Smart grids (SGs) enhance the effectiveness, reliability, resilience, and energy-efficient operation of electrical networks. Nonetheless, SGs suffer from big data transactions which limit their capabilities and can cause delays in the optimal operation and management tasks. Therefore, it is clear that a fast and reliable architecture is needed to make big data management in SGs more efficient. This paper assesses the optimal operation of the SGs using cloud computing (CC), fog computing, and resource allocation to enhance the management problem. Technically, big data management makes SG more efficient if cloud and fog computing (CFC) are integrated. The integration of fog computing (FC) with CC minimizes cloud burden and maximizes resource allocation. There are three key features for the proposed fog layer: awareness of position, short latency, and mobility. Moreover, a CFC-driven framework is proposed to manage data among different agents. In order to make the system more efficient, FC allocates virtual machines (VMs) according to load-balancing techniques. In addition, the present study proposes a hybrid gray wolf differential evolution optimization algorithm (HGWDE) that brings gray wolf optimization (GWO) and improved differential evolution (IDE) together. Simulation results conducted in MATLAB verify the efficiency of the suggested algorithm according to the high data transaction and computational time. According to the results, the response time of HGWDE is 54 ms, 82.1 ms, and 81.6 ms faster than particle swarm optimization (PSO), differential evolution (DE), and GWO. HGWDE’s processing time is 53 ms, 81.2 ms, and 80.6 ms faster than PSO, DE, and GWO. Although GWO is a bit more efficient than HGWDE, the difference is not very significant.