A powertrain system includes a multi-mode transmission configured to transfer torque among an engine, torque machines, and a driveline. A method for controlling operation of the powertrain system includes determining a bias engine speed based upon an engine speed. A search is executed including determining a respective candidate power cost for operating the powertrain system in response to an output torque request, and determining a respective candidate driveability cost for the candidate engine speed based upon the bias engine speed. The search also selects one of the candidate engine speeds and candidate engine torques that achieves a minimum of a combination of the respective candidate driveability cost and the respective candidate power cost as a preferred engine speed and preferred engine torque. Operation of the powertrain system is controlled based upon the preferred engine speed and preferred engine torque.