ArchOR: Contrastive and Signature-Guided Skill Learning for Optimization Modeling

Large Language Models (LLMs) can turn natural-language optimization tasks into solver-checked answers, but current agents remain brittle under narrative rewrites and often store reusable experience at the instance level. We introduce ArchOR, an archetype-centric skill agent that organizes experience by canonical modeling structure. ArchOR adds two retrieval-focused modules to cluster-based skill learning. Contrastive Archetype Representation Learning (CARL) converts preliminary cluster memberships into weak contrastive supervision and trains a small LoRA adapter so the embedding space better respects archetype boundaries. Signature-Guided Retrieval (S3R) attaches open-dimensional structural signatures to skills, filters candidates by Jaccard overlap, and then invokes semantic re-ranking only on structurally plausible skills. Across five in-distribution benchmarks, ArchOR reaches 72.16% Micro-Avg. Pass@1, improving significantly over the archetype-only variant and by 8.70 pp over the strongest prior skill-based baseline. It also reaches 29.15% on MIPLIB-NL and 76.34% on OOD NLCO after Nano-CO adaptation.