The advent of quantum computing can potentially revolutionize how complex problems are solved. This paper proposes a two-loop quantum-classical solution algorithm for generation scheduling by infusing quantum computing, machine learning, and distributed optimization. The aim is to facilitate employing noisy near-term quantum machines with a limited number of qubits to solve practical power system optimization problems such as generation scheduling. The outer loop is a 3-block quantum alternative direction method of multipliers (QADMM) algorithm that decomposes the generation scheduling problem into three subproblems, including one quadratically unconstrained binary optimization (QUBO) and two non-QUBOs. The inner loop is a trainable quantum approximate optimization algorithm (T-QAOA) for solving QUBO on a quantum computer. The proposed T-QAOA translates interactions of quantum-classical machines as sequential information and uses a recurrent neural network to estimate variational parameters of the quantum circuit with a proper sampling technique. T-QAOA determines the QUBO solution in a few quantum-learner iterations instead of hundreds of iterations needed for a quantum-classical solver. The outer 3-block ADMM coordinates QUBO and non-QUBO solutions to obtain the solution to the original problem. The conditions under which the proposed QADMM is guaranteed to converge are discussed. Two mathematical and three generation scheduling cases are studied. Analyses performed on quantum simulators and classical computers show the effectiveness of the proposed algorithm. The advantages of T-QAOA are discussed and numerically compared with QAOA which uses a stochastic gradient descent-based optimizer.
The advent of quantum computing can potentially revolutionize how complex problems are solved. This paper proposes a two-loop quantum-classical solution algorithm for generation scheduling by infusing quantum computing, machine learning, and distributed optimization. The aim is to facilitate employing noisy near-term quantum machines with a limited number of qubits to solve practical power system optimization problems such as generation scheduling. The outer loop is a 3-block quantum alternative direction method of multipliers (QADMM) algorithm that decomposes the generation scheduling problem into three subproblems, including one quadratically unconstrained binary optimization (QUBO) and two non-QUBOs. The inner loop is a trainable quantum approximate optimization algorithm (T-QAOA) for solving QUBO on a quantum computer. The proposed T-QAOA translates interactions of quantum-classical machines as sequential information and uses a recurrent neural network to estimate variational parameters of the quantum circuit with a proper sampling technique. T-QAOA determines the QUBO solution in a few quantum-learner iterations instead of hundreds of iterations needed for a quantum-classical solver. The outer 3-block ADMM coordinates QUBO and non-QUBO solutions to obtain the solution to the original problem. The conditions under which the proposed QADMM is guaranteed to converge are discussed. Two mathematical and three generation scheduling cases are studied. Analyses performed on quantum simulators and classical computers show the effectiveness of the proposed algorithm. The advantages of T-QAOA are discussed and numerically compared with QAOA which uses a stochastic gradient descent-based optimizer.
The advent of quantum computing can potentially revolutionize how complex problems are solved. This paper proposes a two-loop quantum-classical solution algorithm for generation scheduling by infusing quantum computing, machine learning, and distributed optimization. The aim is to facilitate employing noisy near-term quantum machines with a limited number of qubits to solve practical power system optimization problems such as generation scheduling. The outer loop is a 3-block quantum alternative direction method of multipliers (QADMM) algorithm that decomposes the generation scheduling problem into three subproblems, including one quadratically unconstrained binary optimization (QUBO) and two non-QUBOs. The inner loop is a trainable quantum approximate optimization algorithm (T-QAOA) for solving QUBO on a quantum computer. The proposed T-QAOA translates interactions of quantum classical machines as sequential information and uses a recurrent neural network to estimate variational parameters of the quantum circuit with a proper sampling technique. T-QAOA determines the QUBO solution in a few quantum-learner iterations instead of hundreds of iterations needed for a quantum-classical solver. The outer 3-block ADMM coordinates QUBO and non-QUBO solutions to obtain the solution to the original problem. The conditions under which the proposed QADMM is guaranteed to converge are discussed. Two mathematical and three generation scheduling cases are studied. Analyses performed on quantum simulators and classical computers show the effectiveness of the proposed algorithm. The advantages of T-QAOA are discussed and numerically compared with QAOA which uses a stochastic gradient descent-based optimizer.
The reliable and efficient operation of power systems is crucial for the proper functioning of modern society. However, the large and complex nature of power systems presents significant computational challenges for their operation and planning. Traditional computational techniques are insufficient in addressing these complexities, and novel approaches are necessary to enhance the efficiency and effectiveness of power system operations and planning. Although quantum computing algorithms have shown the potential in completing significant computing tasks faster than traditional computers, their application to power systems remains largely unexplored. This dissertation aims to investigate advanced solution techniques for power system optimization problems by proposing and implementing hybrid distributed-quantum computing-based optimization approaches. To address the current limitations of noisy quantum computers and their practical application, a multi-block alternating direction method of multiplier (ADMM) is proposed for solving mixed-integer linear programming (MILP) problems. The proposed algorithm is applied to a large-scale transmission expansion planning problem to demonstrate its performance. Furthermore, the quantum approximate optimization algorithm (QAOA) is integrated into the ADMM algorithm as a hybrid quantum-classical method for solving the MILP problem. The effectiveness of this approach is demonstrated through simulations and numerical experiments on a generation scheduling problem. To reduce the quantum-classical iteration of the QAOA algorithm, a recurrent neural network is designed to estimate the variational parameters of the quantum circuit with an appropriate sampling technique. The simulation results exhibit the effectiveness of the proposed model.
This paper presents a distributed quantum approximate optimization algorithm (DQAOA)-enabled three-block alternating direction method of multipliers (ADMM) framework for unit commitment (UC). The relaxed commitment and dispatch variables are solved in a continuous quadratic programming block, while the binary commitment block is formulated as a quadratic unconstrained binary optimization (QUBO) problem. The DQAOA interface allows this QUBO to be solved using brute-force enumeration, monolithic QAOA, or distributed QAOA, while the remaining ADMM updates are kept unchanged. In the distributed mode, the logical commitment qubits are allocated across multiple capacity-constrained quantum processing units (QPU), avoiding the requirement that the complete binary problem fits on a single device. The framework is evaluated on a five-unit UC instance containing 15 binary variables. All three solver modes reduce the ADMM primal residual below a certain tolerance and recover the same commitment schedule, dispatch, and operating cost. The results demonstrate solution consistency across the three solver modes and the multi-QPU capacity accommodation provided by the distributed QAOA method.
This paper reviews a hybrid quantum-classical distributed algorithm for NP-hard combinatorial optimization problems, which is embedded in IBM Qiskit's Alternating Direction Method of Multipliers (ADMM) optimizer. We demonstrate a proof of concept for solving Mixed-Integer Convex Programs (MICP) in power system applications using a use case on power distribution network reconfiguration in IBM quantum computers. Using the Qiskit ADMM optimizer, the MICP is decomposed into two subproblems: a quadratic unconstrained binary optimization (QUBO) solved by quantum algorithms and a convex one solved by classical solvers. Our essential contribution is integrating the Quantum Random Access Optimization (QRAO) into the quantum-classical distributed framework and the existing Quantum Approximate Optimization Algorithm (QAOA) implemented in the Qiskit ADMM Optimizer. QRAO utilizes Quantum Random Access Codes (QRACs) to minimize qubit requirements and utilizes quantum state rounding for solution extraction. We examine the impact of noise on solutions derived from QRAO and compare them with results from QAOA using a use case on network reconfiguration in response to faults in the power distribution system.
Solving combinatorial optimization problems on current noisy quantum devices is currently being advocated for (and restricted to) binary polynomial optimization with equality constraints via quantum heuristic approaches. This is achieved using, for example, the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA). In this article, we present a decomposition-based approach to extend the applicability of current approaches to “quadratic plus convex” mixed binary optimization (MBO) problems, so as to solve a broad class of real-world optimization problems. In the MBO framework, we show that the alternating direction method of multipliers (ADMM) can split the MBO into a binary unconstrained problem (that can be solved with quantum algorithms), and continuous constrained convex subproblems (that can be solved cheaply with classical optimization solvers). The validity of the approach is then showcased by numerical results obtained on several optimization problems via simulations with VQE and QAOA on the quantum circuits implemented in Qiskit, an open-source quantum computing software development framework.
When talking about rising demand for electricity, shifting to renewable energy sources, and prioritizing grid stability, one thing that is crucial is optimizing the scheduling of electricity load based on the demand. There are various classical machine learning (ML) and meta-heuristic optimization methods (Particle Swarm Optimization, Genetic Algorithms, Differential Evolution, Simulated Annealing) used to forecast load, and then schedule accordingly to minimize cost, reduce the peak load of system, and improve the overall efficiency. However, these methods struggle in handling large-scale combinatorial complexity and multiple constrained systems in real time. This paper presents a comparative study of classical ML-based optimization techniques and introduces a novel quantum-machine-learning approach using the Quantum Approximate Optimization Algorithm (QAOA) for electricity load scheduling. Initially, a survey was conducted and several classical techniques for optimization and forecasting were evaluated on realistic demand data. The paper highlights their strengths and drawbacks in terms of solution quality, computational time, and scalability. Then, the paper proposes and apply QAOA to the same scheduling problem, formulating load scheduling as a quadratic unconstrained binary optimization (QUBO) model suitable for quantum optimization. We assess the performance of QAOA against classical methods under identical constraints. Thus, Simulated Annealing produces a normalized cost of 0.00029 (after 37 seconds) whereas the cost found by Differential Evolution is 0.1314 and by the Genetic Algorithm 0.4379. This tends to confirm the validity of classical heuristics for smaller problems [16]. Our results show that while classical methods perform well for small to medium scale problems, the QAOA approach offers competitive or superior performance in terms of optimization quality and scalability for larger, more complex instances, with potential reductions in computation time under certain conditions. We conclude by discussing the practical challenges of implementing QAOA (e.g. noise, parameter tuning) and suggest directions for future research to advance quantum-assisted optimization in electricity scheduling.