{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/deep-learning-for-data-driven-districting-and","title":"Deep Learning for Data-Driven Districting-and-Routing","arxiv_id":"2402.06040","date":"2024-02-08","proceeding":null,"authors":["Arthur Ferraz","Cheikh Ahmed","Quentin Cappart","Thibaut Vidal"],"abstract":"Districting-and-routing is a strategic problem aiming to aggregate basic geographical units (e.g., zip codes) into delivery districts. Its goal is to minimize the expected long-term routing cost of performing deliveries in each district separately. Solving this stochastic problem poses critical challenges since repeatedly evaluating routing costs on a set of scenarios while searching for optimal districts takes considerable time. Consequently, solution approaches usually replace the true cost estimation with continuous cost approximation formulas extending Beardwood-Halton-Hammersley and Daganzo's work. These formulas commit errors that can be magnified during the optimization step. To reconcile speed and solution quality, we introduce a supervised learning and optimization methodology leveraging a graph neural network for delivery-cost estimation. This network is trained to imitate known costs generated on a limited subset of training districts. It is used within an iterated local search procedure to produce high-quality districting plans. Our computational experiments, conducted on five metropolitan areas in the United Kingdom, demonstrate that the graph neural network predicts long-term district cost operations more accurately, and that optimizing over this oracle permits large economic gains (10.12% on average) over baseline methods that use continuous approximation formulas or shallow neural networks. Finally, we observe that having compact districts alone does not guarantee high-quality solutions and that other learnable geometrical features of the districts play an essential role.","url_abs":"https://arxiv.org/abs/2402.06040v1","url_pdf":"https://arxiv.org/pdf/2402.06040v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"deep-learning-for-data-driven-districting-and","repo_url":"https://github.com/vidalt/districting-routing","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}