SpecAHD：在大规模路由问题中定位以专门化自动启发式设计
SpecAHD: Localize to Specialize for Automated Heuristic Design in Large-Scale Routing Problems
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中文总结 AI 辅助
针对大规模路由问题，提出耦合双层框架SpecAHD，上层搜索确定修复区域，下层为修复任务开发启发式方法，目标具单调次模性可贪婪选择，实验表明其相比基线大幅降低成本，性能更优。
中文摘要 AI 辅助
基于大语言模型的自动启发式设计（AHD）通常在完整实例或固定求解器组件内对可执行程序进行评分。在大规模路由问题中，局部重建可减小每个优化任务的规模，但同一现有解中的修复区域可能呈现出截然不同的结构。因此，一个构建规则必须在它们之间进行权衡。本文提出了SpecAHD，这是一种用于实例内专门化的耦合双层框架。上层搜索学习在何处暴露有界修复区域，而下层搜索则为诱导的修复任务开发一套互补的可执行启发式方法。上层程序确定下层看到的修复任务，而检查后的修复结果决定上层程序的评估方式。下层目标倾向于平均表现良好或解决当前方法集处理不佳的任务的启发式方法。对于由固定的上层程序和固定的下层候选池诱导的修复任务，该目标是单调次模的，允许以（1-1/e）的近似保证进行贪婪方法集选择。在四个路由问题和多个大语言模型主干上，SpecAHD相对于最强的竞争AHD基线将留出的目标成本降低了高达57.7%，并且在大多数公共实例上优于每个实例的基线包络。
英文摘要
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.
