Problems of optimization of flows past a thin body of revolution and a slender profile at a small angle of attack in the presence of local energy release zones and an external force acting on the flow near the surface are considered. Analysis is based on an analytic theory of supersonic flow past thin bodies presented in previous papers. The following problems are considered: drag reduction of a thin body of revolution, lift force enhancement of a profile with infinite aspect ratio, attenuation of acoustic noise generated by supersonic flows past bodies.