关键词: 交通工程, 多车型时刻表, 时空不均衡, 多目标, k最短路, Pareto 最优

Abstract: A multi-type bus timetable optimization method based on the rule of passenger flow change was put forward in order to solve the problem of mismatch between supply and demand caused by unbalanced passenger flow in time and space． The objective function and constraint conditions of the model were determined from the perspectives of bus company and passengers，and the multi-objective optimization model of bus model was established．Graph theory was introduced，and feasible timetable was regarded as branch (path)． Feasible timetable set of public transport vehicles was represented by tree diagram． Public transport operation was described with vehicle space-time track diagram and cumulative passenger flow diagram． Based on this，feasible timetable，vehicle type combination and corresponding departure interval of each branch were determined，and waiting time and other target values of each branch were calculated． Then the multi-objective Pareto optimal solution (optimal schedule) of the model was solved by using the multi-objective K shortest path idea． Finally，the case data (No． 18 bus in Harbin) was calculated and compared with the multi-type bus configuration model with a single target fixed departure interval． The results show that the optimization can effectively reduce the line passenger capacity (30% in this case) and improve the service level of public transport under the condition of low operating cost.

Key words: traffic engineering, multi-vehicle timetable, time-space imbalance, multi-objective, k-shortest path, Pareto optimum