{"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/column-generation-for-multistage-stochastic","title":"Column generation for multistage stochastic mixed-integer nonlinear programs with discrete state variables","arxiv_id":"2406.05052","date":"2024-06-07","proceeding":null,"authors":["Tushar Rathi","Benjamin P. Riley","Angela Flores-Quiroz","Qi Zhang"],"abstract":"Stochastic programming provides a natural framework for modeling sequential optimization problems under uncertainty; however, the efficient solution of large-scale multistage stochastic programs remains a challenge, especially in the presence of discrete decisions and nonlinearities. In this work, we consider multistage stochastic mixed-integer nonlinear programs (MINLPs) with discrete state variables, which exhibit a decomposable structure that allows its solution using a column generation approach. Following a Dantzig-Wolfe reformulation, we apply column generation such that each pricing subproblem is an MINLP of much smaller size, making it more amenable to global MINLP solvers. We further propose a method for generating additional columns that satisfy the nonanticipativity constraints, leading to significantly improved convergence and optimal or near-optimal solutions for many large-scale instances in a reasonable computation time. The effectiveness of the tailored column generation algorithm is demonstrated via computational case studies on a multistage blending problem and a problem involving the routing of mobile generators in a power distribution network.","url_abs":"https://arxiv.org/abs/2406.05052v2","url_pdf":"https://arxiv.org/pdf/2406.05052v2.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":"column-generation-for-multistage-stochastic","repo_url":"https://github.com/ddolab/cg-msminlp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}