Control Schemes in a Generalized Utility for Parallel Branch-and-Bound Algorithms

Branch-and-bound algorithms are general methods applicable to various combinatorial optimization problems and parallelization is one of the most hopeful methods to improve these algorithms. Parallel branch-and-bound algorithm implementations can be divided in two types based on whether a central or a distributed control scheme is used. Central control schemes have reduced scalability because of bottleneck problems frequently encountered. In order to solve problem cases that cannot be solved with sequential branch-and-bound algorithm, distributed control schemes are necessary. However, compared to central control schemes, higher efficiency is not always achieved through the use of a distributed control scheme. In this paper, a mixed control scheme is proposed, changing between the two different types of control schemes during execution. In addition, a dynamic load balancing strategy is applied in the distributed control scheme. Performance evaluation for three different cases is carried out: central, distributed, and mixed control scheme. Several TSP instances from the TSPLIB are experimentally solved, using up to 101 workstations. The results of these experiments show that the mixed control scheme is one of the most promising control schemes and furthermore, the hybrid selection rule, which was introduced in our previous work, has an advantage in parallel branch-and-bound algorithms.