Hierarchical branch and bound algorithm for computational grids

  • Authors:

  • A. Bendjoudi;N. Melab;E. -G. Talbi

  • Affiliations:

  • Centre de Recherche sur l'Information Scientifique et Technique CERIST, DTISI, 3 rue des frères Aissou, 16030 Ben-Aknoun, Algiers, Algeria and Université Abderrahmane Mira de Béjaia ...;Université Lille1, France and LIFL/UMR CNRS 8022, 59655-Villeneuve d'Ascq cedex, France;Université Lille1, France and LIFL/UMR CNRS 8022, 59655-Villeneuve d'Ascq cedex, France

  • Venue:
  • Future Generation Computer Systems
  • Year:
  • 2012

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Abstract

Branch and Bound (B&B) algorithms are efficiently used for exact resolution of combinatorial optimization problems (COPs). They are easy to parallelize using the Master/Worker paradigm (MW) but limited in scalability when solving large instances of COPs on large scale environments such as computational grids. Indeed, the master process rapidly becomes a bottleneck. In this paper, we propose a new approach H-B&B for parallel B&B based on a hierarchical MW paradigm in order to deal with the scalability issue of the traditional MW-based B&B. The hierarchy is built dynamically and evolves over time according to the dynamic acquisition of computing nodes. The inner nodes of the hierarchy (masters) perform branching operations to generate sub-trees and the leaves (workers) perform a complete exploration of these sub-trees. Therefore, in addition to the parallel exploration of sub-trees, a parallel branching is adopted. H-B&B is applied to the Flow-Shop scheduling problem. Unlike most existing grid-based B&B algorithms, H-B&B has been experimented on a real computational grid (Grid'5000). The results demonstrate the scalability and efficiency of H-B&B.