Peak periods are a result of consumers generally using electricity at similar times and periods as each other, for example, turning lights on when returning home from work, or the widespread use of air conditioners during the summer. Without peak shifting, the grid's system operators are forced to use peaked plants to provide additional energy. This operation is incredibly expensive and harmful to the environment due to its high levels of carbon emissions. Battery storage system (BSS) has been proposed to allow purchasing the energy during off-peak periods for later use, with the primary objective of realizing peak shifting occurred. Multi-objective optimization with the reinforcement learning technique has been utilized in order to achieve the primary objective, reduce energy consumption, and minimize the consumers' utility bills. The results revealed that the reduction in energy consumption was more than 20%, the consumers' energy bills were minimized, as well as realizing perfect peak shifting. In addition, the strategy attempted to overcharge the battery with about 7% of the time, and promising methods to address this has been proposed as a direction for future research.