Learning Infused Quantum-Classical Distributed Optimization Technique for Power Generation Scheduling

The advent of quantum computing can potentially revolutionize how complex problems are solved. This article 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 three-block quantum alternating 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. The 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 three-block alternating direction method of multipliers 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.