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High-precision response of the surrogate model is desired in the process of optimisation. An excessive number of sampling points will increase the cost of the calculation. The appropriate number of sampling points cannot only guarantee the accuracy of the surrogate model but also save the calculation cost. The purpose of this research is to demonstrate the eventuality of using an adaptive surrogate model for optimisation problems. The adaptive surrogate model is built on an adaptive sampling approach and an extended radial basis function (ERBF). The adaptive sampling is an approach that new sampling points are placed in the blank area and all the sampling points are uniformly distributed in the design region using Multi-Island GA. The precision of the ERBF surrogate model is checked using standard error measure to determine whether the surrogate model should be updated or not. This adaptive surrogate model is used to optimise a cruise missile head shape. Aerodynamic and stealthy performance of the cruise missile head shape are considered in this research. Different global objective function and different weight factor are used to research the aerodynamic and stealthy performance in this optimisation process. The results show that the drag is reduced with a slender head shape and the radar-cross section (RCS) value is reduced with a short head shape.