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

A parallel Branch-and-Fix Coordination based matheuristic algorithm for solving large sized multistage stochastic mixed 0–1 problems

“…Over the last two decades papers on stochastic optimization have appeared in the relevant literature that use PC for two-stage and multistage stochastic linear as well as mixed 0-1 optimization, see e.g., [1,9,46,21] and references therein. Recently, parallel computing versions of the exact BFC methodology was presented in [4,55]. See also the parallel matheuristic bounding methods presented in [3,6,53,61,64,74] that also allow large sized instances to be solved.…”

“…In particular, we introduce an algorithm so-called Dynamically-guided and stage-ordered Branch-and-Fix Coordination algorithm (for short, DBFC) that, belonging to the multistage BFC methodology, strongly improves the performance of previous BFC algorithms presented in [4,22] and references therein. The main improvements are in the dynamic branching mechanism that allows to solving much larger sized multistage stochastic mixed 0-1 problems, they are as follows: (1) The scenario cluster partitioning is based on the so-called break stage.…”

“…Parallel algorithms have been developed in stochastic optimization for linear programs, see [12,54] as we know for the first parallel versions of Benders decomposition; see [9,19] for two-stage programs and [4,13,47,48,55,61,64,70,74] for multistage ones. For some applications in several fields, see [18,20,27,43,44].…”

“…In order to improve the performance of our matheuristic H-DBFC algorithm for solving large sized problems, Section 4.1 presents some considerations based on the performance of the parallel version presented in [4] for BFC. On one hand, the so-called inner parallelization reduces the execution time for solving the independent submodels that are associated with each TNF.…”

“…We use the following definitions of the three thread types given in [4] for parallelizing H-DBFC (see Algorithm 1): coordinator thread, where the non-parallelized tasks are executed; primary thread, solves the scenario cluster submodels (2) and (9) in parallel; and auxiliary thread, used by each call to the MIP solver of choice. Then, denote as (a × b × h) the thread configuration of a joint outer-inner parallelization execution, where a is the number of coordinator threads (one for each path, see below), b is the number of primary threads associated with each coordinator thread (including itself) and h is the number of auxiliary threads associated with each primary thread (including itself).…”