{
  "abstract": "The Wind Farm Layout Optimization problem consists of placing a given number of turbines within a given area so as to maximize energy production. One of its main challenges is the wake effect between turbines, which can strongly affect production and is a cumbersome function to evaluate and to embed in an optimization framework. In this paper we introduce a new endogenous wake model (EndoWake), based on the idea of treating the wind speed at every grid point as a decision variable, linked to its upwind neighbors through linear propagation constraints. This makes it possible to incorporate the wake equations directly into a Mixed-Integer Linear Programming (MILP) model. We then develop such a MILP model and, in particular, introduce a new class of valid \"band\" inequalities, showing that they substantially strengthen the root bound. Building on this, we design a branch-and-check scheme: the master problem retains only the site variables together with one hypograph variable per cell and scenario, integer solutions are evaluated by an exact linear-time oracle, and the optimality cuts are problem-specific \"upwind cuts\". Computational results are reported on a ladder of square grids under a four-sector axial wind rose, demonstrating the effectiveness of the proposed improvements.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40157",
  "author_total": 2,
  "authors": [
    {
      "name": "Martina Fischetti"
    },
    {
      "name": "Matteo Fischetti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5q5qm1675w3eq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40157",
  "fulltext_url": null,
  "id": "5q5qm1675w3eq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40157",
  "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",
      "2202|Wind Energy Research and Development"
    ]
  ],
  "openalex": "W7215114889",
  "pdf_url": "https://arxiv.org/pdf/2609.40157",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5q5qm1675w3eq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.40157",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40157"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "EndoWake: Modeling Wind by Linear Programming for Wind Farm Layout Optimization",
  "title_text": "EndoWake: Modeling Wind by Linear Programming for Wind Farm Layout Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/5q5qm1675w3eq",
  "venue": "arXiv",
  "versions": []
}