The paper investigates Shock Control Bumps (SCB) on a Natural Laminar Flow (NLF) aerofoil; RAE 5243 for Active Flow Control (AFC). A SCB approach is used to decelerate supersonic flow on the suction/pressure sides of transonic aerofoil that leads delaying shock occurrence or weakening of shock strength. Such an AFC technique reduces signi cantly the total drag at tran- sonic speeds. This paper considers the SCB shape design optimisation at two boundary layer transition positions (0% and 45%) using an Euler software coupled with viscous boundary layer e ects and robust Evolutionary Algorithms (EAs). The optimisation method is based on a canonical Evolution Strategy (ES) algorithm and incorporates the concepts of hierarchical topology and parallel asynchronous evaluation of candidate solution. Two test cases are considered with numerical experiments; the rst test deals with a transition point occurring at the leading edge and the transition point is xed at 45% of wing chord in the second test. Numerical results are presented and it is demonstrated that an optimal SCB design can be found to signi cantly reduce transonic wave drag and improves lift on drag (L=D) value when compared to the baseline aerofoil design.