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.
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.
A series of hybrid quantum-classical generalized Benders decomposition (GBD) algorithms are proposed to address unit commitment (UC) problems under centralized, distributed, and partially distributed frameworks. In the centralized approach, the quantum GBD transforms the master problem (MP) into a quadratic unconstrained binary optimization form suitable for quantum computing. For distributed systems, the distributed consensus quantum GBD employs an average consensus strategy to reformulate subproblems into local subproblems. By leveraging the dual information, local cutting planes are constructed to decompose the MP into local master problems (LMPs). This approach reduces the qubit overhead and addresses the partitioning requirements. The consensus-inspired quantum GBD (CIQGBD) and its partially distributed variant, D-CIQGBD are proposed based on optimizing the allocation of relaxation variables directly, the algorithms construct more rational cutting planes, thereby enhancing the minimum eigenenergy gap of the system Hamiltonian during quantum annealing and improving the computational efficiency. Extensive experiments under various UC scenarios validate the performance of the above-mentioned hybrid algorithms. Compared to the classical solver Gurobi, D-CIQGBD demonstrates a speed advantage in solving the security-constrained UC problem on the IEEE-RTS 24-bus system. These results provide new perspectives on leveraging quantum computing for the distributed optimization of power systems.
Stochastic Unit Commitment (SUC) has been proposed to manage the uncertainties driven by renewable integration, but it leads to significant computational complexity. When accelerated by Benders Decomposition (BD), the master problem becomes binary integer programming, which is still NP-hard and computationally demanding for classical methods. Quantum Annealing (QA), known for efficiently solving Quadratic Unconstrained Binary Optimization (QUBO) problems, presents a potential solution. However, existing quantum algorithms rely on slack variables to handle linear binary inequality constraints, leading to increased qubit consumption and reduced computational efficiency. To solve the problem, this paper introduces the Powell-Hestenes-Rockafellar Augmented Lagrangian Multiplier (PHR-ALM) method to eliminate the need for slack variables, making qubit consumption independent of the increasing number of Benders cuts. To further reduce the qubit overhead, quantum ADMM is applied to break large-scale SUC into smaller blocks for sequential solutions, which does not scale with the number of generators. Finally, the simulation results on both 4-generator and the IEEE bus-118 systems demonstrate the feasibility and scalability of the proposed algorithm, indicating its superior qubit and runtime efficiency over classical and baseline quantum approaches on the D-Wave QPU platform.
This paper introduces D2-UC, a quantum-ready framework for the unit commitment (UC) problem that prepares UC for near-term hybrid quantum-classical solvers by combining distributed classical decomposition with distributed quantum execution. We reformulate deterministic and stochastic UC into a three-block alternating direction method of multipliers (ADMM): (i) a convex quadratic subproblem for dispatch and reserves, (ii) a binary subproblem expressed as a quadratic unconstrained binary optimization (QUBO), and (iii) a proximal slack update for consensus. The core contributions are fivefold. First, we demonstrate how the full UC problem can be expressed as a single monolithic QUBO, establishing a direct interface to quantum solvers. Second, we decompose this large binary block into three type-specific QUBOs for commitment, startup, and shutdown, making the problem more tractable but revealing slower ADMM convergence. Third, we restore local logical couplings through per-unit-time micro-QUBOs, which accelerate convergence. Fourth, we batch micro-QUBOs into K non-overlapping block-diagonal problems, reducing many subproblems to a fixed number of solver-ready QUBOs per iteration, compatible with distributed variational quantum eigensolvers (DVQE). Fifth, we integrate an accept-if-better safeguard with DVQE to stabilize hybrid updates and prevent oscillations. Case studies confirm that the proposed methods deliver feasible schedules, faster convergence, and QUBO sizes aligned with current and near-term quantum hardware capabilities. All detailed data, codes, and parameter values are available at https://github.com/LSU-RAISE-LAB/3B-ADMM-UC-DVQE .
• 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.
Mixed-integer linear programming problems are extensively used in industry for a wide range of optimization tasks. However, as they get larger, they present computational challenges for classical solvers within practical time limits. Quantum annealers can, in principle, accelerate the solution of problems formulated as quadratic unconstrained binary optimization instances, but their limited scale currently prevents achieving practical speedups. Quantum-classical algorithms have been proposed to take advantage of both paradigms and to allow current quantum computers to be used in larger problems. In this work, a hardware-agnostic Benders' decomposition algorithm and a series of enhancements with the goal of taking the most advantage of quantum computing are presented. The decomposition consists of a master problem with integer variables, which is reformulated as a quadratic unconstrained binary optimization problem and solved with a quantum annealer, and a linear subproblem solved by a classical computer. The enhancements consist, among others, of different embedding processes that substantially reduce the pre-processing time of the embedding computation without compromising solution quality, a conservative handling of cut constraints, and a stopping criterion that accounts for the limited size of current quantum computers and their heuristic nature. The proposed algorithm is benchmarked against classical approaches using a D-Wave quantum annealer for a scalable family of transmission network expansion planning problems.
Scheduling multiple federated learning (FL) models within a distributed network, especially in large-scale scenarios, poses significant challenges since it involves solving NP-hard mixed-integer nonlinear programming (MINLP) problems. However, it's imperative to optimize participant selection and learning rate determination for these FL models to avoid excessive training costs and prevent resource contention. While some existing methods focus solely on optimizing a single global FL model, others struggle to achieve optimal solutions as the problem grows more complex. In this paper, exploiting the potential of quantum computing, we introduce the Hybrid Quantum-Classical Benders' Decomposition (HQCBD) algorithm to effectively tackle the joint MINLP optimization problem for multi-model FL training. HQCBD combines quantum and classical computing to solve the joint participant selection and learning scheduling problem. It decomposes the optimization problem into a master problem with binary variables and small subproblems with continuous variables, then leverages the strengths of both quantum and classical computing to solve them respectively and iteratively. Furthermore, we propose the Hybrid Quantum-Classical Multiple-cuts Benders' Decomposition (MBD) algorithm, which utilizes the inherent capabilities of quantum algorithms to produce multiple cuts in each round, to speed up the proposed HQCBD algorithm. Extensive simulation on the commercial quantum annealing machine demonstrates the effectiveness and robustness of the proposed methods (both HQCBD and MBD), with improvements of up to 70.3% in iterations and 81% in computation time over the classical Benders' decomposition algorithm on classical CPUs, even at modest scales.