Fast Distributed Resource Allocation of Smart Grid: A Zeroth-Order Optimization Algorithm

This paper investigates a multi-objective distributed resource allocation problem, where the economic cost including the transmission loss, and the environmental pollution are taken into account simultaneously. To settle this problem, a Pareto-based zeroth-order fast distributed optimization algorithm is proposed, which can always balance the overall energy demand with generation. In the algorithm design, the acceleration idea of the momentum method is tailored for the gradient estimation update, which gives a more accurate descent direction. Moreover, the unknown effect causes the gradient of the objective function to be unavailable and only the function values to be observed. Different from the gradient-based methods, a zeroth-order method is proposed to solve the distributed resource allocation problem with gradient estimation. Furthermore, the convergence of the designed algorithm is proved theoretically, and the convergence rate of linear speedup can be achieved. Finally, numerical simulations verify the validity and applicability of the proposed algorithm.