The power scheduling problem in a smart home (PSPSH) refers to the timely scheduling operations of smart home appliances under a set of restrictions and a dynamic pricing scheme(s) produced by a power supplier company (PSC). The primary objectives of PSPSH are: (I) minimizing the cost of the power consumed by home appliances, which refers to electricity bills, (II) balance the power consumed during a time horizon, particularly at peak periods, which is known as the peak-to-average ratio, and (III) maximizing the satisfaction level of users. Several approaches have been proposed to address PSPSH optimally, including optimization and non-optimization based approaches. However, the set of restrictions inhibit the approach used to obtain the optimal solutions. In this paper, a new formulation for smart home battery (SHB) is proposed for PSPSH that reduces the effect of restrictions in obtaining the optimal/near-optimal solutions. SHB can enhance the scheduling of smart home appliances by storing power at unsuitable periods and use the stored power at suitable periods for PSPSH objectives. PSPSH is formulated as a multi-objective optimization problem to achieve all objectives simultaneously. A robust swarm-based optimization algorithm inspired by the grey wolf lifestyle called grey wolf optimizer (GWO) is adapted to address PSPSH. GWO has powerful operations managed by its dynamic parameters that maintain exploration and exploitation behavior in search space. Seven scenarios of power consumption and dynamic pricing schemes are considered in the simulation results to evaluate the proposed multi-objective PSPSH using SHB (BMO-PSPSH) approach. The proposed BMO-PSPSH approach’s performance is compared with that of other 17 state-of-the-art algorithms using their recommended datasets and four algorithms using the proposed datasets. The proposed BMO-PSPSH approach exhibits and yields better performance than the other compared algorithms in almost all scenarios.