Increasingly, renewable energy resources, energy storage systems (ESSs), and demand response programs (DRPs) are being discussed due to environmental concerns and smart grid developments. An innovative home appliance scheduling scheme is presented in this paper, which incorporates a local energy grid with wind turbines (WTs), photovoltaic (PV), and ESS, which is connected to an upstream grid, to schedule household appliances while considering various constraints and DRP. Firstly, the household appliances are specified as non-shiftable and shiftable (interruptible, and uninterruptible) loads, respectively. Secondly, an enhanced mathematical formulation is presented for smart home energy management which considers the real-time price of upstream grids, the price of WT, and PV, and also the sold energy from the smart home to the microgrid. Three objective functions are considered in the proposed energy management: electricity bill, peak-to-average ratio (PAR), and pollution emissions. To solve the optimization problem, a novel modification-based grey wolf optimizer (GWO) is proposed. When the wolves hunt prey, other wild animals try to steal the prey or some part of the prey, hence they should protect the prey; therefore, this modification mimics the battle between the grey wolves and other wild animals for the hunted prey. This modification improves the performance of the GWO in finding the best solution. Simulations are examined and compared under different conditions to explore the effectiveness and efficiency of the suggested scheme for simultaneously optimizing all three objective functions. Also, both GWO and improved GWO (IGWO) are compared under different scenarios, which shows that IGWO improvement has better performance and is more robust. It has been seen in the results that the suggested framework can significantly diminish the energy costs, PAR, and emissions simultaneously.