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Unsuitable shift control strategies may increase the vehicle jerk and clutch wear. In order to improve the shift quality of electric vehicles (EVs) equipped with dual clutch transmission, this paper proposes an optimal shift control strategy based on linear quadratic regulator, in which weighting matrices are selected by using genetic algorithm (GA). The dynamics of the shift process of the dual clutch transmission is analyzed to establish the dynamic model of the driving system. In addition to the vehicle jerk, the friction work of clutch is also considered as one of the performance criteria and a new linear quadratic objective function is formulated. The optimal weighting matrices for obtaining a globally optimal solution are selected benefit from the global search capacity of genetic algorithm. The optimal target trajectories of the torque of the two clutches and motor are obtained by simulating the linear quadratic regulator (LQR).