This paper presents a residential hybrid thermal/electrical grid-connected home energy system (HES), including a fuel-cell with combined heat and power and a battery-based energy storage system. The minimum operation cost of this integrated energy system is achieved by proper scheduling of different energy resources, found by applying a new powerful optimization algorithm, the Hyper-Spherical Search (HSS) algorithm, to the system's scheduling problem. This is the first time that HSS is used to face the energy resource dispatch problem. The HSS has been only tested in mathematical problems in the previous study. The optimization procedure generates an efficient look-up table in which the powers generated by different energy resources are determined for all time intervals. The effect of different electricity tariffs for purchasing electricity from the main grid on the operation costs of the system is investigated. Moreover, a battery is properly dispatched in the energy system to decrease the operation costs. A real load demand is used in the simulation. The results of HSS are compared with the harmony search algorithm and the colonial competitive algorithm to show the power and effectiveness of HSS to find the optimal dispatch strategy of energy resources for the first time. This is the first time that HSS is compared with CCA. The results of this paper are expected to contribute to home energy systems and real projects.