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See detailSiting Renewable Power Generation Assets with Combinatorial Optimization
Berger, Mathias ULiege; Radu, David-Constantin ULiege; Dubois, Antoine ULiege et al

E-print/Working paper (2020)

This paper studies the problem of siting renewable power generation assets using large amounts of climatological data. The problem is cast as a combinatorial optimisation problem seeking to maximise ... [more ▼]

This paper studies the problem of siting renewable power generation assets using large amounts of climatological data. The problem is cast as a combinatorial optimisation problem seeking to maximise spatiotemporal complementarity between sites while accounting for electrical load level and chronology. Model properties are closely analysed and a formal connection with the problem of maximising a submodular set function subject to a cardinality constraint is established. A custom solution method combining relaxation-based and local search algorithms is also proposed and benchmarked against state-of-the art methods using a realistic instance comprising tens of thousands of variables inspired by the problem of siting onshore wind power plants in Europe. Results show that for the present application, the proposed solution method is competitive with state-of-the-art methods both in terms of computing time and solution quality, as it reaches objective values at least as good as the proposed benchmarks on most instances studied and clearly outperforms them on a number of occasions. In addition, results highlight the importance of combining a relaxation-based method with a local search algorithm to produce high-quality solutions for this application. [less ▲]

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See detailAssessing the Economic Value of Renewable Resource Complementarity for Power Systems: an ENTSO-E Study
Radu, David-Constantin ULiege; Berger, Mathias ULiege; Dubois, Antoine ULiege et al

E-print/Working paper (2020)

Complementarity of variable renewable energy sources (RES) in both space and time has received a great deal of attention recently however, its value for power systems is still not properly understood ... [more ▼]

Complementarity of variable renewable energy sources (RES) in both space and time has received a great deal of attention recently however, its value for power systems is still not properly understood. This research gap is tackled in the current work by evaluating the benefits of siting RES assets according to resource complementarity criteria. For this purpose, a two-stage method is employed. First, the complementarity between RES is assessed and the locations sets that maximize it are selected using an integer programming model. Subsequently, the outcome of the first stage is used within an expansion planning framework which identifies the optimal system design and serves as basis for assessing the economic value of RES complementarity for power systems. The analysis is conducted on a realistic case study targeting the deployment of 450GW of offshore wind in Europe by 2050. Results show that siting based on RES complementarity is particularly attractive when the power density of wind developments is relatively high and when the inter-annual variability of the underlying resource is considered. More specifically, such a siting strategy leads to yearly savings between 0.3 and 1.2 billion EUR compared with conventional schemes seeking to deploy generation capacity at the most productive locations. [less ▲]

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See detailClustering and Kernel Density Estimation for Assessment of Measurable Residual Disease by Flow Cytometry
Jacqmin, Hugues; Chatelain, Bernard; Louveaux, Quentin ULiege et al

in Diagnostics (2020), 10(5),

Standardization, data mining techniques, and comparison to normality are changing the landscape of multiparameter flow cytometry in clinical hematology. On the basis of these principles, a strategy was ... [more ▼]

Standardization, data mining techniques, and comparison to normality are changing the landscape of multiparameter flow cytometry in clinical hematology. On the basis of these principles, a strategy was developed for measurable residual disease (MRD) assessment. Herein, suspicious cell clusters are first identified at diagnosis using a clustering algorithm. Subsequently, automated multidimensional spaces, named “Clouds”, are created around these clusters on the basis of density calculations. This step identifies the immunophenotypic pattern of the suspicious cell clusters. Thereafter, using reference samples, the “Abnormality Ratio” (AR) of each Cloud is calculated, and major malignant Clouds are retained, known as “Leukemic Clouds” (L-Clouds). In follow-up samples, MRD is identified when more cells fall into a patient’s L-Cloud compared to reference samples (AR concept). This workflow was applied on simulated data and real-life leukemia flow cytometry data. On simulated data, strong patient-dependent positive correlation (R2 = 1) was observed between the AR and spiked-in leukemia cells. On real patient data, AR kinetics was in line with the clinical evolution for five out of six patients. In conclusion, we present a convenient flow cytometry data analysis approach for the follow-up of hematological malignancies. Further evaluation and validation on more patient samples and different flow cytometry panels is required before implementation in clinical practice. [less ▲]

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See detailOperation rules of the Vesdre reservoir revisited
Dewals, Benjamin ULiege; Cuvelier, Thibaut; Archambeau, Pierre ULiege et al

Conference (2019, September 13)

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See detailComparison Between Robust and Stochastic Optimisation for Long-term Reservoir Management Under Uncertainty
Cuvelier, Thibaut ULiege; Archambeau, Pierre ULiege; Dewals, Benjamin ULiege et al

in Water Resources Management (2018), 32(5), 15991614

Long-term reservoir management often uses bounds on the reservoir level, between which the operator can work. However, these bounds are not always kept up-to-date with the latest knowledge about the ... [more ▼]

Long-term reservoir management often uses bounds on the reservoir level, between which the operator can work. However, these bounds are not always kept up-to-date with the latest knowledge about the reservoir drainage area, and thus become obsolete. The main difficulty with bounds computation is to correctly take into account the high uncertainty about the inflows to the reservoir. In this article, we propose a methodology to derive minimum bounds while providing formal guarantees about the quality of the obtained solutions. The uncertainty is embedded using either stochastic or robust programming in a model-predictive-control framework. We compare the two paradigms to the existing solution for a case study and find that the obtained solutions vary substantially. By combining the stochastic and the robust approaches, we also assign a confidence level to the solutions obtained by stochastic programming. The proposed methodology is found to be both efficient and easy to implement. It relies on sound mathematical principles, ensuring that a global optimum is reached in all cases. [less ▲]

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See detailOptimising workforce and energy costs by exploiting production flexibility
Cuvelier, Thibaut ULiege; Louveaux, Quentin ULiege

Conference (2017, July)

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 ... [more ▼]

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. Nevertheless, the plants can significantly reduce this impact: some electro-intensive factories could shift their production to time periods where the electricity is cheaper, resulting in large savings. At the same time, the grid operator can remunerate this consumption adaptation as a flexibility service. Our research goal is to optimise the operations of a factory around this flexibility. We compute a production plan that adapts to price forecasts, but also flexibility levers that adjust this plan to react to unexpected price changes. We propose the unifying concept of reservoir to provide sufficiently good models for the plant's processes. Nevertheless, this methodology implies to have frequent production plan changes, which directly impacts the workers, as they may be asked to follow barely predictable schedules. This has a significant detrimental effect on their quality of life. As a consequence, the human aspect of flexibility must also be considered: we seek for production plans that consider both workforce and energy costs, and we then assign workers to work shifts while ensuring their well-being. This HR orientation is the most innovative contribution of this research project. [less ▲]

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See detailA Machine Learning-Based Approximation of Strong Branching
Marcos Alvarez, Alejandro ULiege; Louveaux, Quentin ULiege; Wehenkel, Louis ULiege

in INFORMS Journal on Computing (2017), 29(1), 185-195

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 ... [more ▼]

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, namely strong branching, with a fast approximation. This approximated function is created by a machine learning technique from a set of observed branching decisions taken by strong branching. The philosophy of the approach is similar to reliability branching. However, our approach can catch more complex aspects of observed previous branchings in order to take a branching decision. The experiments performed on randomly generated and MIPLIB problems show promising results. [less ▲]

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See detailA Quantitative Doignon-Bell-Scarf theorem
Aliev, Iskander; Bassett, Robert; De Loera, Jesus et al

in Combinatorica (2017)

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 ... [more ▼]

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 generalization: Given an integer k, we prove that there exists a constant c(n,k), depending only on the dimension n and on the number k, such that if a bounded polyhedron {x in R^n : Ax <= b} contains exactly k integer points, then there exists a subset of the rows, of cardinality no more than c(n,k), defining a polyhedron that contains exactly the same k integer points. In this case c(n,0)=2^n as in the original case of Doignon-Bell-Scarf for infeasible systems of inequalities. We work on both upper and lower bounds for the constant c(n,k) and discuss some consequences, including a Clarkson-style algorithm to find the l-th best solution of an integer program with respect to the ordering induced by the objective function. [less ▲]

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See detailGuided Dive for the Spatial Branch-and-Bound
Gerard, Damien ULiege; Koeppe, Matthias; Louveaux, Quentin ULiege

in Journal of Global Optimization (2017)

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 ... [more ▼]

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-Bound-based solvers use a non-global solver at a few nodes to try to find better incumbents. We show that it is possible to improve the branching rules and the node priority by exploiting the solutions from the non-global solver. We also propose several smart adaptive strategies to choose when to run the non-global solver. We show that despite the time spent in solving more NLP problems in the nodes, the new strategies enable the algorithm to find the first good incumbents faster and to prove the global opti- mality faster. Numerous easy, medium size as well as hard NLP instances from the Coconut library are benchmarked. All experiments are run using the open source solver Couenne. [less ▲]

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See detailDirect control service from residential heat pump aggregation with specified payback
Georges, Emeline ULiege; Cornélusse, Bertrand ULiege; Ernst, Damien ULiege et al

in Proceedings of the 19th Power Systems Computation Conference (PSCC) (2016, June)

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 ... [more ▼]

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, followed by a payback of one hour and 15 minutes. The service modulation is relative to an optimized baseline that minimizes the energy costs. The potential amount of modulable power and the payback effect are computed by solving mixed integer linear problems. Within these problems, the building thermal behavior is modeled by an equivalent thermal network made of resistances and lumped capacitances whose parameters are identified from validated models. Simulations are performed on 100 freestanding houses. For an average 4.3 kW heat pump, results show a potential of 1.2 kW upward modulation with a payback of 600 Wh and 150 Wh of overconsumption. A downward modulation of 500 W per house can be achieved with a payback of 420 Wh and 120 Wh of overconsumption. [less ▲]

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See detailParametric Polyhedra with at least k Lattice Points: Their Semigroup Structure and the k-Frobenius Problem
Aliev, Iskander; De Loera, Jesus; Louveaux, Quentin ULiege

in Beveridge, Andrew; Griggs, Jerold; Hogben, Leslie (Eds.) et al Recent trends in Combinatorics (2016)

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 ... [more ▼]

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 theory that characterizes precisely the set Sg_k(A) of all vectors b in Sg(A) such that their fiber IPA(b) has at least k-solutions. We demonstrate that this set is finitely generated, a union of translated copies of a semigroup which can be computed explicitly via Hilbert bases computations. Related results can be derived for those right-hand-side vectors b for which IPA(b) has exactly k solutions or fewer than k solutions. We also show that, when n, k are fixed natural numbers, one can compute in polynomial time an encoding of Sg_k(A) as a generating function, using a short sum of rational functions. As a consequence, one can identify all right-hand-side vectors that have at least k solutions. Using this tool we prove that for fixed n; k the k-Frobenius number can be computed in polynomial time, generalizing a well-known result of R. Kannan. [less ▲]

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See detailBox search for the data mining of the key parameters of an industrial process
Louveaux, Quentin ULiege; Mathei, Axel; Mathieu, Sébastien ULiege

in Intelligent Data Analysis (2016), 20(6),

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 ... [more ▼]

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 performance of a monitored process. In particular we wish to find a set of rules, i.e. intervals on a reduced number of parameters, for which an output value is maximized. The model-free optimization problem to solve is to find a box, restricted on a limited amount of dimensions, with the maximum mean value of the included points. This article compares a machine learning-based heuristic to the solution computed by a mixed-integer linear program on real-life databases from steel and glass manufacturing. Computational results show that the heuristic obtains comparable solutions to the mixed integer linear approach. However, the exact approach is computationally too expensive to tackle real life databases. Results show that the restriction of five process parameters, on these databases, may improve the quality of the process by 50%. [less ▲]

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See detailFeasibility-oriented Branching Strategies for Global Optimization
Gerard, Damien ULiege; Köppe, Matthias; Louveaux, Quentin ULiege

E-print/Working paper (2016)

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 ... [more ▼]

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-Bound-based solvers use a non global solver at a few nodes to try to find better incumbents. We show that it is possible to improve the branching rules and the node priority by exploiting the solutions from the non global solver. We also propose several smart adaptive strategies to choose when to run the non global solver. We show that despite the time spent in solving many more NLP problems in the nodes, the new strategies enable the algorithm to find the first good incumbents faster and to prove the global optimality faster. Numerous easy, medium size as well as hard NLP instances from the Coconut library are benchmarked. All experiments are run using the open source solver Couenne. [less ▲]

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See detailInteger Programming and Combinatorial Optimization
Louveaux, Quentin ULiege; Skutella, Martin

Book published by Springer (2016)

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See detailOnline Learning for Strong Branching Approximation in Branch-and-Bound
Marcos Alvarez, Alejandro ULiege; Wehenkel, Louis ULiege; Louveaux, Quentin ULiege

E-print/Working paper (2016)

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 ... [more ▼]

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 them to take branching decisions. More specifically, numerical scores are used to rank the branching candidates. If, for a given variable, the learned approximation is deemed reliable, then the score for that variable is computed thanks to the learned function. If the approximation is not reliable yet, the real strong branching score is used instead. The scores that are computed through the real strong branching procedure are fed to the online learning algorithm in order to improve the approximated function. The experiments show promising results. [less ▲]

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See detailDSIMA: A testbed for the quantitative analysis of interaction models within distribution networks
Mathieu, Sébastien ULiege; Louveaux, Quentin ULiege; Ernst, Damien ULiege et al

in Sustainable Energy, Grids and Networks (2016), 5

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 ... [more ▼]

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 the distribution system operator, the transmission system operator, producers and retailers make their decisions based on mixed-integer linear programs. This testbed helps to highlight the characteristics of an interaction model, the benefits for the agents and eases the detection of unwanted or abusive behaviors which decreases the welfare. The testbed is implemented in Python and the optimization problems are encoded in the modeling language ZIMPL. A web interface is coupled with an instance generator using macroscopic parameters of the system such as the total power production. This testbed is, therefore, well suited to test the implemented interaction models on various scenarios and to extend the implementation to other models. Five interaction models developed with industrial partners are simulated over a year on a 75-bus test system. Simulations show that interaction models relying on active network management, as they have been developed, lead to substantial welfare even though they suffer from a lack of coordination between the DSO and the TSO. A conservative interaction model restricting grid users to an access range that is computed ahead of time to prevent any congestion, avoids shedding distributed generation but considerably restrains the amount of distributed production. [less ▲]

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See detailFeasibility-oriented Branching Strategies for Global Optimization
Gerard, Damien ULiege; Köppe, Matthias; Louveaux, Quentin ULiege

Conference (2015, July 13)

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 ... [more ▼]

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-Bound-based solvers use a non global solver at a few nodes to try to find better incumbents. We show that it is possible to improve the branching rules and the nodes priority by exploiting the solutions from the non global solver. We also propose several smart adaptive strategies to choose when to run the non global solver. We show that despite the time spent in solving many more NLP problems in the nodes, the new strategies enable the algorithm to find the first good incumbents much faster and to prove the global optimality faster. NLP instances from the COCONUT library are benchmarked. All experiments are run using the open source solver Couenne. [less ▲]

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See detailThe strength of multi-row models
Louveaux, Quentin ULiege; Poirrier, Laurent; Salvagnin, Domenico

in Mathematical Programming Computation (2015), 7(2), 113-148

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 ... [more ▼]

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 separating cut whenever one exists. The separator is not comparable in speed with the specific cutting-plane generators used in branch-and-cut solvers, but it is general-purpose. We can thus use it to compute cuts derived from any reasonably small relaxation PJ of a general mixed- integer problem, even when there exists no specific implementation for computing cuts with PJ. Exploiting this, we evaluate, from a computational perspective, the usefulness of cuts derived from several types of multi-row relaxations. In particular, we present results with four different strengthenings of the two-row intersection cut model, and multi-row models with up to fifteen rows. We conclude that only fully-strengthened two-row cuts seem to offer a significant advantage over two-row intersection cuts. Our results also indicate that the improvement obtained by going from models with very few rows to models with up to fifteen rows may not be worth the increased computing cost. [less ▲]

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See detailValid inequalities for the single arc design problem with set-ups
Agra, Agostinho; Doostmohammadi, Mahdi; Louveaux, Quentin ULiege

in Discrete Optimization (2015), 16

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 ... [more ▼]

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 integer problems such as lot-sizing and network design problems. We derive several families of valid inequalities that, in particular, generalize the arc resid- ual capacity inequalities and the flow cover inequalities. For the constant capacitated case we provide an extended compact formulation and give a partial description of the convex hull in the original space which is exact under a certain condition. By lifting some basic inequalities we provide some insight on the difficulty of obtaining such a full polyhedral description for the constant capacitated case. Preliminary computational results are presented. [less ▲]

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