A New Nested Benders Decomposition Strategy for Parallel Processing Applied to the Hydrothermal Scheduling Problem

Several optimization strategies are suitable for parallel processing, such as mathematical-programming based decomposition strategies, like Lagrangian relaxation and two-stage Benders decomposition, and evolutionary programming-like algorithms. In such cases, most subproblems can be solved independently by different processors. However, parallel processing is not suitable for some problems solved by nested Benders decomposition, due to the hierarchy between subproblems related to different time steps. In particular, for the deterministic case, parallel programming has been restricted to thread processing in lower-level machine computation and optimization solver codes. This paper proposes a new nested Benders decomposition strategy that is suitable for parallel processing, where time-coupled stages are solved simultaneously and an alternative procedure is employed to share initial conditions for the next stages as well as Benders cuts for the previous stages. The methodology is applied to the deterministic short term hydrothermal scheduling problem for the real large-scale Brazilian system, where the advantages of the proposed approach become more evident. In order to show the applicability of the method in low-budget and small parallel environments, the case study was processed with up to 24 process on multi-core computers.