Hybrid Quantum-Classical Multi-cut Benders Approach with a Power System Application

Abstract: Leveraging the current generation of quantum devices to solve optimization problems of practical interest necessitates the development of hybrid quantum-classical (HQC) solution approaches. In this paper, a multi-cut Benders decomposition (BD) approach that exploits multiple feasible solutions of the master problem (MP) to generate multiple valid cuts is adapted, so as to be used as an HQC solver for general mixed-integer linear programming (MILP) problems. The use of different cut selection criteria and strategies to manage the size of the MP by eliciting a subset of cuts to be added in each iteration of the BD scheme using quantum computing is discussed. The HQC optimization algorithm is applied to the Unit Commitment (UC) problem. UC is a prototypical use case of optimization applied to electrical power systems, a critical sector that may benefit from advances in quantum computing. The validity and computational viability of the proposed approach are demonstrated using the D-Wave Advantage 4.1 quantum annealer.