A quantum-classical hybrid optimization method for restoration of active distribution networks

This paper establishes an optimal restoration model for active distribution networks to rapidly recover from extreme weather events. The optimal restoration problem is defined as a mixed-integer second-order cone programming (MISOCP) model, which is non-deterministic polynomial hard (NP-hard). This paper proposes a quantum-classical hybrid optimization method to solve this model. First, the optimal restoration model is split into a mixed-integer linear programming (MILP) subproblem and a second-order cone programming (SOCP) subproblem, wherein the MILP subproblem is converted to a quadratic unconstrained binary optimization (QUBO) model. A decentralized optimization architecture based on alternating direction method of multipliers (ADMM) is then developed, where quantum computing is used to solve the MILP subproblem (i.e., the QUBO model), and classical computing is employed to solve the SOCP subproblem. Numerical simulations validate that the proposed hybrid optimization method fully leverages the advantages of quantum computing for integer problems and classical computing for continuous problems.