# SpecAHD: Localize to Specialize for Automated Heuristic Design in Large-Scale Routing Problems

arXiv: https://arxiv.org/abs/2607.23676 · HTML: https://mlsanity.com/paper/2607.23676/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 35 references that are in the map.
- First posted on arXiv 26 Jul 2026.

## Builds on (most cited first, 13 of 13)

- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Learning to Delegate for Large-scale Vehicle Routing](https://mlsanity.com/paper/2107.04139/) (2021)
- [HSEvo: Elevating Automatic Heuristic Design with Diversity-Driven Harmony Search and Genetic Algorithm Using LLMs](https://mlsanity.com/paper/2412.14995/) (2024)
- [PyVRP: a high-performance VRP solver package](https://mlsanity.com/paper/2403.13795/) (2023)
- [EoH-S: Evolution of Heuristic Set using LLMs for Automated Heuristic Design](https://mlsanity.com/paper/2508.03082/) (2025)
- [CO-Bench: Benchmarking Language Model Agents in Algorithm Search for Combinatorial Optimization](https://mlsanity.com/paper/2504.04310/) (2025)
- [In-the-loop Hyper-Parameter Optimization for LLM-Based Automated Design of Heuristics](https://mlsanity.com/paper/2410.16309/) (2024)
- [LLM-Driven Instance-Specific Heuristic Generation and Selection](https://mlsanity.com/paper/2506.00490/) (2025)
- [Multimodal LLM-assisted Evolutionary Search for Programmatic Control Policies](https://mlsanity.com/paper/2508.05433/) (2025)
- [G-LNS: Generative Large Neighborhood Search for LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2602.08253/) (2026)
- [BOP-Elites, a Bayesian Optimisation Approach to Quality Diversity Search with Black-Box descriptor functions](https://mlsanity.com/paper/2307.09326/) (2023)
- [Large Language Model-Driven Full-Component Evolution of Adaptive Large Neighborhood Search](https://mlsanity.com/paper/2603.06996/) (2026)

## Built on by (most cited first, 1 of 1)

- [SPO: Discovering Adaptive Large Neighborhood Search Operators via Stackelberg Program Optimization](https://mlsanity.com/paper/2609.31179/) (2026)

## Abstract (arXiv)

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.