Machine Learning–Enhanced Quantum–Classical Benders Decomposition for Stochastic Unit Commitment

Abstract

This paper proposes a learning-based quantum–classical Benders decomposition method for solving large-scale two-stage stochastic unit commitment (UC) problems. The approach integrates a long short-term memory (LSTM) network to approximate subproblem costs and a support vector machine (SVM) classifier to filter dominant Benders cuts, thereby reducing problem size, facilitating quantum computing implementation, and improving scalability. The master problem is reformulated into a quadratic unconstrained binary optimization (QUBO) problem, enabling its solution on quantum hardware. The key contributions are: (i) a quantum–classical decomposition framework tailored for stochastic UC, (ii) an LSTM-based subproblem proxy to facilitate iterations, (iii) an SVM-based cut filtering method to retain only dominant cuts, and (iv) a QUBO reformulation suitable for quantum solvers. Numerical experiments demonstrate that the proposed method significantly reduces computational overhead and quantum resource requirements compared with conventional approaches.