This paper presents a surrogate-assisted optimisation approach to speed up the substructure analysis in the preliminary design phase. The approach consists of replacing the radiation-diffraction analysis in a frequency domain analysis model for floating wind turbines with a data-driven surrogate model predicting the hydrodynamic coefficients for parameterised substructure geometries. This procedure is compared with the reference approach of estimating the hydrodynamic coefficients via radiation-diffraction analysis. A representative use case of assessing the trade-off between minimising the capital cost and reducing the wave-induced nacelle acceleration standard deviation for a semi-submersible substructure is presented. The accuracy of the surrogate model is found to increase significantly up to training datasets consisting of 400 designs and less noticeably afterwards. For a dataset consisting of 400 designs, the mean error on the prediction of the hydrodynamic coefficients and the error at one standard deviation from the mean are generally below 7% and 10%, respectively. For the same dataset size, the mean error on the most probable maximum wave-induced pitch over a 3h storm period is below 17%, while the error at one standard deviation from the mean is lower than 27%. The same values for the most probable maximum nacelle acceleration are under 7% and 12%, respectively. The surrogate model can capture the trade-off between the two objective functions, and the optimal designs identified with the surrogate model generally follow the same trend as those obtained with the reference model. However, relying on the surrogate model for performing the analysis of the substructure introduces local minima in the objective function that cause a discrepancy between the optimal designs identified with the surrogate model and those identified with the reference model.