On parallelization of a stochastic dynamic programming algorithm for solving large-scale mixed 0–1 problems under uncertainty

Résumé

A parallel computing implementation of a Serial Stochastic Dynamic Programming approach referred to as the S-SDP algorithm is introduced to solve large-scale multiperiod mixed 0–1 optimization problems under uncertainty. The paper presents Inner and Outer Parallelization versions of the S-SDP algorithm, referred to as Inner P-SDP and Outer P-SDP, respectively, so that the problem solving elapsed time and gap reduction is analyzed. The basic idea of Inner P-SDP consists of parallelizing the optimization of variations of the MIP subproblems attached to the sets of scenario clusters created by the modeler-defined stages to decompose the original problem. The Outer P-SDP performs simultaneous interconnected executions of the serial algorithm, so that a wider feasibility area is explored using iterative communication to redefine search directions. Strategies are presented to analyze the performance of parallel computation based on Message-Passing Interface threads to solve stage-related subproblems versus the serial version of SDP methodology. The results of using the parallelization are remarkable, as not only faster but also better solutions than the serial version are obtained. In particular, we report up to 10 times speedup for 12 threads on the Inner P-SDP algorithm. The new approach allows problems to be solved using less computing time than a state-of-the-art MIP solver. It can thus solve very large-scale problems that could not otherwise be achieved by plain use of the solver or by the S-SDP algorithm in acceptable elapsed time, if any.