Large Language Models (LLMs) have advanced the field of Combinatorial Optimization through automated heuristic generation. Instead of relying on manual design, this LLM-Driven Heuristic Design (LHD) process leverages LLMs to iteratively generate and refine solvers to achieve high performance. However, existing LHD frameworks face two critical limitations: (1) Endpoint-only evaluation, which ranks solvers solely by final gap to a reference solution, ignoring the convergence process and runtime efficiency; (2) High adaptation costs, where distribution shifts necessitate re-adaptation to generate specialized solvers for heterogeneous instance groups. To address these issues, we propose Dynamics-Aware Solver Heuristics (DASH), a framework that co-optimizes solver search mechanisms and runtime schedules guided by a convergence-aware metric, thereby identifying efficient and high-performance solvers. Furthermore, to mitigate expensive re-adaptation, DASH incorporates Profiled Library Retrieval (PLR), which maintains group-specialized solvers for profile-aware warm starts. These solvers are archived concurrently during evolution, allowing DASH to reuse matched specialists across heterogeneous distributions without restarting adaptation. Experiments on four combinatorial optimization problems demonstrate that DASH improves runtime efficiency by over 4 times while outperforming prior LHD baselines in the overall balance between gap and runtime across diverse problem scales. Furthermore, by enabling profile-aware warm starts, DASH maintains lower gap under distribution shift while reducing LLM adaptation costs by about 90%.

翻译：大语言模型（LLMs）通过自动化启发式生成推进了组合优化领域。与依赖人工设计不同，这种LLM驱动的启发式设计（LHD）过程利用LLMs迭代生成并优化求解器以实现高性能。然而，现有LHD框架面临两个关键局限：（1）仅端点评估，即仅根据与参考解的最终差距对求解器进行排名，忽略收敛过程与运行时效率；（2）高适应成本，即分布偏移导致需要重新适应以生成针对异构实例组的专用求解器。为解决这些问题，我们提出动态感知求解器启发式（DASH）框架，该框架通过收敛感知指标协同优化求解器搜索机制与运行时调度，从而识别高效且高性能的求解器。此外，为缓解昂贵的重新适应过程，DASH引入配置文件库检索（PLR），该机制维护面向组专用的求解器用于配置文件感知的热启动。这些求解器在进化过程中同步归档，使DASH能够在异构分布间复用匹配的专门化求解器而无需重启适应。在四个组合优化问题上的实验表明，DASH在提升运行时效率超4倍的同时，在不同问题规模下，其在解质量与运行时之间的总体平衡优于先前LHD基线。此外，通过启用配置文件感知热启动，DASH在分布偏移下维持更低的解差距，同时将LLM适应成本降低约90%。