定制公交多目标鲁棒优化模型与算法

Multiobjective Robust Optimization Model and Algorithm for Customized Bus

为了确定定制公交在路网中的行驶路径,文章研究了乘客等车时间不确定环境中定制公交行驶路线的鲁棒优化问题:(1)以最小化运营公司的经营费用、最小化乘客的出行时间为优化目标,以车辆的容量限制、乘客的上、下车时间窗、不确定的乘客等车时间等为约束条件,建立了定制公交多目标鲁棒优化模型;(2)采用改进的NSGA-Ⅱ算法(Nondominated Sorting Genetic AlgorithmⅡ)进行求解,用基于未到达交通节点顺序的自然数编码方法进行编码,以锦标赛选择策略进行选择操作以及采用均匀变异方式进行变异操作;(3)选取兰州市局部路网进行案例研究。研究结果表明,运用本文建立的定制公交多目标鲁棒优化模型及求解算法,能快速得到满足优化目标的行驶路径。选用合理的行驶路线能够节约乘客的出行成本,增加运营公司的收益。

In order to determine the driving route of customized bus in the road network,this article studied the Robust optimization problem of customized bus driving route under uncertain passenger waiting time environment:(1)With the minimized operating costs of operating companies and the minimized passenger travel time as the optimization objective,and with the capacity constraints of vehicles,the get-on/off time window of passengers,and the uncertain waiting time of passengers as the constraint conditions,this article established the multi-objective Robust optimization model of customized bus.(2)Then it was solved by improved NSGA-II algorithm(Nondominated Sorting Genetic AlgorithmⅡ),and was programmed by natural number coding method based on the sequence of non-reached traffic nodes,with the tournament selection strategy for selection operation and the uniform mutation method for mutation operation;(3)Part of road network in Lanzhou was selected for case studies.The research results showed that using the multi-objective Robust optimization model and the solution algorithm of customized bus established in this article can quickly get the driving route to meet the optimization objectives.Choosing the reasonable travel route can save the travel cost of passengers and increase the income of operation company.