MOSAIC: Modular Search Architecture Evolution for LLM-Driven Heuristic Design in Multi-Objective Combinatorial Optimization

Large language model (LLM)-driven automated heuristic design (AHD) has attracted increasing attention for its potential to reduce labor-intensive manual design. However, existing LLM-driven multi-operator AHD methods typically optimize search behaviors within predefined operator organizations, which constrains the exploration of potential synergies among different search behaviors. To address this limitation, we propose MOSAIC, a modular search architecture evolution framework for LLM-driven AHD. MOSAIC represents each heuristic as an ordered, variable-length architecture composed of multiple search modules, where each module implements a search behavior and the architecture determines how these behaviors are organized. Based on this representation, MOSAIC jointly evolves modules and architectures through module rewriting and architecture variation. The former rewrites modules to explore and refine search behaviors, while the latter evolves module composition, execution order, and architecture length, enabling broader exploration of potential synergies among search behaviors. Experiments on multiple multi-objective combinatorial optimization problems show that MOSAIC outperforms advanced LLM-driven AHD methods and exhibits strong cross-scale generalization.