公交网络时刻表再协同设计的多目标优化模型

摘要

Transit operators try to synchronize vehicle timetables of lines at transfer nodes to facilitate passenger transfers by adjusting bus departure times of the existing timetable,which aims to improve the bus service quality.Regarding this situation,a multi-objective re-synchronizing of bus timetable(MSBT)problem is studied.We propose a multi-objective optimization model for the MSBT,which is characterized by headway-sensitive passenger demand,flexible synchronization and service regularity.By clarifying the mathematical properties and complexity of the model,we prove that the MSBT problem is NP-hard,and its Pareto-optimal front is non-convex.A non-dominated sorting genetic(NSGA-Ⅱ) based algorithm is designed to solve the MSBT model.Compared with enumeration method,numerical experiments show that the designed algorithm can generate high-quality Pareto solutions within reasonable times.%为了改善公交服务质量,公交运营者试图调整现有时刻表的发车时间,使不同线路的车次协同到达换乘站点以方便乘客换乘.针对此场景,研究了公交时刻表重新协同设计问题,提出了求解该问题的多目标模型.模型考虑了对发车间隔灵敏的乘客需求、灵活的车次协同到站方式和发车时间的规则性,分析了该多目标模型的特征和计算复杂性,表明本文研究的问题是NP-hard问题,且它的帕累托最优前沿是非凸的,设计了基于非支配排序的遗传算法求解模型.算例表明,与枚举算法相比,提出的求解算法在较短的时间内可获得高质量的帕累托解.