## 1 Introduction
Reference [18] improves the quintic polynomial by dynamically planning the lane-changing time and adding comfort constraints, calculates the transit state by considering the surrounding traffic conditions during the lane-changing process, and uses two improved quintic polynomials to avoid obstacles to improve security. [PERSON] et al. [19] analyzed the unmanned lane-changing entry criteria and safety assessment, designed an index function that takes into account vehicle characteristics and driving comfort, and obtained the trajectory of the unmanned vehicle lane-changing. [PERSON] et al. [20] proposed a path planning algorithm based on extension goodness evaluation for changing lanes and tracked it through model predictive control. [PERSON] et al. [21] considered the longitudinal speed and lateral overtaking path of lane changing to ensure the stability and comfort of driving on high-speed turning lanes. In order to improve the safety of intelligent vehicles in high-speed driving, avoiding obstacles and changing lanes, the literature [22] constructed anti-collision constraints and combined the six-degree polynomial path planning for planning. Based on the selected curve, [PERSON] et al. [23] used an improved artificial potential field method to consider the driver's style and reaction time and comprehensively considered lane-changing efficiency and comfort to select the optimal path. [PERSON] et al. [24] compared three polynomial lane-changing models; selected the fifth polynomial; and used the TOP-SIS algorithm to solve multi-objective optimization problems for lane-changing comfort, smoothness, and efficiency to obtain the optimal trajectory. [PERSON] et al. [25] planned the horizontal track and vertical track according to the target state for autonomous vehicle lane change track planning under the multi-lane traffic scenario. Secondly, a cost evaluation function for the trajectory was established, and the optimal trajectory was selected from three aspects: safety, comfort, and lane change time. [PERSON] et al. [26] studied the situation of vehicles returning to their original lane when they failed to change lanes. In the study, a quintic polynomial path planning method was used, and a comprehensive benefit function considering comfort, lateral displacement, longitudinal displacement, and time was set up to evaluate the model. Based on the lane change trajectory research conducted by the above scholars, the following deficiencies still exist in the research and application of lane change trajectory of autonomous vehicles:  
1. In most studies on lane change trajectory planning, the lane change time and longitudinal distance are artificially given, which is arbitrary and results in insufficient trajectory performance planning. 2. There are a few factors considered in the trajectory solution. Even if the comfort and safety factors are taken into account during the lane-changing process, the economic factor is hardly considered. 3. In the study of lane-changing trajectory optimization, there is a lack of consideration for the needs of different drivers in completing driving tasks, and there is a lack of optimization for trajectory optimization algorithms, resulting in a long computational time. In response to the above issues, this article conducts a polynomial lane change trajectory planning based on electric intelligent vehicles, considering different driving needs. For the issue of insufficient trajectory planning performance in current research, we decouple the vertical and horizontal lane-changing trajectories, with lane-changing time as a variable, and select horizontal quintic polynomials and vertical quartic polynomials. At the same time, economic indicators are added to the trajectory planning objective function to achieve energy saving by changing lanes to fill the gap in insufficient consideration of energy consumption issues in research. Considering different driving needs, the Analytic Hierarchy Process is used to adjust the weight coefficients of each indicator to cope with different lane-changing scenarios.