundamental yet challenging task that traditionally requires extensive domain expertise. Recently, Large Language Model (LLM)-based Automated Heuristic Design (AHD) has shown promise in autonomously generating heuristic components with minimal human intervention. However, most existing LLM-based AHD methods enforce fixed algorithmic templates to ensure executability, which confines the search to component-level tuning and limits system-level algorithmic expressiveness. To enable open-ended solver synthesis beyond rigid templates, we propose Automated Algorithm Design via Evolutionary Program Trees (A2DEPT), which treats LLMs as system-level algorithm architects. A2DEPT explores the vast program space via a tree-structured evolutionary search with hybrid selection and hierarchical operators, enabling iterative refinement of complete algorithms. To make open-ended generation practical, we enforce executability with a lightweight program-maintenance loop that performs feedback-driven repair. In experiments, A2DEPT consistently outperforms representative LLM-based baselines on both standard and highly constrained benchmarks. On the standard benchmarks, it reduces the mean normalized optimality gap by 9.8% relative to the strongest competing AHD baseline.
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.
Large Language Model-assisted Evolutionary Search (LES) has emerged as a powerful paradigm for automated algorithm design. However, existing LES methods primarily optimize for average performance, inherently directing search effort toward instances that contribute most to this metric while leaving others poorly served, resulting in weak tail robustness and limited real-world reliability. To address this limitation, we propose Dynamic Instance Clustering and Specialized Algorithm Design (DyCA), an LES framework with a feature-free, structure-aware mechanism for constructing reliable algorithm portfolios under heterogeneous instance distributions. DyCA treats instance clustering as a co-evolving component within the search process, reusing accumulated evaluation data as feature-free signals to progressively partition instances with similar algorithmic response patterns. The uncovered clusters decompose the mixed objective into a set of structure-aware sub-objectives, thereby enabling finer-grained and more adaptive guidance for specialized algorithm design. Experimental results across four algorithm design tasks with heterogeneous instances demonstrate that DyCA outperforms state-of-the-art LES baselines, improving tail robustness by an average of 15.2% and overall performance by 7.1% while maintaining competitive head performance.