In this paper we propose some mixed integer linear programming formulations for the K clusters with fixed cardinality problem. These formulations are strengthened by valid inequalities and all the mixed integer linear models are compared from a theoretical and practical point of view. The continuous linear relaxation bounds of the developed models are tested on randomly generated instances, by using standard software, with promising results.
- Clusters with fixed cardinality
- Combinatorial optimization
- Mixed integer linear formulations
- Upper bounds
- Valid inequalities