This study aims to provide a comprehensive assessment of single-objective and multi-objective optimisation algorithms for the design of an elbow-type draft tube, as well as to introduce a computationally efficient optimisation workflow. The proposed workflow leverages deep neural network surrogates trained on data obtained from numerical simulations. The use of surrogates allows for a more flexible and faster evaluation of novel designs. The success history-based adaptive differential evolution with linear reduction and the multi-objective evolutionary algorithm based on decomposition were identified as the best-performing algorithms and used to determine the influence of different objectives in the single-objective optimisation and their combined impact on the draft tube design in the multi-objective optimisation. The results for the single-objective algorithm are consistent with those of the multi-objective algorithm when the objectives are considered separately. Multi-objective approach, however, should typically be chosen, especially for computationally inexpensive surrogates. A multi-criteria decision analysis method was used to obtain optimal multi-objective results, showing an improvement of 1.5% and 17% for the pressure recovery factor and drag coefficient, respectively. The difference between the predictions and the numerical results is less than 0.5% for the pressure recovery factor and 3% for the drag coefficient. As the demand for renewable energy continues to increase, the relevance of data-driven optimisation workflows, as discussed in this study, will become increasingly important, especially in the context of global sustainability efforts.