Single layer latticed domes are lightweight and elegant structures that provide cost-effective solutions to cover the large areas without intermediate supports. The topological design of these structures present difficulty due to the fact that the number of joints and members as well as the height of the dome keeps on changing during the design process. This makes it necessary to automate the numbering of joints and members and the computation of the coordinates of joints in the dome. On the other hand the total number of joints and members in a dome is function of the total number of rings exist in the dome. Currently no study is available that covers the topological design of dome structures that give the optimum number of rings, the optimum height of crown and the tubular cross-sectional designations for the dome members under the given general external loading. The algorithm presented in this study carries out the optimum topological design of single layer lattice domes. The serviceability and strength requirements are considered in the design problem as specified in BS5950. The algorithm takes into account the nonlinear response of the dome due to effect of axial forces on the flexural stiffness of members. The optimum solution of the design problem is obtained using coupled genetic algorithm. Having the total number of rings and the height of crown as design variables provides the possibility of having a dome with different topology for each individual in the population. It is shown in the design example considered that the optimum number of joints, members and the optimum height of a geodesic dome under a given external loading can be determined without designer's interference. (C) 2007 Published by Elsevier Ltd.