This thesis examines several aspects of multi-point aerodynamic shape optimization in two dimensions, including testing of an automated weighting formula, automated introduction of design points, and three methods of imposing geometric constraints. A quasi-Newton algorithm is used, with a quadratic penalty approach for the constraints. A Newton-Krylov algorithm is used to solve the compressible Navier-Stokes equations; the same Krylov algorithm is used to solve the discrete adjoint problem to calculate the gradient. Several different multi-point problems with varying Mach number and target lift coefficients are examined to consider trade-offs in the solution and design point weighting. The automated weighting formula and automated design point addition successfully achieve optimization over a broad range of Mach numbers. The floating thickness and area constraints prove advantageous in providing more flexibility in the optimization.