On a hybrid MPI-Pthread approach for parallel branch-and-bound

A pure MPI code is not necessarily the best solution to obtain the maximum performance [3]. When the search space is irregular, load balance problems usually appear and they may deteriorate performance as the number of MPI processes increases. For the code to scale to a larger number of cores, one solution is to combine MPI with a threaded model which has load balancing capabilities. The POSIX threads (Pthreads) model used here permits dynamic load balancing through thread generation facilitating to handle irregular data structures as those presented in B&B algorithms [4]. A mixture of MPI and Pthreads is studied. An MPI model is used for the initial work distribution and gathering the final solution. A threaded model (with intrinsic dynamic load balancing) is used for parallelism within a node. This will generally produce a code with better scaling properties than the MPI approach without dynamic workload balance. Every MPI process performs a sequential phase in which the feasible region is divided by face-to-face vertex triangulation. If the number of generated subsimplices is less than the number of processes, a sequential B&B process is initiated until the number of unexamined simplices becomes equal to the number of MPI processes. Then, each MPI process selects the corresponding simplices it is in charge of. In this schema there is not communications between MPI processes. Therefore, upper bounds are not interchanged and the load balancing is static. This model is similar to [2]. Within each MPI process, the execution starts using one thread. A thread can create a new thread if a core is idle, there is enough work to share with the new thread and the maximum number of threads is not reached. The new generated thread will receive half of the simplices stored in its parent [4]. The best upper bound is shared between the 8 16 32 64 128