The paper presents results of aerodynamic design of a rectangular wing in subsonic inviscid flow using surrogate-based local and global search algorithms. The aerodynamic design problem is formulated in Benchmark Cases 3 and 6 developed by the AIAA Applied Aerodynamics Discussion Group. Both involve lift-constrained drag minimization at a Mach number of 0.5 with relatively low lift coefficients (0.2625 and 0.375) with several nonlinear constraints and a small number design variables (up to 15). In this work, the local search is performed using variable-fidelity modelling and output space mapping, whereas the global search is performed using approximation-based surrogates. The paper presents the details of the computational modelling, shape parameterization, optimization algorithms, and results for each benchmark case. The approaches yield comparable results for Benchmark Case 3. Only the local search algorithm is applied to Benchmark Case 6. The results indicate the multimodality of that design case.