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Start Over Topic mathematical optimization Publication Year Range Last 3 years Language english
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1. Stability of optimal traffic plans in the irrigation problem

Author

Antoine Prouff, Antonio De Rosa, Andrea Marchese, Maria Colombo, Paul Pegon, Ecole Polytechnique Fédérale de Lausanne (EPFL), Courant Institute of Mathematical Sciences [New York] (CIMS), New York University [New York] (NYU), NYU System (NYU)-NYU System (NYU), Department of mathematics/Dipartimento di Matematica [Univ. Trento], Università degli Studi di Trento (UNITN), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales (MOKAPLAN), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay), Maria Colombo was partially supported by the Swiss National Science Foundation grant 200021_182565. Antonio De Rosa has been supported by the NSF DMS Grant No. 1906451. Andrea Marchese acknowledges partial support from GNAMPA-INdAM., Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, Bocconi Institute for Data Science and Analytics (BIDSA), Bocconi University [Milan, Italy], Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, M. C. was partially supported by the Swiss National Science Foundation grant 200021_182565. A. D. R. has been supported by the NSF DMS Grant No. 1906451 and the NSF DMS Grant No. 2112311. A. M. acknowledges partial support from GNAMPA-INdAM. A.P. was supported by the Fondation Mathématiques Jacques Hadamard. P.P and A.P. both acknowledge EPFL for hosting them during the semester this paper was prepared., Inria de Paris, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)

Subjects
BRANCHED TRANSPORT, Mathematical optimization, Irrigation, TRAFFIC PLANS, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], 01 natural sciences, Stability (probability), symbols.namesake, Mathematics - Analysis of PDEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Computer Science::Networking and Internet Architecture, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Discrete Mathematics and Combinatorics, Limit (mathematics), 0101 mathematics, Mathematics - Optimization and Control, Mathematics, TRANSPORTATION NETWORK, BRANCHED TRANSPORT, IRRIGATION PROBLEM, TRAFFIC PLANS, STABILITY, STABILITY, IRRIGATION PROBLEM, Applied Mathematics, TRANSPORTATION NETWORK, 010102 general mathematics, Eulerian path, Flow network, 010101 applied mathematics, Optimization and Control (math.OC), Mathematics - Classical Analysis and ODEs, symbols, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Analysis, Lagrangian, Analysis of PDEs (math.AP)
Abstract

We prove the stability of optimal traffic plans in branched transport. In particular, we show that any limit of optimal traffic plans is optimal as well. This result goes beyond the Eulerian stability proved in [7], extending it to the Lagrangian framework.

Published
2022

2. An iterative dynamic programming approach for the temporal knapsack problem

Author

Boris Detienne, Gaël Guillot, François Clautiaux, Reformulations based algorithms for Combinatorial Optimization (Realopt), Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), This work was funded by Investments for the future Program IdEx Bordeaux, Cluster of ExcellenceSySNum.Experiments presented in this paper were carried out using the PLAFRIM experimental testbed,being developed under the Inria PlaFRIM development action with support from Bordeaux INP, LABRIand IMB and other entities: Conseil R ́egional d’Aquitaine, Universit ́e de Bordeaux, CNRS and ANR inaccordance to the programme d’investissements d’Avenir (see https://www.plafrim.fr/), Plafrim, RealOpt, Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université Sciences et Technologies - Bordeaux 1-Université Bordeaux Segalen - Bordeaux 2-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université Sciences et Technologies - Bordeaux 1-Université Bordeaux Segalen - Bordeaux 2-Institut de Mathématiques de Bordeaux (IMB), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest

Subjects
Mathematical optimization, Information Systems and Management, General Computer Science, Computer science, Generalization, Temporal knapsack, 0211 other engineering and technologies, 02 engineering and technology, Management Science and Operations Research, Industrial and Manufacturing Engineering, Set (abstract data type), symbols.namesake, Lagrangian Relaxation, 0502 economics and business, 050210 logistics & transportation, 021103 operations research, 05 social sciences, Exact algorithm, Successive Sublimation Dynamic Programming method, Exponential function, Dynamic programming, Lagrangian relaxation, Knapsack problem, Modeling and Simulation, symbols, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

International audience; In this paper, we address the temporal knapsack problem (TKP). In this generalization of the classical knapsack problem, selected items enter and leave the knapsack at fixed dates. We solve the TKP with a dynamic program of exponential size, which is solved using a method called Successive Sublimation Dynamic Programming (SSDP). This method starts by relaxing a set of constraints from the initial problem, and iteratively reintroduces them when needed. We show that a direct application of SSDP to the temporal knapsack problem does not lead to an effective method, and that several improvements are needed to compete with the best results from the literature.

Published
2021