In a smart home with distributed energy resources, the home energy management system (HEMS) controls the photovoltaic (PV) storage system by executing the optimization algorithm to achieve the lowest power cost. The existing mixed integer linear programming (MILP) algorithm is not suitable for execution on the end-user side due to its high computational complexity. The HEMS algorithm based on a long short-term memory neural network (LSTM-HEMS) can effectively solve the problem of the high computational complexity of MILP, but its optimization outcome is not high due to the accumulation of prediction errors. In order to achieve a better balance between computational complexity and optimization outcome, this paper proposes a lightweight optimization algorithm called the FastInformer-HEMS, which introduces the E-Attn attention mechanism based on Informer and uses global average pooling to extract the attention characteristics. Meanwhile, the proposed method introduces the maximum self-consumption algorithm as a backup strategy to ensure the safe operation of the system. The simulated results show that the computational complexity of the proposed FastInformer-HEMS is the lowest among the existing algorithms. Compared with the existing LSTM-HEMS, the proposed algorithm reduces the power consumption cost by 12.3% and 6.6% in the two typical scenarios, while the execution time decreases by 13.6 times.