This article analyses three energy management strategies for an electric vehicle powertrain in order to maximize its global efficiency. The considered electric motor supply system is a multi-source system that consists of a fuel cell as a main energy source and an additional element that supplies peak power (at start-up and during fast transients) and charges by regenerative braking. Energy management is achieved by formulating an optimization problem, aiming to minimize the fuel cell hydrogen mass consumption while satisfying the system physical constraints (strictly positive fuel cell power, limited capacity of the storage element). First, the optimization is realized using dynamic programming, an off-line optimization method that requires the knowledge of the entire power load profile. Secondly, two on-line optimization approaches are used: the equivalent consumption management strategy and the model predictive control strategy, for which only the current power demand or its knowledge over a finite time horizon are demanded. The optimization strategies are tested in simulation using a power load profile that corresponds to an urban driving cycle.