This paper proposes three online real-time energy management strategies for fuel cell hybrid electric vehicles aimed at minimizing the total running cost over the vehicle's lifecycle. The cost comprises hydrogen consumption, battery electricity consumption, and the degradation of fuel cell and battery systems. The first strategy is a rule-based approach that controls fuel cell power at several fixed levels, with the battery state-of-charge serving as the shifting condition between these levels. The second strategy is an optimization-based approach that determines the fuel cell power by minimizing the instantaneous running cost. Two coefficients, dependent on the battery state-of-charge, are employed to adjust the cost weights of hydrogen consumption, battery electricity consumption, and fuel cell system degradation. The third strategy combines rules with optimization, incorporating the rules as constraints into the cost optimization model. To account for practical driving conditions throughout the vehicle's lifecycle, short distance driving cycles, long distance driving cycles, and commuter driving cycles are separately investigated. The rule and optimization combined energy management strategy outperforms the others in all driving conditions, benefiting from fewer fuel cell system start-stop cycles and increased opportunities for operating in high-efficiency regions.