A strengthened mixed-integer linear formulation for the K clusters problem with fixed cardinality

Authors:
Graça Marques Gonçalves;Lídia Lampreia Lourenço
Affiliations:
Department of Mathematics, Faculty of Science and Technology, New University of Lisbon, Monte da Caparica, Portugal and Operational Research Center, Faculty of Science, University of Lisbon, Lisbo ...;Department of Mathematics, Faculty of Science and Technology, New University of Lisbon, Monte da Caparica, Portugal and Operational Research Center, Faculty of Science, University of Lisbon, Lisbo ...
Venue:
MATH'09 Proceedings of the 14th WSEAS International Conference on Applied mathematics
Year:
2009

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Abstract

In this paper we study the K clusters with fixed cardinality problem that consists in finding K clusters, where each cluster has a fixed cardinality. We propose a mixed-integer linear programming formulation and deduce valid inequalities to strengthen the linear relaxation bound. The quality of the model is tested on randomly generated instances, by using standard software, with promising results.