Scramjet propulsion is a promising technology for reliable and economical access to space and high-speed atmospheric transport. The inlet plays a key role in determining the performance of scramjets, in particular for the axisymmetric class of scramjet engines that are currently explored due to their advantages in numerous aspects. In the present study a multi-objective design optimisation (MDO) has been conducted with respect to four major inlet design criteria: compression efficiency, drag, adverse pressure gradient, and exit temperature. The former three criteria are used as the objective functions and the last as the constraint function to evaluate the inlet flowfields in the state-of-the-art coupled CFD / MDO approach. The influential parameters and key physics have been identified by scrutinising the flowfields that have been obtained as an outcome of the optimisation.