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Electric vehicles are being increasingly adopted worldwide to support the sustainable development of society. However, various technologies that are related to electric vehicles still require further investigation. In this study, we consider a gearshift control architecture that combines offline trajectory planning and online control for improved shifting in multispeed transmission electric vehicles. For gearshift trajectory planning, we establish a dynamic model and apply the multi-objective optimization Radau pseudospectral method. Simulations of this method provide a Pareto solution set under three optimization objectives, namely duration, friction work, and jerk, thereby establishing a new approach for satisfying the requirements for shift quality. Moreover, the relations among these objectives are detailed on the Pareto solution set. We conducted a hardware-in-the-loop simulation to verify the performance of the proposed control architecture and trajectory planning method. The simulation results indicate that the gearshift control delivers a suitable response for different driving intentions based on the obtained Pareto solution set.