A smart house generally has a Photovoltaic panel (PV), a Heat Pump (HP), a Solar Collector (SC) and a fixed battery. Since the fixed battery can buy and store inexpensive electricity during the night, the electricity bill can be reduced. However, a large capacity fixed battery is very expensive. Therefore, there is a need to determine the economic capacity of fixed battery. Furthermore, surplus electric power can be sold using a buyback program. By this program, PV can be effectively utilized and contribute to the reduction of the electricity bill. With this in mind, this research proposes a multi-objective optimization, the purpose of which is electric demand control and reduction of the electricity bill in the smart house. In this optimal problem, the Pareto optimal solutions are searched depending on the fixed battery capacity. Additionally, it is shown that consumers can choose what suits them by comparing the Pareto optimal solutions.