A Parallel Best-First B&B with Synchronization Phases

We present a new parallel best-first Branch and Bound algorithm conceived for machines with distributed memory. Based on the notion of problems having the same lower bound, the algorithm evaluates these problems in parallel, during each phase of its execution. These computationally intensive phases alternate with control phases where synchronization and information exchange between processors takes place. We propose a probabilistic model for predicting the performances of this algorithm and discuss the results obtained on a MIMD multiprocessor for the Asymmetric Non-Euclidean TSP.