Lagrangean bounds for the optimum communication spanning tree problem

• Ivan Contreras ^[1] ; Elena Fernández ^[1] ; Alfredo Marín ^[2]
  1. [1] Universitat Politècnica de Catalunya

     Universitat Politècnica de Catalunya

     Barcelona, España

     
  2. [2] Universidad de Murcia

     Universidad de Murcia

     Murcia, España

     
• Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 18, Nº. 1, 2010, págs. 140-157
• Idioma: inglés
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• Resumen

  • This paper considers the Optimum Communication Spanning Tree Problem. An integer programming formulation that yields tight LP bounds is proposed. Given that the computational effort required to obtain the LP bounds considerably increases with the size of the instances when using commercial solvers, we propose a Lagrangean relaxation that exploits the structure of the formulation. Since feasible solutions to the Lagrangean function are spanning trees, upper bounds are also obtained. These bounds are later improved with a simple local search. Computational experiments have been run on several benchmark instances from the literature. The results confirm the interest of the proposal since tight lower and upper bounds are obtained, for instances up to 100 nodes, in competitive computational times.