这篇论文用双层优化让LLM自动写出针对不同区域的启发式规则，在多个大规模路由问题上比现有方法好57%，还有理论保证，值得一看。
SpecAHD提出了一种耦合双层优化框架，用于在单个问题实例内部实现启发式规则的区域特化。上层搜索学习暴露有界修复区域的位置，下层进化互补的可执行启发式程序池。在四个大规模路由问题（CVRP、VRPTW、PDP等）上，SpecAHD相比最强AHD基线将目标成本降低了最高57.7%，并且在大多数公开实例上超越了每实例基线包络线。该框架具有子模性，提供了(1-1/e)的贪婪选择近似保证。
SpecAHD: Localize to Specialize for Automated Heuristic Design in Large-Scale Routing Problems
LLM-based automated heuristic design (AHD) typically scores executable programs on complete instances or within fixed solver components. In large-scale routing problems, localized reconstruction reduces the size of each optimization task, but repair regions within the same incumbent can exhibit substantially different structures. One construction rule must therefore compromise across them. In this paper, we propose SpecAHD, a coupled bilevel framework for within-instance specialization. An upper-level search learns where to expose bounded repair regions, while a lower-level search evolves a complementary repertoire of executable heuristics for the induced repair tasks. The upper-level program determines the repair tasks seen by the lower level, while checked repair outcomes determine how upper-level programs are evaluated. The lower-level objective favors heuristics that perform well on average or solve tasks that the current repertoire handles poorly. For the repair tasks induced by a fixed upper-level program and a fixed lower-level candidate pool, this objective is monotone submodular, allowing greedy repertoire selection with a (1-1/e) approximation guarantee. Across four routing problems and multiple LLM backbones, SpecAHD reduces held-out objective cost by up to 57.7% against the strongest competing AHD baseline and outperforms the per-instance baseline envelope on most public instances.