This paper addresses a benchmark aerodynamic design problem proposed by the AIAA Aerodynamic Design Optimization Discussion Group: Drag minimization of the RAE 2822 in transonic viscous flow at a fixed lift coefficient with constraints on the pitching moment coefficient and the cross-sectional area. The single-objective optimization (SOO) problem is solved using surrogate-based optimization (SBO) with the surrogates constructed through output space mapping and variable-resolution Reynolds-Averaged Navier-Stokes computational fluid dynamics models. Improving the implementation of our search algorithms enabled us to obtain the SOO optimal design four times faster than in our prior work in terms of CPU time. To explore the design space in the vicinity of the SOO optimal design, the problem is recast as a multi-objective optimization (MOO) one by treating the drag and pitching moment coefficients as the objectives while fulfilling the given constraints on the lift coefficient and the cross-sectional area. The MOO algorithm yields the Pareto front of the two conflicting objective functions in close proximity of the design obtained by the SOO formulation in the feasible and infeasible space of the original SOO problem.