In this paper, we used the Imperialist Competitive Algorithm (ICA) and Genetic Algorithm (GA) to find the minimum weight design of torispherical dome ends under external pressure load. According to fabrication and strength of material requirements, a group of compromised counters are selected and studied. Based on ASME Section VIII and BS5500 pressure vessel codes, a reasonable buckling pressure limit is proposed. Four-centered ellipse method is quite effective in designing and constructing the dome structure and it is used here to construct the torispherical dome ends. Two different size torispherical dome end models are selected and studied. Imperialist competitive algorithm is found to be very efficient and easy to use for the applications.