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Due to the new CO2 targets for vehicles, electrification of powertrains and operation strategies for electrified powertrains have drawn more attention. This article presents a predictive multi-objective operation strategy for hybrid electric vehicles (HEVs), which simultaneously minimizes the fuel consumption and the cycle aging of traction batteries. This proposed strategy shows better performance by using predictive information and high robustness to inaccuracy of predictive information. In this work, the benefits of the developed operation strategies are demonstrated in a strong hybrid electric vehicle (sHEV) with P2-configuration. For the cycle aging of a lithium-ion battery, an empirical model is built up with Gaussian processes based on experimental data.