The paper investigates a robust optimisation for detail design of active shock control bump on a transonic Natural Laminar Flow (NLF) aerofoil using a Multi-Objective Evolutionary Algorithm (MOEA) coupled to Computational Fluid Dynamics (CFD) software. For MOEA, Robust Multi-objective Optimisation Platform (RMOP) developed in CIMNE is used. For the active shock control bump design, two different optimisation methods are considered; the first method is a Pareto- Game based Genetic Algorithm in RMOP (denoted as RMOGA). The second method uses a Hybridised RMOGA with Game-Strategies and a parallel computation for high performance computation. The paper not only shows how a shock control bump approach coupled to CFD improves aerodynamic performance of original transonic aerofoil but also it shows how high performance computation with applying Hybrid- Game and parallel computation increase the efficiency of optimisation in terms of computational cost and result accuracy.