{
  "abstract": "Learning-based approaches to combinatorial optimization often predict solutions directly or use predictions to restrict search, while expressive energy-based models typically rely on approximate inference. We introduce EnerGNN, a framework that learns energy functions over complete binary configurations and minimizes them under explicit hard constraints through mixed integer programming (MIP). EnerGNN combines a graph neural network encoder with an optimization-compatible readout and a nonlinear energy head, enabling exact constrained inference over the learned energy. An optimality-aware contrastive loss trains the energy to reflect solution quality and constraint violations. Across Quadratic Knapsack, Combinatorial Auctions, and a personalized cell therapy supply chain problem, EnerGNN achieves near-optimal solutions with 100% feasibility. On the supply chain problem, it achieves a 0.05% mean primal gap and a 17.4$\\times$ speedup over the monolithic MIP. The learned energy also generalizes to larger instances and supports zero-shot constraint injection, adapting to changing constraints without retraining while preserving feasibility.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33930",
  "author_total": 2,
  "authors": [
    {
      "name": "Niki Triantafyllou"
    },
    {
      "name": "Maria M. Papathanasiou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/61j147dy1cawv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33930",
  "fulltext_url": null,
  "id": "61j147dy1cawv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33930",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2612|Advanced Optimization Algorithms Research"
    ]
  ],
  "openalex": "W7223962168",
  "pdf_url": "https://arxiv.org/pdf/2610.33930",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/61j147dy1cawv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33930",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33930"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "EnerGNN: Learning Optimization-Compatible Energy Functions for Exact Constrained Combinatorial Inference",
  "title_text": "EnerGNN: Learning Optimization-Compatible Energy Functions for Exact Constrained Combinatorial Inference",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/61j147dy1cawv",
  "venue": "arXiv",
  "versions": []
}