{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T11:50:55Z","timestamp":1790250655357,"version":"4.1.0"},"reference-count":39,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,7,30]],"date-time":"2020-07-30T00:00:00Z","timestamp":1596067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper studies the hybridization of Mixed Integer Programming (MIP) with dual heuristics and machine learning techniques, to provide dual bounds for a large scale optimization problem from an industrial application. The case study is the EURO\/ROADEF Challenge 2010, to optimize the refueling and maintenance planning of nuclear power plants. Several MIP relaxations are presented to provide dual bounds computing smaller MIPs than the original problem. It is proven how to get dual bounds with scenario decomposition in the different 2-stage programming MILP formulations, with a selection of scenario guided by machine learning techniques. Several sets of dual bounds are computable, improving significantly the former best dual bounds of the literature and justifying the quality of the best primal solution known.<\/jats:p>","DOI":"10.3390\/a13080185","type":"journal-article","created":{"date-parts":[[2020,7,30]],"date-time":"2020-07-30T12:15:38Z","timestamp":1596111338000},"page":"185","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Machine Learning-Guided Dual Heuristics and New Lower Bounds for the Refueling and Maintenance Planning Problem of Nuclear Power Plants"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3775-5629","authenticated-orcid":false,"given":"Nicolas","family":"Dupin","sequence":"first","affiliation":[{"name":"Laboratoire de Recherche en Informatique (LRI), CNRS UMR 8623, Department of Computer Science, Universit\u00e9 Paris-Saclay, 91190 Saint-Aubin, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4549-1010","authenticated-orcid":false,"given":"El-Ghazali","family":"Talbi","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Lille, CNRS UMR 9189-Centre de Recherche en Informatique Signal et Automatique de Lille (CRIStAL), F-59000 Lille, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s10479-015-2034-y","article-title":"Combining metaheuristics with mathematical programming, constraint programming and machine learning","volume":"240","author":"Talbi","year":"2016","journal-title":"Ann. Oper. Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1016\/j.ejor.2007.07.035","article-title":"Hybridizing exact methods and metaheuristics: A taxonomy","volume":"199","author":"Jourdan","year":"2009","journal-title":"Eur. J. Oper. Res."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Peschiera, F., Dell, R., Royset, J., Ha\u00eft, A., Dupin, N., and Batta\u00efa, O. (2020). A novel solution approach with ML-based pseudo-cuts for the Flight and Maintenance Planning problem. OR Spectr., 1\u201330.","DOI":"10.1007\/s00291-020-00591-z"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1016\/j.orl.2015.05.007","article-title":"A dual heuristic for mixed integer programming","volume":"43","author":"Li","year":"2015","journal-title":"Oper. Res. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Powell, M.J.D., and Scholtes, S. (2000). MIP: Theory and practice-closing the gap. System Modelling and Optimization, Springer.","DOI":"10.1007\/978-0-387-35514-6"},{"key":"ref_6","unstructured":"Wolsey, L.A. (1998). Integer Programming, Springer."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Talbi, E.G. (2013). The heuristic (dark) side of MIP solvers. Hybrid Metaheuristics, Springer.","DOI":"10.1007\/978-3-642-30671-6"},{"key":"ref_8","first-page":"1","article-title":"Matheuristics to stabilize column generation: Application to a technician routing problem","volume":"2018","author":"Dupin","year":"2018","journal-title":"Matheuristics"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1287\/opre.16.4.741","article-title":"Surrogate constraints","volume":"16","author":"Glover","year":"1968","journal-title":"Oper. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1287\/opre.39.4.553","article-title":"Aggregation and disaggregation techniques and methodology in optimization","volume":"39","author":"Rogers","year":"1991","journal-title":"Oper. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1016\/j.ejor.2016.09.051","article-title":"Iterative aggregation and disaggregation algorithm for pseudo-polynomial network flow models with side constraints","volume":"258","author":"Clautiaux","year":"2017","journal-title":"Eur. J. Oper. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1111\/itor.12445","article-title":"An iterative time-bucket refinement algorithm for a high-resolution resource-constrained project scheduling problem","volume":"27","author":"Riedler","year":"2020","journal-title":"Int. Trans. Oper. Res."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Bienstock, D., and Zambelli, G. (2020). On Generalized Surrogate Duality in Mixed-Integer Nonlinear Programming. Integer Programming and Combinatorial Optimization, Springer.","DOI":"10.1007\/978-3-030-45771-6"},{"key":"ref_14","unstructured":"Porcheron, M., Gorge, A., Juan, O., Simovic, T., and Dereu, G. (2020, June 15). Challenge ROADEF\/EURO 2010: A Large-Scale Energy Management Problem with Varied Constraints. Available online: https:\/\/www.fondation-hadamard.fr\/sites\/default\/files\/public\/bibliotheque\/roadef-euro2010.pdf."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/978-3-642-20364-0_15","article-title":"Local Search for Mixed-Integer Nonlinear Optimization: A Methodology and an Application","volume":"6622","author":"Gardi","year":"2011","journal-title":"Lect. Notes Comput. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1007\/s10951-012-0281-1","article-title":"A constraint programming-based approach to a large-scale energy management problem with varied constraints","volume":"16","author":"Brandt","year":"2013","journal-title":"J. Sched."},{"key":"ref_17","first-page":"60","article-title":"Dual Heuristics and New Lower Bounds for the Challenge EURO\/ROADEF 2010","volume":"2016","author":"Dupin","year":"2016","journal-title":"Matheuristics"},{"key":"ref_18","unstructured":"Khemmoudj, M. (2007). Mod\u00e9lisation et R\u00e9solution de Syst\u00e8mes de Contraintes: Application au Probl\u00e8me de Placement des Arr\u00eats et de la Production des R\u00e9acteurs Nucl\u00e9aires d\u2019EDF. [Ph.D. Thesis, University Paris 13]."},{"key":"ref_19","unstructured":"Griset, R. (2018). M\u00e9thodes pour la R\u00e9solution Efficace de Tr\u00e8s Grands Probl\u00e8mes Combinatoires Stochastiques. Application \u00e0 un Probl\u00e8me Industriel d\u2019EDF: Application \u00e0 un Probl\u00e8me Industriel d\u2019EDF. [Ph.D. Thesis, Universit\u00e9 de Bordeaux]."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/s13675-016-0078-7","article-title":"Tighter MIP formulations of the discretised Unit Commitment Problem with min-stop ramping constraints","volume":"5","author":"Dupin","year":"2017","journal-title":"EURO J. Comput. Optim."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1111\/itor.12557","article-title":"Parallel matheuristics for the discrete unit commitment problem with min-stop ramping constraints","volume":"27","author":"Dupin","year":"2020","journal-title":"Int. Trans. Oper. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1016\/j.ejor.2015.08.045","article-title":"Maintenance scheduling in the electricity industry: A literature review","volume":"251","author":"Froger","year":"2015","journal-title":"Eur. J. Oper. Res."},{"key":"ref_23","unstructured":"Dupin, N. (2015). Mod\u00e9lisation et R\u00e9solution de Grands Probl\u00e8mes Stochastiques Combinatoires: Application \u00e0 la Gestion de Production d\u2019\u00e9lectricit\u00e9. [Ph.D. Thesis, University of Lille]."},{"key":"ref_24","unstructured":"Dupin, N., and Talbi, E. (2020, June 15). Matheuristics to Optimize Refueling and Maintenance Planning of Nuclear Power Plants. Available online: https:\/\/arxiv.org\/pdf\/1812.08598.pdf."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1007\/s10951-013-0322-4","article-title":"A 0\u20131 integer linear programming approach to schedule outages of nuclear power plants","volume":"16","author":"Jost","year":"2013","journal-title":"J. Sched."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1007\/s10951-012-0310-0","article-title":"A solution approach based on Benders decomposition for the preventive maintenance scheduling problem of a stochastic large-scale energy system","volume":"16","author":"Lusby","year":"2013","journal-title":"J. Sched."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1007\/s10951-012-0286-9","article-title":"Solving the electricity production planning problem by a column generation based heuristic","volume":"16","author":"Rozenknop","year":"2013","journal-title":"J. Sched."},{"key":"ref_28","unstructured":"(2020, June 15). Final Results and Ranking of the ROADEF\/EURO Challenge 2010. Available online: https:\/\/www.roadef.org\/challenge\/2010\/en\/results.php."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/s10288-011-0165-9","article-title":"Localsolver 1. x: A black-box local-search solver for 0-1 programming","volume":"9","author":"Benoist","year":"2011","journal-title":"4OR"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/978-3-642-29843-1_19","article-title":"A Matheuristic Algorithm for a Large-Scale Energy Management Problem","volume":"7116","author":"Anghinolfi","year":"2012","journal-title":"Lect. Notes Comput. Sci."},{"key":"ref_31","unstructured":"Brandt, F. (2010). Solving a Large-Scale Energy Management Problem with Varied Constraints. [Master\u2019s Thesis, Karlsruhe Institute of Technology]."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1051\/ro\/2013053","article-title":"A Hybrid Approach Combining Local Search and Constraint Programming for a Large Scale Energy Management Problem","volume":"47","year":"2013","journal-title":"RAIRO Oper. Res."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1007\/s10951-012-0279-8","article-title":"Solving a real-life, large-scale energy management problem","volume":"16","author":"Godskesen","year":"2013","journal-title":"J. Sched."},{"key":"ref_34","unstructured":"Dell\u2019Amico, M., and Diaz, J. (2020, June 15). Constructive Heuristics and Local Search for a Large-Scale Energy Management Problem. EURO Conference 2011, Lisboa. Available online: http:\/\/www.roadef.org\/challenge\/2010\/files\/talks\/S04%20-%20Diaz%20Diaz.pdf."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/s10287-012-0148-0","article-title":"Stochastic nuclear outages semidefinite relaxations","volume":"9","author":"Gorge","year":"2012","journal-title":"Comput. Manag. Sci."},{"key":"ref_36","unstructured":"(2020, June 15). Data Instances of the ROADEF\/EURO Challenge 2010. Available online: https:\/\/www.roadef.org\/challenge\/2010\/en\/instances.php."},{"key":"ref_37","unstructured":"Joncour, C. (2010). Probl\u00e8mes de Placement 2D et Application \u00e0 L\u2019ordonnancement: Mod\u00e9lisation par la Th\u00e9orie des Graphes et Approches de Programmation Math\u00e9matique. [Ph.D. Thesis, Universit\u00e9 Bordeaux]."},{"key":"ref_38","unstructured":"Dupin, N., and Talbi, E. (2016, January 27\u201331). Multi-objective Robust Scheduling to maintain French nuclear power plants. Proceedings of the 6th International Conference on Metaheuristics and Nature Inspired Computing (META 2016), Marrakech, Morocco."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1287\/ijoc.6.4.445","article-title":"Preprocessing and probing techniques for mixed integer programming problems","volume":"6","author":"Savelsbergh","year":"1994","journal-title":"ORSA J. Comput."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/8\/185\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:52:55Z","timestamp":1760176375000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/13\/8\/185"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,30]]},"references-count":39,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2020,8]]}},"alternative-id":["a13080185"],"URL":"https:\/\/doi.org\/10.3390\/a13080185","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,7,30]]}}}