需求响应式公交车辆调度模型和算法研究综述

Review of demand-responsive transit vehicle scheduling models and algorithms

需求响应式公交车辆调度(Demand Responsive Transit Vehicle Scheduling,DRTVS)是需求响应式公交运营计划中的重要内容,一个合理的车辆调度方案对降低运营成本、提高运营效率具有重要意义,为此分析和总结了近十年来国内外关于DRTVS的优化模型和求解算法.首先,简要介绍了DRTVS模型及求解算法的分类和定义;其次,分别从调度方式、站点类型、时间约束和车辆类型4个角度对调度模型的构建和优化进行了阐述;再次,整理总结了常见的算法类型,以及每种算法的求解效果和适用条件;最后,针对当前研究中存在的建模时考虑因素不全面、假设条件过于理想化、算法求解精确度较差等问题,对优化模型及求解算法未来的研究方向进行了探讨.研究结果表明:近年来有关研究主要以动态调度、可变站点、软时间窗和多车型为主;调度模型的优化目标同时考虑出行时间、运营里程、服务质量等因素;现有车辆调度模型缺乏广泛适用性和实际可操作性;针对求解算法研究发现,小规模调度问题主要采用精确算法求解,对于大规模调度问题,使用启发式算法进行求解.

Demand-Responsive Transit Vehicle Scheduling(DRTVS)is an important part of demandresponsive transit operation planning.A well-designed vehicle scheduling scheme is of great signifi⁃cance in reducing operation costs and improving operational efficiency.Therefore,this study analyzes and summarizes the optimization models and solution algorithms of DRTVS from the past decade,both domestically and internationally.Firstly,a brief introduction is given to the classification and defi⁃nition of DRTVS models and algorithms.Secondly,the construction and optimization of scheduling models are discussed from four aspects:scheduling methods,stop type,time constraints,and vehicle types.Then,several common algorithm types are summarized,along with their solution effectiveness and applicability conditions.Finally,in consideration of the current research limitations,such as in⁃complete consideration of modeling factors,overly idealized assumptions,and poor solution accuracy,the future research directions for optimization models and solution algorithms for DRTVS are dis⁃cussed.The research findings indicate that recent studies primarily focus on dynamic scheduling,vari⁃able stops,soft time windows,and multiple vehicle types.In addition,the optimization objectives of DRTVS models commonly encompass factors such as travel time,operating mileage,and service quality.The existing vehicle scheduling models lack broad applicability and operational feasibility.Ac⁃cording to research on the solution algorithm,precise algorithms are mainly employed for small-scale scheduling problems,while heuristic algorithms are predominantly used for large-scale scheduling problems.