An algorithmic framework for solving large-scale multistage stochastic mixed 0-1 problems with nonsymmetric scenario trees. Part II: Parallelization

This note is a sequel of paper (Escudero et al. (2012) [1]), in which the sequential Branch-and-Fix Coordination referred to as the BFC-MS algorithm was introduced for solving large-scale multistage mixed 0-1 optimization problems up to optimality under uncertainty. The aim of the note is to present the parallelization version of the BFC algorithm, referred to as PC-BFCMS, so that the elapsed time reduction on problem solving is analyzed. The parallelization is performed at two levels. The inner level parallelizes the optimization of the MIP submodels attached to the set of scenario clusters that have been created by the modeler-defined break stage to decompose the original problem, where the nonanticipativity constraints are partially relaxed. Several strategies are presented for analyzing the performance of the inner parallel computation based on MPI (Message Passing Interface) threads to solve scenario cluster submodels versus the sequential version of the BFC-MS methodology. The outer level of parallelization defines a set of 0-1 variables, the combinations of whose 0-1 values, referred to as paths (one for each combination), allow independent models to be optimized in parallel, such that each one can itself be internally optimized with the inner parallelization approach. The results of using the outer-inner parallelization are remarkable: the larger the number of paths and MPI threads (in addition to the number of threads that the MIP solver allows to be used), the smaller the elapsed time to obtain the optimal solution. This new approach allows problems to be solved faster, and, can thus solve very large scale problems that could not otherwise be solved by plain use of a state-of the-art MIP solver, or could not be solved by the sequential version of the decomposition algorithm in acceptable elapsed time.