In this study, the design of a flexible cable–strut tensile structure was optimised according to the importance of elements to achieve high structural robustness. First, the importance coefficients of elements were determined by comparing their structural prefailure and postfailure strain energy. Moreover, the effects of the external load, the initial prestress, and the cross-sectional areas of elements on the importance coefficients were analysed. Second, a genetic algorithm was used to optimise element section design and minimise the maximum importance coefficient. Third, an optimised cable arrangement scheme was developed by adding an alternative load transfer path to the outer hoop cable with the highest importance coefficient. In this scheme, outer elements have a Levy-type arrangement rather than a Geiger-type arrangement so that a Geiger–Levy composite cable dome is formed. Finally, the cable arrangement and element section design for the aforementioned scheme were comprehensively optimised to reduce the maximum importance coefficient. The results of this study indicated that different elements had different importance coefficients, which exhibited different trends with changes in the external load, the initial prestress, and the cross-sectional areas of elements. Element section optimisation, cable arrangement optimisation, and the comprehensive optimisation reduced the maximum importance coefficient by 20.5%, 11.6%, and 27.7%, respectively, which indicated that these optimisation processes can effectively improve the robustness of cable–strut tensile structures.
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