{
  "abstract": "Wind Farm Layout Optimization places turbines to maximize the expected energy under a wind rose, each turbine lowering the wind downwind. In the EndoWake model the wind field is a variable, propagated by linear inequalities, and layouts are certified by branch-and-check. On a ladder of grids it certifies the $10\\times10$ grid and leaves the larger grids open after one hour. We tighten the relaxation by a convexification computed rather than derived: every pattern of turbines inside a small tile of the grid is enumerated once with its power and enters the master as a column. The device is valid because the wind field is antitone, and exact, for the cubic power curve, with a Benders cut at integer layouts. Reduced-cost fixing and propagation between overlapping tiles shrink the master before the tree search, and the tree repeats the fixing at every improving incumbent. The incumbent comes from a tile heuristic or an LP dive. On the same computer as the branch-and-check, the $12\\times12$ and $14\\times14$ grids close in 48 and 395 seconds. The $16\\times16$ grid is certified on five seeds from random starts, one job per seed, the heuristic on a GPU, in 1413 seconds under the uniform rose and 6484 seconds under a non-uniform one. Times are medians. A pre-specified test set of 36 unseen instances with forbidden cells confirms the advantage in the axial setting. Certified means closed at the solver's gap of $10^{-4}$: the optimum lies within it plus a residual of at most 0.00042%.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39503",
  "author_total": 2,
  "authors": [
    {
      "name": "Martina Fischetti"
    },
    {
      "name": "Matteo Fischetti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2vy50ykwxakpf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39503",
  "fulltext_url": null,
  "id": "2vy50ykwxakpf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39503",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CE"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39503",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2vy50ykwxakpf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39503",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39503"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A Dantzig-Wolfe reformulation of the EndoWake model for optimal wind farm layouts",
  "title_text": "A Dantzig-Wolfe reformulation of the EndoWake model for optimal wind farm layouts",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/2vy50ykwxakpf",
  "venue": "arXiv",
  "versions": []
}