The construction of a household integrated energy system will reduce greenhouse gas emissions and promote sustainable development. Firstly, a household energy system is proposed, which consists of a photovoltaic, wind turbine, electrolysis cell, hydrogen storage tank, and hydrogen‐fired gas turbine. The proposed system is modelled as a bi‐objective optimization problem in which the minimum daily system economic cost, and the minimum loss of energy supply probability. Secondly, a novel multi‐objective egret swarm optimization algorithm with strong search capability and fast convergence is proposed. Thirdly, a household load corresponding to a typical day in spring is chosen as the study case. The optimization results show that the daily system economic cost with the optimal number of devices is 97.48 RMB, and the loss of energy supply probability is 8.33% at the lowest. Finally, to validate the efficiency of the proposed method, the proposed method is compared with NSGA‐II (a widely used multi‐objective evolutionary algorithm). The comparison indicates that the proposed method has a better diversity due to the random searchability. As a consequence, the proposed method can be used in the optimization capacity design of the integrated energy system.