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With the increasing development of electric vehicles (EVs), their demand for charging has increased. To satisfy their demand with limited public charging posts while minimizing their charging cost online, the charging operation of EV charging stations (EVCSs) should be optimized. In this context, we propose an online multi-objective optimization framework for EVCS charging operation optimization with the quality of service (QoS) and the total charging cost of EVCSs as objectives. In the framework, a novel quantitative definition of QoS for online optimization of EVCSs charging operation is proposed based on the difference between the cumulative charging power demand and supply.We introduce a target-based online dynamic weighted algorithm (TBODWA) into the proposed framework to solve the online multi-objective optimization problem. The advantage of proposed framework is that it can lead the average objectives to converge to a pre-set target. In the numerical experiment, a real EVCS charging example in California, USA is employed to verify the effectiveness and efficiency of the proposed framework.