Flapping motion parameters of airfoils in a biplane configuration are optimized for maximum thrust and/or propulsive efficiency. Unsteady, viscous flowfields over airfoils flapping in a combined plunge and pitch are computed with a parallel flow solver on moving and deforming overset grids. The amplitudes of the sinusoidal pitch and plunge motions and the phase shift between them are optimized for a range of flapping frequencies. A gradient-based optimization algorithm is implemented in a parallel computing environment. The deforming overset grids employed remove the restriction on the flapping motion of airfoils, and improve the optimization results obtained earlier. In the Strouhal number range 0.17 < Sr < 0.25, an airfoil in a biplane configuration produces more thrust than a single airfoil. Yet, at a higher Strouhal number, the airfoil in a biplane configuration produced less thrust at a significantly lower efficiency than a single flapping airfoil.