A vehicle powertrain includes an engine, an electric machine operable to output torque to at least one vehicle wheel, and an electric power source operable to provide electric power to the electric machine. A method for optimizing powertrain efficiency includes generating a plurality of three-dimensional maps of optimized engine speeds for combinations of vehicle power and vehicle speed at a plurality of predetermined powers of the electrical power source. Each of the maps corresponds to one of the predetermined powers of the electrical power source. The maps are used to determine an optimized engine speed for a given power of the electrical power source, a given vehicle power and a given vehicle speed.