### 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.

Original language | Unknown |
---|---|

Title of host publication | Mathematics and Computers in Science and Engineering |

Editors | C Bulucea, V Mladenov, E Pop, M Leba, N Mastorakis |

Place of Publication | AG LOANNOU THEOLOGOU 17-23, 15773 ZOGRAPHOU, ATHENS, GREECE |

Publisher | World Scientific and Engineering Acad and Soc |

Pages | 229-232 |

ISBN (Print) | 978-960-474-138-0 |

Publication status | Published - 1 Jan 2009 |

Event | 14th WSEAS International Conference on Applied Mathematics - Duration: 1 Jan 2009 → … |

### Conference

Conference | 14th WSEAS International Conference on Applied Mathematics |
---|---|

Period | 1/01/09 → … |

## Cite this

Lourenço, L. L. L. C. P., & Gonçalves, G. M. M. D. S. (2009). A strengthened mixed-integer linear formulation for the K clusters problem with fixed cardinality. In C. Bulucea, V. Mladenov, E. Pop, M. Leba, & N. Mastorakis (Eds.),

*Mathematics and Computers in Science and Engineering*(pp. 229-232). AG LOANNOU THEOLOGOU 17-23, 15773 ZOGRAPHOU, ATHENS, GREECE: World Scientific and Engineering Acad and Soc.