In turbomachines, a properly dimensioned gap between the rotating blade tip and the stationary casing is required in order to avoid mechanical failures due to blade rubbing. Maintaining a tip gap allows the relative motion of the blade, however a leakage flow almost always exists due to the strong pressure differentials existing near the tip airfoil boundaries. Tip leakage flow which is a 3-dimensional and highly complex flow system is responsible from a considerable amount of total pressure loss in a turbine stage. Besides, tip leakage flows induce adverse thermal effects near the blade tip, eventually causing an increase in cooling demand. Various passive control methods exist to weaken the adverse effects of tip leakage flows, in an effort to increase turbine stage efficiency. In this paper, a novel tip carving approach is applied to mitigate the undesired aerothermal effects of the tip leakage flow. A numerical investigation is carried out to obtain the optimum shape of the carved blade tip with an objective function to minimize both heat transfer and leakage loss. A genetic algorithm is used for the optimization, integrated with a meta model which predicts the objective functions quickly. Various meta-models such as Artificial Neural Network (ANN), Extreme Learning Machine (ELM) and Support Vector Machine (SVM) are tested for this purpose. An initial database consisting of 55 blade tip geometries is created for meta-model training using "Sobol design of experiments" methodology. This database is then successively enlarged using a coarse-to-fine approach in order to improve the prediction capabilities of the meta-models. Once a sufficient level of prediction error and a proper consistency is achieved, the optimization process is terminated. Current results indicate that carved blade tip designs are likely to achieve a considerable improvement in aero-thermal performance of axial turbine stages. Multi-objective optimization of the blade tip surface of the carved type is a promising approach in gas turbines since it paves the way for undiscovered blade tip designs for further performance improvements. (C) 2019 Elsevier Ltd. All rights reserved.