Aliev, I., Bassett, R., De Loera, J., & Louveaux, Q. (in press). A Quantitative Doignon-Bell-Scarf theorem.

*Combinatorica*.Peer reviewed (verified by ORBi)

The famous Doignon-Bell-Scarf theorem is a Helly-type result about the existence of integer solutions to systems of linear inequalities. The purpose of this paper is to present the following quantitative ...

Gerard, D., Koeppe, M., & Louveaux, Q. (in press). Guided Dive for the Spatial Branch-and-Bound.

*Journal of Global Optimization*.Peer reviewed (verified by ORBi)

We study the spatial Brand-and-Bound algorithm for the global opti- mization of nonlinear problems. In particular we are interested in a method to find quickly good feasible solutions. Most spatial Branch-and ...

Cuvelier, T., & Louveaux, Q. (2017, July).

*Optimising workforce and energy costs by exploiting production flexibility*. Paper presented at 21st Conference of the International Federation of Operational Research Societies, Québec, Canada.Peer reviewed

In a world where the electricity prices become more and more volatile, notably due to renewable energies, the industry is suffering from cost variations never seen before, especially when electro-intensive ...

Marcos Alvarez, A., Louveaux, Q., & Wehenkel, L. (2017). A Machine Learning-Based Approximation of Strong Branching.

*INFORMS Journal on Computing, 29*(1), 185-195.Peer reviewed (verified by ORBi)

We present in this paper a new generic approach to variable branching in branch-and-bound for mixed- integer linear problems. Our approach consists in imitating the decisions taken by a good branching strategy ...

Georges, E., Cornélusse, B., Ernst, D., Louveaux, Q., Lemort, V., & Mathieu, S. (2016). Direct control service from residential heat pump aggregation with specified payback.

*Proceedings of the 19th Power Systems Computation Conference (PSCC)*.Peer reviewed

This paper addresses the problem of an aggregator controlling residential heat pumps to offer a direct control flexibility service. The service is defined by a 15 minute power modulation, upward or downward ...

Aliev, I., De Loera, J., & Louveaux, Q. (2016). Parametric Polyhedra with at least k Lattice Points: Their Semigroup Structure and the k-Frobenius Problem. In A., Beveridge, J., Griggs, L., Hogben, G., Musiker, & P., Tetali (Eds.),

*Recent trends in Combinatorics*(pp. 753-778). Springer.Peer reviewed

The well-studied semigroup Sg(A) = {b : b = Ax; x in Z^n; x >= 0} can be
stratified by the sizes of the polyhedral fibers IPA(b) = {x : Ax = b; x >= 0; x in Z^n}. The
key theme of this paper is a structure ...

Gerard, D., Köppe, M., & Louveaux, Q. (2016).

*Feasibility-oriented Branching Strategies for Global Optimization*. Eprint/Working paper retrieved from http://orbi.ulg.ac.be/handle/2268/200219.We study the spatial Brand-and-Bound algorithm for the global optimization of nonlinear problems. In particular we are interested in a method to find quickly good feasible solutions. Most spatial Branch-and ...

Louveaux, Q., Mathei, A., & Mathieu, S. (2016). Box search for the data mining of the key parameters of an industrial process.

*Intelligent Data Analysis, 20*(6).Peer reviewed (verified by ORBi)

To increase their competitiveness, many industrial companies monitor their production process, collecting large amount of measurements. This paper describes a technique using this data to improve the ...

Marcos Alvarez, A., Wehenkel, L., & Louveaux, Q. (2016).

*Online Learning for Strong Branching Approximation in Branch-and-Bound*. Eprint/Working paper retrieved from http://orbi.ulg.ac.be/handle/2268/192361.We present an online learning approach to variable branching in branch-and-bound for mixed-integer linear problems. Our approach consists in learning strong branching scores in an online fashion and in using ...

Mathieu, S., Louveaux, Q., Ernst, D., & Cornélusse, B. (2016). DSIMA: A testbed for the quantitative analysis of interaction models within distribution networks.

*Sustainable Energy, Grids and Networks, 5*, 78 - 93.Peer reviewed (verified by ORBi)

This article proposes an open-source testbed to simulate interaction models governing the exchange of flexibility services located within a distribution network. The testbed is an agent-based system in which ...

Gerard, D., Köppe, M., & Louveaux, Q. (2015, July 13).

*Feasibility-oriented Branching Strategies for Global Optimization*. Paper presented at International Symposium on Mathematical Programming (ISMP), Pittsburgh, PA.We study the spatial Brand-and-Bound algorithm for the global optimization of nonlinear
problems. In particular we are interested in a method to find quickly good feasible solutions.
Most spatial Branch-and ...

Louveaux, Q., Poirrier, L., & Salvagnin, D. (2015). The strength of multi-row models.

*Mathematical Programming Computation, 7*(2), 113-148.Peer reviewed (verified by ORBi)

We develop a method for computing facet-defining valid inequalities for any mixed-integer set PJ. Our practical implementation does not return only facet- defining inequalities, but it is able to find a ...

Agra, A., Doostmohammadi, M., & Louveaux, Q. (2015). Valid inequalities for the single arc design problem with set-ups.

*Discrete Optimization, 16*, 17-35.Peer reviewed

We consider a mixed integer set which generalizes two well-known sets: the single node fixed- charge network set and the single arc design set. Such set arises as a relaxation of feasible sets of general mixed ...

Gerard, D., Louveaux, Q., & Cornélusse, B. (2015).

*A NLP-MILP iterating algorithm for operational planning in electrical distribution systems*. Eprint/Working paper retrieved from http://orbi.ulg.ac.be/handle/2268/200220.We consider a class of optimal power flow (OPF) applications where some loads offer a modulation service in exchange for an activation fee. These applications can be modeled as multi-period formulations of the ...

Marcos Alvarez, A., Wehenkel, L., & Louveaux, Q. (2015).

*Machine Learning to Balance the Load in Parallel Branch-and-Bound*. Eprint/Working paper retrieved from http://orbi.ulg.ac.be/handle/2268/181086.We describe in this paper a new approach to parallelize branch-and-bound on a certain number of processors. We propose to split the optimization of the original problem into the optimization of several ...

Merciadri, L., Mathieu, S., Ernst, D., & Louveaux, Q. (2014). Optimal Assignment of Off-Peak Hours to Lower Curtailments in the Distribution Network.

*Proceedings of the 5th European Innovative Smart Grid Technologies (ISGT)*.Peer reviewed

We consider a price signal with two settings: off-peak tariff and on-peak tariff.
Some loads are connected to specific electricity meters which allow the consumption of power only in off-peak periods ...

Gemine, Q., Ernst, D., Louveaux, Q., & Cornélusse, B. (2014). Relaxations for multi-period optimal power flow problems with discrete decision variables.

*Proceedings of the 18th Power Systems Computation Conference (PSCC'14)*.Peer reviewed

We consider a class of optimal power flow (OPF) applications where some loads offer a modulation service in exchange for an activation fee. These applications can be modeled as multi-period formulations of the ...

Mathieu, S., Louveaux, Q., Ernst, D., & Cornélusse, B. (2014). A quantitative analysis of the effect of flexible loads on reserve markets.

*Proceedings of the 18th Power Systems Computation Conference (PSCC)*.Peer reviewed

We propose and analyze a day-ahead reserve market model that handles bids from flexible loads.
This pool market model takes into account the fact that a load modulation in one direction must usually be ...

Aliev, I., De Loera, J., & Louveaux, Q. (2014, June). Integer Programs with Prescribed Number of Solutions and a Weighted Version of Doignon-Bell-Scarf’s Theorem.

*Lecture Notes in Computer Science*.Peer reviewed

In this paper we study a generalization of the classical fesibility problem in integer linear programming, where an ILP needs to have a prescribed number of solutions to be considered solved.
We first provide ...

St-Pierre, D. L., Maes, F., Ernst, D., & Louveaux, Q. (2014). A learning procedure for sampling semantically different valid expressions.

*International Journal of Artificial Intelligence, 12*(1), 18-35.Peer reviewed

A large number of problems can be formalized as finding the best symbolic expression to maximize a given numerical objective. Most approaches to approximately solve such problems rely on random exploration of ...

Louveaux, Q., & Poirrier, L. (2014). An algorithm for the separation of two-row cuts.

*Mathematical Programming, 143*(1-2), 111-146.Peer reviewed (verified by ORBi)

We consider the question of finding deep cuts from a model with two rows of the type PI = {(x,s) ∈ Z2 ×Rn+ : x = f +Rs}. To do that, we show how to reduce the complexity of setting up the polar of conv(PI ...

Fonteneau, R., Ernst, D., Boigelot, B., & Louveaux, Q. (2014). Lipschitz robust control from off-policy trajectories.

*Proceedings of the 53rd IEEE Conference on Decision and Control (IEEE CDC 2014)*.Peer reviewed

We study the minmax optimization problem introduced in [Fonteneau et al. (2011), ``Towards min max reinforcement learning'', Springer CCIS, vol. 129, pp. 61-77] for computing control policies for batch mode ...

Marcos Alvarez, A., Louveaux, Q., & Wehenkel, L. (2014).

*A Supervised Machine Learning Approach to Variable Branching in Branch-And-Bound*. Eprint/Working paper retrieved from http://orbi.ulg.ac.be/handle/2268/167559.We present in this paper a new approach that uses supervised machine learning techniques to improve the performances of optimization algorithms in the context of mixed-integer programming (MIP). We focus on ...

Mathieu, S., & Louveaux, Q. (2014). A combinatorial branch-and-bound algorithm for box search.

*Discrete Optimization, 13*, 36-48.Peer reviewed

Considering a set of points in a multi-dimensional space with an associated real value for each point, we want to find the box with the maximum sum of the values of the included points.
This problem has ...

Mathieu, S., Ernst, D., & Louveaux, Q. (2013). An efficient algorithm for the provision of a day-ahead modulation service by a load aggregator.

*Proceedings of the 4th European Innovative Smart Grid Technologies (ISGT)*.Peer reviewed

This article studies a decision making problem faced by an aggregator willing to offer a load modulation service to a Transmission System Operator. This service is contracted one day ahead and consists in a ...

Fonteneau, R., Ernst, D., Boigelot, B., & Louveaux, Q. (2013). Généralisation Min Max pour l'Apprentissage par Renforcement Batch et Déterministe : Relaxations pour le Cas Général T Etapes.

*8èmes Journées Francophones de Planification, Décision et Apprentissage pour la conduite de systèmes (JFPDA'13)*.Peer reviewed

Cet article aborde le problème de généralisation minmax dans le cadre de l'apprentissage par renforcement batch et déterministe. Le problème a été originellement introduit par [Fonteneau, 2011], et il a déjà ...

Fonteneau, R., Ernst, D., Boigelot, B., & Louveaux, Q. (2013). Min max generalization for deterministic batch mode reinforcement learning: relaxation schemes.

*SIAM Journal on Control & Optimization, 51*(5), 3355–3385.Peer reviewed (verified by ORBi)

We study the min max optimization problem introduced in Fonteneau et al. [Towards min max reinforcement learning, ICAART 2010, Springer, Heidelberg, 2011, pp. 61–77] for computing policies for batch mode ...

Mathieu, S., Karangelos, E., Louveaux, Q., & Ernst, D. (2012, October 08).

*A computationally efficient algorithm for the provision of a day-ahead modulation service by a load aggregator*. Poster session presented at DYSCO Study Day : Dynamical systems, control and optimization Kickoff of phase VII.We study a decision making problem faced by an aggregator willing to offer a load modulation service to a Transmission System Operator (TSO). In particular, we concentrate on a day-ahead service consisting of ...

Fonteneau, R., Ernst, D., Boigelot, B., & Louveaux, Q. (2012). Généralisation min max pour l'apprentissage par renforcement batch et déterministe : schémas de relaxation.

*Septièmes Journées Francophones de Planification, Décision et Apprentissage pour la conduite de systèmes (JFPDA 2012)*.Peer reviewed

On s’intéresse au problème de généralisation min max dans le cadre de l’apprentissage par renforcement batch et déterministe. Le problème a été originellement introduit par Fonteneau et al. (2011). Dans un ...

Fonteneau, R., Ernst, D., Boigelot, B., & Louveaux, Q. (2011). Relaxation schemes for min max generalization in deterministic batch mode reinforcement learning.

*4th International NIPS Workshop on Optimization for Machine Learning (OPT 2011)*.Peer reviewed

We study the min max optimization problem introduced in [Fonteneau, 2011] for computing policies for batch mode reinforcement learning in a deterministic setting. This problem is NP-hard. We focus on the two ...

Dey, S., & Louveaux, Q. (2011). Split rank of triangle and quadrilateral inequalities.

*Mathematics of Operations Research, 36*(3), 432-461.Peer reviewed (verified by ORBi)

A simple relaxation of two rows of a simplex tableau is a mixed integer set consisting of two
equations with two free integer variables and non-negative continuous variables. Recently
Andersen et al. and ...

Louveaux, Q. (2011). Lift-and-project inequalities.

*Wiley Encylopedia of Operations Research and Management Science*. John Wiley & sons.The lift-and-project technique is a systematic way to generate valid inequalities
for a mixed binary program. The technique is interesting both on the theoretical and
on the practical point of view. On the ...

Lupien St-Pierre, D., Louveaux, Q., & Teytaud, O. (2011). Online Sparse Bandit for Card Games.

*Advance in Computer Games*.Peer reviewed

Finding an approximation of a Nash equilibria in matrix games is an important topic that reaches beyond the strict application to matrix games. A bandit algorithm commonly used to approximate a Nash ...

Andersen, K., Louveaux, Q., & Weismantel, R. (2010). Mixed-integer sets from two rows of two adjacent simplex bases.

*Mathematical Programming, 124*(1-2), 455-480.Peer reviewed (verified by ORBi)

In 2007 we studied a mixed-integer set arising from two rows of a
simplex tableau. We showed that facets of such a set can be obtained from
lattice point free triangles and quadrilaterals associated with ...

Louveaux, Q. (2010, July).

*Sparse Two-Row Cuts and an Algorithm for the Separation Problem*. Paper presented at Mixed Integer Programming workshop, Atlanta, USA.We propose a systematic way to generate sparse cuts from multiple rows of the simplex tableau. We also discuss the question of separation for a multi-row model. To this end, we consideer the polar system ...

Andersen, K., Louveaux, Q., & Weismantel, R. (2010). An analysis of mixed integer linear sets based on lattice point free convex sets.

*Mathematics of Operations Research, 35*(1), 233-256.Peer reviewed (verified by ORBi)

The set obtained by adding all cuts whose validity follows from a maximal lattice free polyhedron with max-facet-width at most w is called the w th split closure. We show the w th split closure is a polyhedron ...

Louveaux, Q. (2009, December).

*Split rank of two-row cuts*. Paper presented at Workshop on multi-row cuts, Bertinoro, Italy.A simple relaxation consisting of two rows of a simplex tableau is a mixed-integer set with two equations, two free integer variables, and nonnegative continuous variables. Recently, Andersen et al. and ...

Louveaux, Q. (2009, August).

*Geometric Study of Mixed-integer Sets from Two Rows of Two Adjacent Simplex Bases*. Paper presented at 20th International Symposium on Mathematical Programming, Chicago, USA.We generalize the study of sets arising from two rows of a simplex tableau by considering bounds on the nonbasic variables. We show that new classes of facets arise that cannot be obtained from triangles and ...

Louveaux, Q. (2009, January).

*Split rank of triange and quadrilateral inequalities*. Paper presented at 13th combinatorial optimization workshop, Aussois, France.A simple relaxation consisting of two rows of a simplex tableau is a mixed-integer set with two equations, two free integer variables, and nonnegative continuous variables. Recently, Andersen et al. and ...

Andersen, K., Louveaux, Q., & Weismantel, R. (2008). Certificates of linear mixed integer infeasibility.

*Operations Research Letters, 36*(6), 734-738.Peer reviewed (verified by ORBi)

We derive a certificate of integral infeasibility for linear systems with equations and inequalities by generating algebraically an outer description of a lattice point free polyhedron that contains the given ...

Köppe, M., Louveaux, Q., & Weismantel, R. (2008). Intermediate integer programming representations using value disjunctions.

*Discrete Optimization, 5*(2), 293-313.Peer reviewed

We introduce a general technique to create an extended formulation
of a mixed-integer program. We classify the integer variables into blocks,
each of which generates a finite set of vector values. The ...

Louveaux, Q., & Weismantel, R. (2008). Polyhedral properties for the intersection of two knapsacks.

*Mathematical Programming, 113*(1), 15-37.Peer reviewed (verified by ORBi)

We address the question to what extent polyhedral knowledge about
individual knapsack constraints suffices or lacks to describe the convex hull of
the binary solutions to their intersection. It turns out ...

Louveaux, Q. (2007, July).

*Cutting planes and infeasibility certificates from lattice-point-free polyhedra*. Paper presented at Workshop on Mixed-Integer Programming, Montreal, Canada.A central result in the theory of integer optimization states that a system of linear diophantine equations Ax = b has no integral solution if and only if there exists a vector in the dual lattice, yT A ...

Andersen, K., Louveaux, Q., Weismantel, R., & Wolsey, L. A. (2007, June). Inequalities from two rows of the simplex tableau.

*Lecture Notes in Computer Science*, 1-15.Peer reviewed

In this paper we explore the geometry of the integer points in
a cone rooted at a rational point. This basic geometric object allows us to
establish some links between lattice point free bodies and the ...

Louveaux, Q. (2007, January).

*Cutting planes from lattice-point-free polyhedra*. Paper presented at 11th combinatorial optimization workshop, Aussois, France.In this talk, we generalize the concept of a split (that leads to split cuts) to any lattice-point-free polyhedron. We show how we can generate cutting planes for a polyhedron from these objects. Associated to ...

Louveaux, Q., & Wolsey, L. A. (2007). Lifting, Superadditivity, Mixed Integer Rounding and Single Node Flow Sets Revisited.

*Annals of Operations Research, 153*(1), 47-77.Peer reviewed (verified by ORBi)

In this survey we attempt to give a unified presentation of a variety of
results on the lifting of valid inequalities, as well as a standard procedure com-
bining mixed integer rounding with lifting for ...

Louveaux, Q. (2006, January).

*Intermediate integer programming representations using value disjunctions*. Paper presented at 10th workshop on combinatorial optimization, Aussois, France.We introduce a general technique for creating an extended formulation of a mixed-integer program. We classify the integer variables into blocks, each of which generates a finite set of vector values. The ...

Louveaux, Q. (2005, September).

*Discrete optimization*. Poster session presented at Making Europe more attractive for researchers, Pisa, Italy.Have you ever wondered what is the shortest route to join the office? What is the best way to plan a trip through several cities? You have maybe already played with magical squares? Then you have met one of ...

Louveaux, Q. (2005, March).

*Valid inequalities for the intersection of two knapsacks*. Paper presented at 9th combinatorial optimization workshop, Aussois, France.We address the question to what extent polyhedral knowledge about individual knapsack constraints suffices or lacks to describe the convex hull of the binary solutions to their intersection. It turns out that ...

Louveaux, Q. (2004).

*Exploring Structure and Reformulations in Different Integer Programming Algorithms*. Unpublished doctoral thesis, Université catholique de Louvain, Belgique.In this thesis we consider four topics all related to using problem reformulations in order to solve integer programs, i.e. optimization problems in which the decision variables must be integer.
We first ...

Köppe, M., Louveaux, Q., Weismantel, R., & Wolsey, L. A. (2004). Extended formulations for Gomory Corner polyhedra.

*Discrete Optimization, 1*(2), 141-165.Peer reviewed

We present several types of extended formulations for integer programs, based on irreducible integer solutions to Gomory’s group relaxations. We present algorithmic schemes based on an iterative reformulation ...

Louveaux, Q., & Wolsey, L. A. (2003). Lifting, Superadditivity, Mixed Integer Rounding and Single Node Flow Sets Revisited.

*4OR : Quarterly Journal of the Belgian, French and Italian Operations Research Societies, 1*, 173-207.Peer reviewed

In this survey we attempt to give a unified presentation of a variety of
results on the lifting of valid inequalities, as well as a standard procedure combining
mixed integer rounding with lifting for the ...

Louveaux, Q., & Wolsey, L. A. (2002). Combining problem structure and basis reduction to solve a class of hard integer programs.

*Mathematics of Operations Research, 27*(3), 470-484.Peer reviewed (verified by ORBi)

We consider a hard integer programming problem that is difficult for the standard
branch-and-bound approach even for small instances. A reformulation based
on lattice basis reduction is known to be more ...