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.