Solving Non-linear Optimization Problem in Engineering by Model-Informed Generative Adversarial Network (MI-GAN)

Abstract

Optimization models have been widely used in many engineering systems to solve the problems related to system operation and management. For instance, in power systems, the optimal power flow (OPF) problem, which is a critical component of power system operations, can be formulated using optimization models. Specifically, the alternating current OPF (AC-OPF) problems are challenging since some of the constraints are non-linear and non-convex. Moreover, due to the high variability that the power system may have, the coefficients of the optimization model may change, increasing the difficulty of solving the OPF problem. Although the conventional optimization tools and deep learning approaches have been investigated, the feasibility and optimality of the solutions may still be unsatisfactory. Hence, in this paper, based on the recently developed model-informed generative adversarial network (MI-GAN) framework, a tailored version for solving the non-linear AC-OPF problem under uncertainties is proposed. The contributions of this work can be summarized into two main aspects: (1) To ensure the feasibility and improve the optimality of the generated solutions, two important layers, namely, the feasibility filter layer and optimality-filter layer, are considered and designed; and (2) An efficient model-informed selector is designed and integrated to the GAN architecture, by incorporating these two new layers to inform the generator. Experiments on the IEEE test systems demonstrate the efficacy and potential of the proposed method for solving non-linear AC-OPF problems.