With the increasing number of electricity consumers, production, distribution, and consumption problems of produced energy have appeared. This paper proposed an optimization method to reduce the peak demand using smart grid capabilities. In the proposed method, a hybrid Grasshopper Optimization Algorithm (GOA) with the self-adaptive Differential Evolution (DE) is used, called HGOA. The proposed method takes advantage of the global and local search strategies from Differential Evolution and Grasshopper Optimization Algorithm. Experimental results are applied in two scenarios; the first scenario has universal inputs and several appliances. The second scenario has an expanded number of appliances. The results showed that the proposed method (HGOA) got better power scheduling arrangements and better performance than other comparative algorithms using the classical benchmark functions. Moreover, according to the computational time, it runs in constant execution time as the population is increased. The proposed method got 0.26 % enhancement compared to the other methods. Finally, we found that the proposed HGOA always got better results than the original method in the worst cases and the best cases.