Accelerating L-shaped Two-stage Stochastic SCUC with Learning Integrated Benders Decomposition

Abstract

Benders decomposition is widely used to solve large mixed-integer problems. This paper takes advantage of machine learning and proposes enhanced variants of Benders decomposition for solving two-stage stochastic security-constrained unit commitment (SCUC). The problem is decomposed into a master problem and subproblems corresponding to a load scenario. The goal is to reduce the computational costs and memory usage of Benders decomposition by creating tighter cuts and reducing the size of the master problem. Three approaches are proposed, namely regression Benders, classification Benders, and regression-classification Benders. A regressor reads load profile scenarios and predicts subproblem objective function proxy variables to form tighter cuts for the master problem. A criterion is defined to measure the level of usefulness of cuts with respect to their contribution to lower bound improvement. Useful cuts that contain the necessary information to form the feasible region are identified with and without a classification learner. Useful cuts are iteratively added to the master problem, and non-useful cuts are discarded to reduce the computational burden of each Benders iteration. Simulation studies on multiple test systems show the effectiveness of the proposed learning-aided Benders decomposition for solving two-stage SCUC as compared to conventional multi-cut Benders decomposition.