BELSPO

Combinatorial Optimization: Metaheuristics and Exact Methods

Coordinator: Bernard Fortz (Université libre de Bruxelles) and Mathieu Van Vyve (CORE and LSM, UCL)
Date: 20/9/2012 - 30/09/2017
Project: PAI P7/36

The main objectives of this project are:

  • Bring together the available Belgian expertise on combinatorial optimization problems, exploit synergies between the partner research groups, and create a network with a sufficient mass to attract young and experienced top-level scientists in Belgium, and further financing for research in the field.
  • Train young researchers in the field of combinatorial optimization. These profiles are in high demand, both in academic research centers worldwide and in private organizations.
  • Develop new models, algorithmic techniques and implementations for complex, large-scale combinatorial optimization problems.
  • Develop new international collaborations with other large teams working in the field of combinatorial optimization. An active and recognized Belgian network would facilitate international collaborations, in particular in the framework of large scale international projects.

Successful achievement of these objectives will lead to (i) a number of important, fundamental research contributions, (ii) a significant impact on the different sectors where combinatorial optimization problems arise, and (iii) to a considerable added value for the Belgian economy.

Exact Nonnegative Matrix Factorization: Algorithms, Bounds and Applications to Optimization

Coordinator: François Glineur (CORE and INMA, UCL)
Date:
Project: IAP DYSCO VII/19

Many combinatorial optimization problems can be formulated as the optimization of a linear objective over a polytope. However, this polytope may have a very large number of facets, possibly growing exponentially with the dimension. Because of the high number of facets, computing the optimal solution can be very time consuming. However, if one can find an extension of this polytope with a moderate number of facets, one can solve the optimization problem over the extension efficiently and project the optimal solution on the original polytope. Finding an extension for a convex polytope can be done with exact nonnegative matrix factorization. The goals of this research are (i) the development of algorithms that compute exact nonnegative factorizations and (ii) the development of lower bounds (optimality guarantees for the algorithms) on the minimum inner dimension of such factorizations.

Measuring Equivalent Incomes: The Implementation of Individual Well-being Measures from Belgian Data (MEqIn)

Coordinators: Bea Cantillon (Universiteit Antwerpen), Bram De Rock (Université libre de Bruxelles), François Maniquet (CORE, UCL) and Erik Schokkaert (KU Leuven)
Date: 1/10/2013 - 31/12/2017
Project: BR/121/A5/MEQIN

This research project aims at defining the statistical methodology that will allow one to build well-being measures that are consistent with the following principles:

  • Well-being is a multi-dimensional phenomenon;
  • One reason what anti-poverty policies have had such disappointing outcomes is that the point of view of the poor people themselves has not sufficiently be taken into account;
  • The aggregation of the many dimensions of well-being and insecurity has to be made first at the level of the person, and then be aggregated at the social level;
  • The dominant paradigm of the even distribution of well-being in the household should be dropped;
  • Social policies will not be designed adequately without a precise account of how potential beneficiaries themselves react to the induced changes in their environment.