The over-tip leakage represents a third of the loss encountered in a typical high-pressure turbine stage. In this paper, numerical investigations are carried out to study the effects of different tip designs on the aerodynamic performance and cooling requirements. A parametric design tool is used to conduct an automatic optimisation of the blade tip. The parameterisation allows overhangs to be added to the tip of the aerofoil to form a winglet, and in addition, a recessed cavity can be applied to produce a squealer tip. The squealer rim may also be opened near the leading-edge and the trailing-edge of the aerofoil. Flow computations are performed by an in-house 3D high fidelity computational fluid dynamic solver for predicting the performance of the component. The solver has been validated with experimental data. Following a preliminary design of experiment, a meta-model is built and an automatic, multi-objective optimisation is carried out to reduce the loss introduced by the over-tip leakage and minimise the heat load on the blade. Three novel designs from the Pareto front have been further analysed. They show a significant improvement over a reference closed squealer in terms of the aerodynamic performance and the heat load. The flow mechanisms providing these benefits are explained in detail.