Combinatorial optimization

A combinatorial optimization problem consists in determining a best solution among a discrete set of solutions, called feasible solutions. In general, such a set is finite but huge, and is described implicitly, i.e., by means of a list of constraints that any feasible solution must satisfy. In order to formalize the notion of a best solution, some function, called the objective function, is considered. It associates a real value to each solution, and a best, or optimal, solution, is then a feasible solution minimizing or maximizing this objective function. In particular, combinatorial optimization deals with practical problems such as optimizing the design and operating of production systems, or, more generally, optimizing the decision making process of a company.

The research work carried out in the Combinatorial optimization (OC) team covers two main topics: Mathematical programming and applications and Graphs and optimization.

« Mathematical programming and applications »

This topic is essentially about discrete optimization (either linear or non linear). This kind of very general models can be used to formulate almost every single combinatorial optimization problem. Such problems are generally hard to solve, and, in many cases, only small ones can be solved efficiently. The researchers of the OC team that work on this topic aim at acquiring a better understanding of these problems, in order to be able to solve them more efficiently. They are also interested in solving efficiently practical optimization problems related to different fields: telecommunications, transport, energy, environment, etc. Finally, another aspect of interest is the one of finding robust optimal solutions for such problems. Indeed, in an industrial setting, it is usually more relevant to look for a “robust” solution, which will perform rather well in any possible situation, instead of looking for an “optimal” one for a very specific case. The OC team has already worked on the problem of computing such solutions, as the notion of robustness is a very rich and useful one.

« Graphs and optimization »

Graphs are mathematical tools which play a central role in Operational Research. They can be used to model various types of systems. Finding an optimal solution then generally consists in identifying an optimal structure in a graph. Because of the sizes of the associated real instances, even a powerful computer is not sufficient to provide an optimal solution within a reasonable amount of time. In order to make such a solution easier to find, one often needs to prove structural properties of optimal solutions, and then, whenever this is possible, use them to design efficient algorithms to solve the problem, either exactly, or approximately. The researchers of the OC team that work on this topic aim at applying this approach to some graph optimization problems, that are general enough to model many real-life situations. They are also interested in approximation algorithms, parameterized algorithms, and online algorithms.

Publications

2021

Articles de revue

  1. Chen, Z.; Fampa, M.; Lambert, A. and Lee, J. Mixing convex-optimization bounds for maximum-entropy sampling. In Mathematical Programming, 188: 539-568, 2021. doi  www 
  1. Falq, A-E.; Fouilhoux, P. and Kedad-Sidhoum, S. Mixed integer formulations using natural variables for single machine scheduling around a common due date. In Discrete Applied Mathematics, 290: 36-59, 2021. doi  www 
  1. Bouquet, V.; Delbot, F. c. and Picouleau, C. On the vertices belonging to all, some, none minimum dominating set. In Discrete Applied Mathematics, 288: 9-19, 2021. doi  www 
  1. Frosini, A.; Picouleau, C. and Rinaldi, S. Characterization of the degree sequences of (quasi) regular uniform hypergraphs. In Theoretical Computer Science, 868: 97-111, 2021. doi  www 
  1. Elloumi, S.; Lambert, A. and Lazare, A. Solving unconstrained 0-1 polynomial programs through quadratic convex reformulation. In Journal of Global Optimization, 80 (2): 231-248, 2021. doi  www 
  1. Elloumi, S.; Hudry, O.; Marie, E.; Martin, A.; Plateau, A. and Rovedakis, S. Optimization of wireless sensor networks deployment with coverage and connectivity constraints. In Annals of Operations Research, 298 (1-2): 183-206, 2021. doi  www 

2020

Articles de revue

  1. Costa, M.-C.; de Werra, D. and Picouleau, C. Minimal graphs for 2-factor extension. In Discrete Applied Mathematics, 2020. doi  www 
  1. Porumbel, D. C. Projective Cutting-Planes. In SIAM Journal on Optimization, 30 (1): 1007-1032, 2020. doi  www 
  1. Bentz, C. and Le Bodic, P. Complexity of the multicut problem, in its vanilla, partial and generalized versions, in graphs of bounded treewidth. In Theoretical Computer Science, 809: 239-249, 2020. doi  www 
  1. Alès, Z. and Knippel, A. The K -partitioning problem: Formulations and branch-and-cut. In Networks, 76 (3): 323-349, 2020. doi  www 
  1. Bentz, C.; Costa, M-C. and Hertz, A. On the edge capacitated Steiner tree problem. In Discrete Optimization, 38: 100607, 2020. doi  www 
  1. Quezada, F.; Gicquel, C.; Kedad-Sidhoum, S. and Vu, D. Q. A multi-stage stochastic integer programming approach for a multi-echelon lot-sizing problem with returns and lost sales. In Computers and Operations Research, 116: 104865, 2020. doi  www 
  1. Phouratsamay, S-L.; Kedad-Sidhoum, S. and Pascual, F. Coordination of a two-level supply chain with contracts. In 4OR: A Quarterly Journal of Operations Research, 2020. doi  www 
  1. Bucarey, V.; Elloumi, S.; Labbé, M. and Plein, F. Models and Algorithms for the Product Pricing with Single-Minded Customers Requesting Bundles. In Computers and Operations Research, 2020. doi  www 

2019

Articles de revue

  1. Paulusma, D.; Picouleau, C. and Ries, B. Critical vertices and edges in H-free graphs. In Discrete Applied Mathematics, 257: 361-367, 2019. doi  www 
  1. Elloumi, S. and Lambert, A. Global solution of non-convex quadratically constrained quadratic programs. In Optimization Methods and Software, 34 (1): 98-114, 2019. doi  www 
  1. Bentz, C. Weighted and locally bounded list-colorings in split graphs, cographs, and partial k-trees. In Theoretical Computer Science, 782: 11-29, 2019. doi  www 
  1. Bentz, C. An FPT Algorithm for Planar Multicuts with Sources and Sinks on the Outer Face. In Algorithmica, 81 (1): 224-237, 2019. doi  www 
  1. B"ulb"ul, K.; Kedad-Sidhoum, S. and c Sen, H. Single-machine common due date total earliness/tardiness scheduling with machine unavailability. In Journal of Scheduling, 22 (5): 543-565, 2019. doi  www 

Articles de conférence

  1. Quezada, F.; Gicquel, C. and Kedad-Sidhoum, S. A Stochastic Dual Dynamic Integer Programming for the Uncapacitated Lot-Sizing Problem with Uncertain Demand and Costs. In 29th International Conference on Automated Planning and Scheduling ICAPS2019, pages 353-361, AAAI Press, Berkeley, United States, 2019. www 

2018

Articles de revue

  1. Porumbel, D. C. From the separation to the intersection sub-problem in Benders decomposition models with prohibitively-many constraints. In Discrete Optimization, 29: 148-173, 2018. doi  www 
  1. Costa, M-C.; de Werra, D. and Picouleau, C. Minimal graphs for matching extension. In Discrete Applied Mathematics, 234: 47-55, 2018. doi  www 
  1. Porumbel, D. C. Prize-collecting set multicovering with submodular pricing. In International Transactions in Operational Research, 25 (4): 1221-1239, 2018. doi  www 
  1. Bendotti, P.; Fouilhoux, P. and Kedad-Sidhoum, S. The Unit-capacity Constrained Permutation Problem. In European Journal of Operational Research, 268 (2): 463-472, 2018. doi  www 
  1. Diner, ". Y. s.; Paulusma, D.; Picouleau, C. and Ries, B. Contraction and deletion blockers for perfect graphs and H-free graphs. In Theoretical Computer Science, 746: 49-72, 2018. doi  www 
  1. Watel, D. and Faye, A. Taxi-Sharing: Parameterized Complexity and Approximability of the Dial-a-ride problem with money as an incentive. In Theoretical Computer Science, 745: 202-223, 2018. doi  www 
  1. Billionnet, A. Phylogenetic conservation prioritization with uncertainty. In Biodiversity and Conservation, 27 (12): 3137-3153, 2018. doi  www 
  1. Billionnet, A. Quantifying extinction probabilities of endangered species for phylogenetic conservation prioritization may not be as sensitive as might be feared. In Biodiversity and Conservation, 27 (5): 1189-1200, 2018. doi  www 
  1. Phouratsamay, S-L.; Kedad-Sidhoum, S. and Pascual, F. Two-level lot-sizing with inventory bounds. In Discrete Optimization, 30: 1-19, 2018. doi  www 
  1. Bentz, C.; Costa, M-C.; Poirion, P-L. and Ridremont, T. Formulations for designing robust networks. An application to wind power collection. In Electronic Notes in Discrete Mathematics, 64: 365-374, 2018. doi  www 
  1. Artigues, C.; Bourreau, E.; Jost, V.; Kedad-Sidhoum, S. and Ramond, F. c. Trains do not vanish: the ROADEF/EURO challenge 2014. In Annals of Operations Research, 271 (2): 1091-1105, 2018. doi  www 
  1. Kedad-Sidhoum, S.; Monna, F.; Mounié, G. and Trystram, D. A Family of Scheduling Algorithms for Hybrid Parallel Platforms. In International Journal of Foundations of Computer Science, 29 (1): 63-90, 2018. doi  www 
  1. Helal, N.; Pichon, F.; Porumbel, D. C.; Mercier, D. and Lefevre, E. The capacitated vehicle routing problem with evidential demands. In International Journal of Approximate Reasoning, 95: 124-151, 2018. doi  www 

Articles de conférence

  1. Falq, A-E.; Fouilhoux, P. and Kedad-Sidhoum, S. MIP Formulations for Just-in-Time Scheduling with Common Due-Date. In International Symposium on Combinatorial Optimization (ISCO 2018), Marrakesh, Morocco, 2018. www 

2017

Articles de revue

  1. Billionnet, A.; Elloumi, S.; Lambert, A. and Wiegele, A. Using a Conic Bundle Method to Accelerate Both Phases of a Quadratic Convex Reformulation. In INFORMS Journal on Computing, 29 (2): 318-331, 2017. doi  www 
  1. Porumbel, D. C.; Goncalves, G.; Allaoui, H. and Hsu, T. Iterated Local Search and Column Generation to solve Arc-Routing as a permutation set-covering problem. In European Journal of Operational Research, 256 (2): 349-367, 2017. doi  www 

Communications

Publications

2020

Articles de conférence

  1. Silva, I. F.; Bouhtou, M.; Chardy, M.; Bentz, C. and Kedad-Sidhoum, S. Battery Energy Management of a Telecommunications Company to Participate in the Curtailment Market and Reduce the Total Energy Cost. In 2020 IEEE 8th International Conference on Smart Energy Grid Engineering (SEGE), pages 121-127, IEEE, Oshawa, France, 2020. doi  www 
  1. Bentz, C.; Costa, M-C.; Poirion, P-L.; Ridremont, T. and Zakour, C. Wind farm cable layout optimization with constraints of load flow and robustness. In ICREEE 2020: International Conference on Renewable Energy and Environment Engineering, Tokyo (on line), Japan, 2020. www 

2019

Articles de conférence

  1. Ethève, M.; Alès, Z.; Bissuel, C.; Juan, O. and Kedad-Sidhoum, S. A Graph-based Heuristic for Variable Selection in Mixed Integer Linear Programming. In PGMO Days, Paris, France, 2019. www 
  1. Lucas, R.; Alès, Z.; Ramond, F. c. and Elloumi, S. Reducing the Adaptation Costs of a Rolling Stock Schedule with Adaptive Solution: the Case of Demand Changes. In RailNorrk"oping 2019. 8th International Conference on Railway Operations Modelling and Analysis (ICROMA), pages 857-876, Norrk"oping, Sweden, Link"oping Electronic Conference Proceedings 69, 2019. www 
  1. Lambert, A.; Elloumi, S.; Godard, H.; Maeght, J. and Ruiz, M. Solving Alternative Current Optimal Power Flow to Global Optimality with Quadratic Reformulation Using Semi-Definite Programming and Branch-and-Bound. In PGMO days, Palaiseau, France, 2019. www 
  1. Lambert, A.; Elloumi, S.; Lazare, A. and Rodriguez-heck, e. The Impact of Quadratization in Convexification-Based Resolution of Polynomial Binary Optimization. In PGMO days, Palaiseau, France, 2019. www 
  1. Elloumi, S.; Lambert, A. and Lazare, A. Semidefinite programming relaxations through quadratic reformulation for box-constrained polynomial optimization problems. In 2019 6th International Conference on Control, Decision and Information Technologies (CoDIT), pages 1498-1503, IEEE, Paris, France, 2019. doi  www 
  1. Falq, A-E.; Fouilhoux, P. and Kedad-Sidhoum, S. MIP formulations for just-in-time scheduling around a common due-date. In 14th Workshop on Models and Algorithms for Planning and Scheduling Problems (MAPSP 2019), Renesse, Netherlands, 2019. www 
  1. Silva, I. F.; Bentz, C.; Bouhtou, M.; Chardy, M. and Kedad-Sidhoum, S. Optimizing Battery Usage for a Telecommunications Company Participating in a Curtailing Market. In PGMODays 2019, Paris, France, 2019. www 
  1. Silva, I. F.; Bentz, C.; Bouhtou, M.; Chardy, M. and Kedad-Sidhoum, S. Energy storage management with energy curtailing incentives in a telecommunications context. In 10th International Workshop on Lot sizing - IWLS 2019, Paris, France, 2019. www 
  1. Charles, M.; Dauzère-Pérès, S. and Kedad-Sidhoum, S. More realistic test instances for the Capacitated Lot-Sizing Problem. In 30th European Conference On Oparational Research, EURO2019, Dublin, Ireland, 2019. www 
  1. Charles, M.; Dauzère-Pérès, S.; Kedad-Sidhoum, S. and Mazhoud, I. Parallelized approaches to solve the capacitated lot-sizing problem with lost sales and setup times. In 10th International Workshop on Lot sizing - IWLS 2019, Paris, France, 2019. www 
  1. Godard, H.; Elloumi, S.; Lambert, A.; Maeght, J. and Ruiz, M. Novel Approach Towards Global Optimality of Optimal Power Flow Using Quadratic Convex Optimization. In 6th International Conference on Control, Decision and Information Technologies (CoDIT), Paris, France, 2019. doi  www 
  1. Quezada, F.; Gicquel, C. and Kedad-Sidhoum, S. Stochastic dual dynamic integer programming for a multi-echelon lot-sizing problem with remanufacturing and lost sales. In IEEE International Conference on Control, Decision and Information Technologies CODIT 2019, pages 1254-1259, IEEE, Paris, France, 2019. doi  www 
  1. Quezada, F.; Gicquel, C. and Kedad-Sidhoum, S. Stochastic lot-sizing problem with remanufacturing: a dual dynamic decomposition approach. In PGMO Days, Paris, France, 2019. www 

2018

Articles de conférence

  1. Lambert, A.; Elloumi, S.; Godard, H.; Maeght, J. and Ruiz, M. Solve Alternative Current Optimal Power Flow to global optimality. In ISMP 18, bordeaux, France, 2018. www 
  1. Lambert, A.; Elloumi, S. and Lazare, A. Unconstrained 0-1 polynomial optimization through convex quadratic reformulation. In ISMP 18, Bordeaux, France, 2018. www 
  1. Lambert, A. Valid inequalities for QCQPs. In ISMP 18, Bordeaux, France, 2018. www 
  1. Falq, A-E.; Fouilhoux, P. and Kedad-Sidhoum, S. Extreme points for scheduling around a common due date. In ISMP International Conference on Mathematical Programming (ISMP 2018), Bordeaux, France, 2018. www 
  1. Ngueveu, S. U.; Absi, N.; Artigues, C.; Kedad-Sidhoum, S. and Goupil, F. Decomposition method in a scheduling problem with energy storage and costs. In International Symposium on Mathematical Programming - ISMP 2018, Bordeaux, France, 2018. www 
  1. Milliet de Faverges, M.; Russolillo, G.; Picouleau, C.; Merabet, B. and Houzel, B. Modelling passenger train arrival delays with Generalized Linear Models and its perspective for scheduling at main stations. In 8th International Conference on Railway Engineering (ICRE 2018), IET, London, United Kingdom, 2018. doi  www 
  1. Quezada, F.; Gicquel, C. and Kedad-Sidhoum, S. Stochastic lot-sizing for remanufacturing planning with lost sales and returns. In IWLS 2018 - 9th International Workshop on Lot sizing, Ubatuba, Brazil, 2018. www 
  1. Quezada, F.; Gicquel, C. and Kedad-Sidhoum, S. Valid inequalities for solving a stochastic lot-sizing problem with returns. In 23rs Symposium on Mathematical Programming - ISMP 2018, Bordeaux, France, 2018. www 
  1. Bentz, C.; Costa, M-C. and Hertz, A. Minimum length disjoint paths and Capacitated (rooted) Steiner Tree. In Euro-Alio International Conference on Applied Combinatorial Optimization Aims and Objectives, Bologna, Italy, 2018. www 
  1. Absi, N.; Artigues, C.; Kedad-Sidhoum, S.; Ngueveu, S. U. and Goupil, F. Upper and lower bounds for an energy scheduling problem with piecewise-linear costs and storageresources. In PGMO Days, Paris, France, 2018. www 
  1. Absi, N.; Artigues, C.; Kedad-Sidhoum, S.; Ngueveu, S. U.; Rannou, J. and Saadi, O. Scheduling energy-consuming jobs on parallel machines with piecewise-linear costs and storage resources: A lot-sizing and scheduling perspective. In 16th International Conference on Project Management and Scheduling - PMS 2018, pages 1-4, TexMat, Rome, Italy, 2018. www 
  1. Dauzère-Pérès, S.; Absi, N.; Kedad-Sidhoum, S.; Penz, B. and Rapine, C. The single-item green lot-sizing problem with fixed carbon emissions. In European Conference on Operational Reasearch, Valencia, Spain, 2018. www 

2017

Articles de conférence

  1. Lambert, A. and Elloumi, S. Quadratic convex reformulation for partitioning problems. In EUROPT 17, Montreal, Canada, 2017. www 
  1. Elloumi, S.; Lambert, A. and Lazare, A. Global optimisation of binary polynomial programs. In PGMO Days, Palaiseau, France, 2017. www 
  1. Elloumi, S.; Godard, H.; Lambert, A.; Maeght, J. and Ruiz, M. Solving Optimal Power Flow through reformulation. In 15th EUROPT Workshop on Advances in Continuous Optimization, montréal, Canada, 2017. www 

Ongoing projects

    Past projects

      Top