Robust optimization (RO) provides a principled framework for decision-making under uncertainty, but its practical use is often limited by the need to manually reformulate uncertain optimization models into tractable deterministic counterparts. Recent large language models (LLMs) have been shown promising for automating optimization formulation, yet RO reformulation remains challenging because it requires precise multi-step reasoning and mathematically consistent transformations. To facilitate systematic evaluation of LLM-based reformulation, for which no dedicated benchmark currently exists, we develop AutoRO-Bench, a benchmark featuring an automated data generation pipeline for the core RO reformulation task and a curated dataset for the RO application task. To address the reformulation challenge, we propose Automated Reformulation with Experience Memory (AutoREM), a tuning-free memory-augmented framework that autonomously builds a structured textual experience memory by reflecting on past failed trajectories through a tailored offline adaptation procedure. AutoREM requires neither domain-specific expert knowledge nor parameter updates, and the resulting memory readily transfers across different base LLMs. Experimental results show that AutoREM consistently improves the accuracy and efficiency of RO reformulation across in-distribution datasets, out-of-distribution datasets, and diverse base LLMs.
Rounded capacity cuts (RCCs) are among the most effective cuts for capacitated vehicle-routing relaxations, but exact separation is computationally prohibitive at scale. Existing heuristic and neural separators can be fast, but often fail to produce sufficiently many effective cuts within practical separation budgets. We introduce SAG-Sep, a separator that scores node membership in RCC-inducing subsets across vehicle-count levels from a fractional LP solution in a single encoder forward pass, avoiding the iterative predict-and-coarsen inference used by NeuralSEP-style separators. SAG-Sep encodes the LP solution as a Sparse Augmented Graph (SAG), adding flow-informed multi-hop edges that expose long-range routing structure without densifying attention. Beyond LP-aware sparse encoding, we observe that high-value exact RCCs are typically nested, organizing into onion-like subset families, and SAG-Sep's node scores track subset nesting depth. This motivates Onion-Sweep (OS), a training-free decoder that ranks customers by their scores, evaluates the RCC violation of every prefix of the ranking in one vectorized pass, and emits the most violated prefix of each replica together with a cross-replica family of nested proposals, converting independent node scores into structurally coordinated RCC candidates without a tuned threshold or probing band. On the NeuralSEP benchmark with N=1000 customer instances, SAG-Sep with OS reduces the average root gap by 17.7% relative to the strongest NeuralSEP baseline, while the single-pass SAG-Sep separator achieves a roughly 30-fold per-iteration neural separation speedup. Our findings suggest that LP-aware sparse encoding and the nested structure of high-value cuts are structural patterns worth leveraging in neural separation more broadly.