The path of dual airfoils in a biplane configuration undergoing a combined, non-sinusoidal pitching and plunging motion is optimized for maximum thrust and/or propulsive efficiency. The non-sinusoidal, periodic flapping motion is described using Non-Uniform Rational B-Splines (NURBS). The Response Surface Methodology (RSM) is employed for the optimization of NURBS parameters in a parallel computing environment. A gradient based optimization algorithm, steepest ascent method is started from the optimum point of response surfaces. Unsteady, low speed laminar flows are also computed in parallel using a Navier-Stokes solver based on domain decomposition. It is shown that the parallel optimization process with RSM suggests a quick and accurate initial guess for a gradient based optimization algorithm. © 2010 Springer.