Cooperative control in the presence of connected and automated vehicles has attracted substantial attention due to its pronounced benefits on the network compared with human-driven vehicles. They make possible a significant reduction of travel time/waiting time, energy consumption and emissions. In this context of new emerging technologies, traffic lights are still recognized as one of the most effective strategies in terms of energy and environmental benefits, which can be further improved by considering the integration with greener powertrains. The paper proposes a cooperative network traffic management framework for Electric Vehicles (EVs) based on a multi-objective optimization aimed at minimizing the total time spent (TTS) and energy consumption (EC) of EVs. Such framework is composed of i) a traffic control model that incorporates traffic lights design, ii) a traffic flow model to estimate TTS as a network performance indicator, and iii) an EVs model to estimate EC at the intersections. The EC function has been derived from a VT-CPEM model to simulate consumptions and thoroughly calibrated based on real-world individual trajectories. The optimization framework was implemented on a nine-node network and the results of the multi-criteria optimization (aiming at minimizing the TTS and EC of EV) are compared with results of the benchmark mono - criterion optimization (aiming at minimizing the TTS) and the mono-criterion optimization combined with the speed advisory (GLOSA; Green Light Optimized Speed Advisory). All the proposed analyses were carried out for different powertrain vehicle categories; ICEVs, and EVs.