Abstract: With the rapid development of technology and the improvement of people’s living standard, the volume of the vehicles on the road is rising year by year. Especially, traffic congestion is becoming more and more serious and it causes a waste of time. To avoid traffic congestion and reduce travel time, firstly, the road network information is expressed in the form of matrix, and the objective function of vehicle travel time is established. Then, the objective function of travel time is computed by Lagrange multiplier to get the vehicle’s driving path. Lastly, by using the simulation via MATLAB, the vehicular driving path is obtained in the case of minimizing the objective function and the more travel time can be reduced with taking the level of altruism into consideration.

Key words: travel time, traffic network, Lagrange multiplier, the level of altruism

摘要： 随着科技的不断发展和人民生活水平的不断提高，汽车的保有量日益增加，交通堵塞问题愈加严重，造成了时间的浪费。为了防止城市交通拥堵，节约驾驶员出行的时间，将路网信息表示成矩阵的形式，建立了车辆行驶时间目标函数。运用拉格朗日乘子法求解目标函数，从而得到各车辆的行驶路径。最后，利用MATLAB实验仿真，在目标函数最小的情况下，能得到车辆的行驶路径，当有利他因子时，更节省出行时间。

关键词: 行驶时间, 交通路网, 拉格朗日乘子法, 利他因子