The scope of this study is to develop a turbocharger turbine wheel with improved aerodynamic performance at low mass flow rates and with reduced inertia for better transient response. The contrasting effect of geometrical shape and size parameters on the objectives of aerodynamic performance and transient response gives rise to the need to explore the design space for the best design having good trade-off between the multi-objective requirements. The search for an optimum aerodynamic design is a challenge due to structural requirements as well. A turbine wheel that is best suited for the current application is selected from the library as a baseline and this wheel is further optimized to meet the targets. Preliminary screening allowed the identification of parameters having major impact on the objectives and these results have been used to train a Response Surface (RS). Further, in the interest of reducing computational cost, a virtual optimization algorithm based on the RS has been employed to predict optimum design within the design constraints. The optimum designs thus obtained are validated with Computational Fluid Dynamics simulations for flow performance and Finite Element solver for satisfying structural requirements. This approach has allowed for application-based design of turbine wheel for instance, by changing key parameters like blade angle distribution, number of blades, axial length, blade height and width. An inertia reduction up to 10% has been obtained while retaining the performance at low mass flow rates.