A Distributed Algorithm for Large-scale Stochastic Optimization Problems
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This thesis presents a parallel algorithm for non-convex large-scale stochastic optimization problems, specifically scenario-based two-stage stochastic mixed-integer nonlinear programming problems. The method is called the Non-convex Generalized Benders Decomposition method, which is presented together with the Generalized Benders Decomposition method of which it is an extension. A parallel version of the algorithm is presented and a distributed implementation is developed and presented. We test the method on a case study based on a stochastic unit commitment problem based on the Brazilian electrical system. There are two main goals of this thesis: (1) to show that the non-convex generalized Benders decomposition method is parallelizable and that it scales well in a distributed computing environment and (2) to solve the stochastic unit commitment problem formulated as a non-convex two-stage mixed integer nonlinear programming problem. Three sets of results are presented: one for a reduced convex version of the case study to test scalability, another for the full convex version of the case study and the last set for the non-convex version of the case study. The results suggests that the method has potential in terms of parallelization, but that it is essential to keep the parallelizable portion of the algorithm large.