The use of differential evolution is investigated for the optimization of a novel rocket based combined cycle (RBCC) engine inlet, over the supersonic flight regime. This novel inlet design, referred to as the exchange inlet, is designed to entrain air using a semi-annular rocket-ejector exhaust profile. In supersonic flight, the exchange inlet external geometry generates shock waves which affect both the air mass flow and total pressure recovery of the entrained air. By treating each unique exchange inlet geometry as an individual in a population, the DE algorithm can narrow in on potential optimal designs using a process similar to natural selection. A single optimum is selected for three flight conditions M=1.5, 2.5 and 3.5. By comparing their off-design performance over the supersonic flight range each geometry is compared to determine an optimal for a fixed geometry design. The fixed geometry design is selected as the optimum at M=2.5.