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With the growth of people's environmental awareness and the encouragement of government policies, the use of electric vehicles in logistics distribution is gradually increasing. In order to solve the dual demand of customers' simultaneous pick-up and delivery in the "last kilometer logistics", an electric vehicle routing problem with simultaneous pick-up and delivery and time window (EVRPSPDTW) is considered from the perspective of multi-objective distribution in this paper. Firstly, a decision-making model based on distribution cost and power consumption function is established. In this model, distribution cost includes transportation cost, vehicle use cost, penalty cost of not arriving on time and charging cost. Power consumption function is the energy loss caused by air resistance, tire rolling friction and transmission system. Secondly, a multi-objective genetic algorithm (NSGA-II) optimization solution with fast nondominated ranking and elite strategy is designed, and in view of the shortcomings of traditional NSGA-II, it is proposed to complete population initialization through greedy algorithm and random rules, introduce adaptive cross-mutation strategy in the chromosome crossing and mutation stage, and design three different neighborhood operators in mutation operation based on variant fitness function. Finally, the sensitivity analysis of traffic congestion coefficient further proves the effectiveness of the proposed model and the improved algorithm. [ABSTRACT FROM AUTHOR]