Accelerating L-shaped Two-stage Stochastic SCUC with Learning Integrated
  Benders Decomposition
Fouad Hasan Amin Kargarian
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.