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.
LLM workflows, which coordinate structured calls to individual LLMs (each augmented with varying instructions and tools) to achieve a particular goal, offer a promising path towards extending the capabilities of LLMs and building powerful systems that can tackle diverse tasks. However, existing approaches for building such workflows generally rely on human-crafted pipelines and prompts, which presents a substantial bottleneck in real world deployment. How can automatically induce and optimize such workflows in a data-driven way? This paper describes a simple data-driven approach for automatically inducing LLM workflows. We formulate workflow induction as a bilevel optimization problem: an outer loop which optimizes a high-level sketch of the workflow (in particular how the LLM calls should be structured), and an inner loop which optimizes each individual LLM call one-by one. Both loops are optimized with ``textual gradients'' where for the inner loop we optimize each component in a modular way through ``backpropagating'' textual gradients layer-by-layer. We find that LLM workflows discovered through our \textsc{FlowBot} (work\textbf{flow} induction through \textbf{b}ilevel \textbf{o}ptimization and \textbf{t}extual gradients) approach performs competitively against strong baselines that make use of human-crafted or automatically-generated workflows.