Hybrid quantum-classical optimization of the resource scheduling problem

• We propose a new hybrid quantum-classical algorithm for solving the UC problem. • The hybrid model successfully optimizes 24-hour UC systems from 10 to 1000 units. • The model outperforms classical metaheuristics (GA and SA) and classical MINLP. • This represents an improvement over previous QCUC methods, a step to real-world use. Resource scheduling is critical in many industries, especially in power systems where the Unit Commitment (UC) problem determines the on/off status and output levels of generators under physical and economic constraints. Traditional exact methods, such as Branch‑and‑Bound, Branch‑and‑Cut, dynamic programming and mixed‑integer linear programming (MILP), remain the backbone of UC solution techniques, but they often rely on linear approximations or exhaustive search, leading to high computational burdens as system size grows. Metaheuristic approaches, such as genetic algorithms, particle swarm optimization, and other evolutionary methods, have been explored to mitigate this complexity; however, they typically lack optimality guarantees, exhibit sensitivity to initial conditions, and can become prohibitively time‑consuming for large‑scale systems. In this paper, we introduce a quantum‑classical hybrid algorithm for UC, and other resource scheduling problems by extension, that leverages Benders decomposition to decouple binary commitment decisions from continuous economic dispatch. The binary “master problem” is formulated as a quadratic unconstrained binary optimization (QUBO) model and solved on a quantum annealer. The continuous “subproblem,” which minimizes generation costs, with Lagrangian cuts feeding back to the master until convergence. We evaluate our hybrid framework on systems scaled from 10 to 1,000 generation units. Compared against a classical mixed‑integer nonlinear programming (MINLP) baseline, the hybrid algorithm achieves a consistently lower computation‑time growth rate and maintains an absolute optimality gap below 1.63%. These results demonstrate that integrating quantum annealing within a hybrid quantum-classical Benders decomposition loop can significantly accelerate large‑scale resource scheduling without sacrificing solution quality, pointing toward a viable path for addressing the escalating complexity of modern power grids.