For high-speed trains, high noise levels are generated in the bogie from wheel-rail contact and aero-acoustic sources. Manufacturers try to minimize the floor transmission to the interior, e.g. by applying damping layers or by other measures. For vehicle noise control measures, the goal is often to achieve the sound reduction needed at lowest possible mass. Here, an optimization scheme is applied to minimize the mass of an extruded floor panel. Constraints are defined by limiting the maximum local floor deflection from passenger loads according to EN 12663-1 and the A-weighted interior sound level. Recognizing the periodic nature of the floor structure, a Finite Element model of a single periodic cell is set up, using periodic boundary conditions and the floor sound reduction is determined using a Statistical Energy Analysis approach. An analytic beam model is applied to determine the floor deflection from the passenger load. Design solutions meeting the constraints with the smallest possible mass are sought. Starting with a floor structure with 23.3 kg/m2, a final design with 18.0 kg/m2 is reached. In addition, the transmitted sound through the floor is reduced by 8 dBA. Convergence from different starting points is verified.