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See detailBatch mode reinforcement learning based on the synthesis of artificial trajectories
Fonteneau, Raphaël ULg; Murphy, Susan A.; Wehenkel, Louis ULg et al

in Annals of Operations Research (2013), 208(1), 383-416

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See detailThe Mathematics of Peter L. Hammer (1936-2006): Graphs, Optimization, and Boolean Models
Boros, Endre; Crama, Yves ULg; de Werra, Dominique et al

in Annals of Operations Research (2011), 188

This volume contains a collection of papers published in memory of Peter L. Hammer (1936-2006). Peter Hammer made substantial contributions to several areas of operations research and discrete mathematics ... [more ▼]

This volume contains a collection of papers published in memory of Peter L. Hammer (1936-2006). Peter Hammer made substantial contributions to several areas of operations research and discrete mathematics, including, in particular, mathematical programming (linear and quadratic 0--1 programming, pseudo-Boolean optimization, knapsack problems, etc.), combinatorial optimization (transportation problems, network flows, MAXSAT, simple plant location, etc.), graph theory (special classes of graphs, stability problems, and their applications), data mining and classification (Logical Analysis of Data), and, last but not least, Boolean theory (satisfiability, duality, Horn functions, threshold functions, and their applications). The volume contains 23 contributed papers along these lines. [less ▲]

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See detailLogical Analysis of Data: Classification with justification
Boros, Endre; Crama, Yves ULg; Hammer, Peter L. et al

in Annals of Operations Research (2011), 188

Learning from examples is a frequently arising challenge, with a large number of algorithms proposed in the classification, data mining and machine learning literature. The evaluation of the quality of ... [more ▼]

Learning from examples is a frequently arising challenge, with a large number of algorithms proposed in the classification, data mining and machine learning literature. The evaluation of the quality of such algorithms is frequently carried out ex post, on an experimental basis: their performance is measured either by cross validation on benchmark data sets, or by clinical trials. Few of these approaches evaluate the learning process ex ante, on its own merits. In this paper, we dis- cuss a property of rule-based classifiers which we call "justifiability", and which focuses on the type of information extracted from the given training set in order to classify new observations. We investigate some interesting mathematical properties of justifiable classifiers. In partic- ular, we establish the existence of justifiable classifiers, and we show that several well-known learning approaches, such as decision trees or nearest neighbor based methods, automatically provide justifiable clas- sifiers. We also identify maximal subsets of observations which must be classified in the same way by every justifiable classifier. Finally, we illustrate by a numerical example that using classifiers based on "most justifiable" rules does not seem to lead to over fitting, even though it involves an element of optimization. [less ▲]

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See detailSpace and time allocation in a shipyard assembly hall
Bay, Maud ULg; Crama, Yves ULg; Langer, Yves et al

in Annals of Operations Research (2010), 179(1), 57-76

We present a space and time allocation problem that arises in assembly halls producing large building blocks (namely, a shipyard which assembles prefabricated keel elements). The building blocks are very ... [more ▼]

We present a space and time allocation problem that arises in assembly halls producing large building blocks (namely, a shipyard which assembles prefabricated keel elements). The building blocks are very large, and, once a block is placed in the hall, it cannot be moved until all assembly operations on this block are complete. Each block must be processed during a predetermined time window. The objective is to maximize the number of building blocks produced in the hall. The problem is modeled as a 3-dimensional bin packing problem (3D-BPP) and is handled by a Guided Local Search heuristic initially developed for the 3D-BPP. Our com- putational experiments with this heuristic demonstrate that excellent results can be found within minutes on a workstation, and that the heuristic outperforms a standard constraint programming approach. We also describe some additional real-life constraints arising in the industrial application and show how these constraints can be conveniently integrated in the model. [less ▲]

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See detailOptimal selection of a portfolio of options under Value-at-Risk constraints: a scenario approach
Schyns, Michael ULg; Crama, Yves ULg; Hübner, Georges ULg

in Annals of Operations Research (2010), 181

This paper introduces a multiperiod model for the optimal selection of a financial portfolio of options linked to a single index. The objective of the model is to maximize the expected return of the ... [more ▼]

This paper introduces a multiperiod model for the optimal selection of a financial portfolio of options linked to a single index. The objective of the model is to maximize the expected return of the portfolio under constraints limiting its Value-at-Risk. We rely on scenarios to represent future security prices. The model contains several interesting features, like the consideration of transaction costs, bid-ask spreads, arbitrage-free option pricing, and the possibility to rebalance the portfolio with options introduced at the start of each period. The resulting mixed integer programming model is applied to realistic test instances involving options on the S&P500 index. In spite of the large size and of the numerical difficulty of this model, near-optimal solutions can be computed by a standard branch-and-cut solver or by a specialized heuristic. The structure and the financial features of the selected portfolios are also investigated. [less ▲]

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See detailLifting, Superadditivity, Mixed Integer Rounding and Single Node Flow Sets Revisited
Louveaux, Quentin ULg; Wolsey, Laurence A.

in Annals of Operations Research (2007), 153(1), 47-77

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 ... [more ▼]

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 the development of strong valid inequalities for knapsack and single node flow sets. Our hope is that the latter can be used in practice to generate cutting planes for mixed integer programs. The survey contains essentially two parts. In the first we present lifting in a very general way, emphasizing superadditive lifting which allows one to lift simultane- ously different sets of variables. In the second, our procedure for generating strong valid inequalities consists of reduction to a knapsack set with a single continuous variable, construction of a mixed integer rounding inequality, and superaddilifting. It is applied to several generalizations of the 0-1 single node flow set. [less ▲]

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See detailCause-effect relationships and partially defined Boolean functions
Crama, Yves ULg; Ibaraki, Toshihide

in Annals of Operations Research (1988), 16

This paper investigates the use of Boolean techniques in a systematic study of cause-effect relationships. The model uses partially defined Boolean functions. Procedures are provided to extrapolate from ... [more ▼]

This paper investigates the use of Boolean techniques in a systematic study of cause-effect relationships. The model uses partially defined Boolean functions. Procedures are provided to extrapolate from limited observations, concise and meaningful theories to explain the effect under study, and to prevent (or provoke) its occurrence [less ▲]

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