Review of urban resilient transportation systems: Assessment methods and optimization improvements
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摘要: 为系统性梳理城市韧性交通系统的评估方法与优化策略，构建了一个以鲁棒性与恢复性为核心的分析框架，并以此对现有研究进行整理和评述。在韧性评估方面，系统剖析了图论与复杂网络、概率统计模型、数据驱动及多指标评估等4类主流方法；在韧性优化方面，从单维度和复合维度出发，探讨了以网络结构加固为代表的预防性策略和以应急资源调度为代表的响应式策略；通过解析决策变量与目标函数，构建了评估指标与优化策略之间的理论映射机制。分析结果表明：现有评估方法正由单一物理拓扑度量向融合时空因果推理的智能评估转型；优化策略则从局部路网的静态均衡向跨系统耦合的动态博弈演进；研究明确了评估和优化的协同机理，鲁棒性边界与脆弱性节点识别直接定义了预防性优化的解空间约束，而恢复力曲线与性能损失量化则为响应式优化的目标函数构建提供了标准化基准。未来研究需重点关注评估与优化的深度一体化设计，建立能够动态反馈、自我调整的闭环决策模型；同时，应加强物理模型与人工智能方法的融合，发展面向复杂情景的预测性评估与主动式优化技术，从而为构建智慧化、高韧性的城市交通系统提供关键理论与技术支撑。Abstract: To systematically review the assessment methods and optimization strategies of urban resilient transportation systems, an analytical framework centered on robustness and recoverability was constructed, and existing studies were synthesized and reviewed based on this. Regarding resilience assessment, four types of mainstream methods were systematically analyzed: graph theory and complex networks, probability statistical models, data-driven approaches, and multi-indicator assessment. Regarding resilience optimization, from single- and multi-dimensional perspectives, preventive strategies represented by network structure reinforcement and responsive strategies represented by emergency resource dispatching were investigated. By analyzing decision variables and objective functions, a theoretical mapping mechanism between assessment indicators and optimization strategies was constructed. The analysis results show that existing assessment methods are transforming from single physical topology measurement to intelligent assessment integrating spatiotemporal causal inference. Meanwhile, optimization strategies are evolving from static equilibrium of local road networks to dynamic games of cross-system coupling. The study clarifies the synergistic mechanism between assessment and optimization, and the identification of robustness boundaries and vulnerable nodes directly defines the solution space constraints for preventive optimization. In addition, the recoverability curve and performance loss quantification provide standardized benchmarks for constructing the objective functions of responsive optimization. Future research needs to focus on the deep integrated design of assessment and optimization, establishing closed-loop decision-making models capable of dynamic feedback and self-adjustment. Simultaneously, the integration of physical models and artificial intelligence methods should be strengthened to develop predictive assessment and proactive optimization technologies for complex scenarios, thus providing key theoretical and technical support for constructing intelligent and highly resilient urban transportation systems.
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图 1 韧性交通系统研究关键词共现知识图谱
Figure 1. Knowledge map of keywords co-occurrence for resilient transportation systems research
图 2 韧性交通系统研究关键词聚类图谱
Figure 2. Knowledge map of keywords clustering for resilient transportation systems research
图 3 城市韧性交通系统综述框架
Figure 3. Review framework for urban resilient transportation systems
图 4 韧性交通系统评估方法发展脉络
Figure 4. Development trajectory of assessment methods for resilient transportation systems
图 6 地铁-公路交通网络相互依存的耦合关系
Figure 6. Interdependent coupling relationship between subway-highway traffic network
图 7 韧性交通系统优化方法发展脉络
Figure 7. Development trajectory of optimization methods for resilient transportation systems
图 8 韧性交通系统评估和优化方法文献发展总结
Figure 8. Summary of literature development on assessment and optimization methods for resilient transportation systems
表 1 交通网络韧性的评估方法
Table 1. Assessment methods for transportation network resilience
类型 作者 研究方法 研究对象 核心评估维度 拟优化方向 基于图和复杂网络的方法 Gao等[23] 基于网络模型的节点故障和边故障模型 公路/地铁交通网络（故障） 恢复性 网络结构优化 Morelli等[24] 基于网络拓扑、几何形状和旅行分布数据方法 步行/自行车/驾车交通网络（内涝） 鲁棒性、恢复性 网络结构优化 Wei等[25] 结合复杂网络理论和韧性曲线特征 公路交通网络（地震） 鲁棒性、恢复性 网络结构优化 Zhang等[26] 基于复杂网络的新型脆弱性评估和可视化框架 公路交通网络（服务中断） 鲁棒性 网络结构优化、修复策略 Bell等[27] 基于容量加权谱分析的交通网络韧性评估方法 城市公交网络 鲁棒性 网络结构优化 Ganin等[28] 基于图渗透理论的模型 智能交通系统（网络干扰） 鲁棒性 网络结构优化、修复策略 Xu等[29] 构建相互依赖网络模型 相互依赖网络模型（轨道-公交网络） 鲁棒性、恢复性 网络结构优化 Wang等[30] 基于层次网络结构，模拟风险传播 多式联运网络（轨道-道路网络） 鲁棒性 网络结构优化 Jiang等[31] 基于最短路径以及跨层的交通流分配方法 多式联运网络（轨道-航空网络） 鲁棒性 网络结构优化、资源分配优化 Wang等[32] 基于网络拓扑结构与交通需求识别关键节点 多式联运网络 鲁棒性 网络结构优化、资源分配优化 王永岗等[33] 多式联运复合交通网络拓扑模型受攻击下的脆弱性表现 多式联运网络 鲁棒性 网络结构优化 基于概率统计模型的方法 Nogal等[34] 基于动态随机受限均衡模型 公路交通网络（破坏事件） 恢复性 网络结构优化 Nogal等[35] 基于专家结构化判断的方法 公路/高速公路交通网络（灾害） 鲁棒性 资源分配优化 Gao等[36] 使用概率建模技术 公路交通网络（降雨） 鲁棒性、恢复性 资源分配优化、修复策略优化 Farahmand等[37] 概率性区域韧性评估框架 公路交通网络（洪水） 恢复性 资源分配优化 候宗昊等[38] 利用多智能体仿真，通过贝叶斯网络量化设备损伤概率 机场交通系统 恢复性 资源分配优化 基于数据驱动方法 Hu等[39] 使用多源众包数据，利用广义可加模型 公路交通网络（洪水、风暴、雾） 恢复性 资源分配优化 Peng等[40] 基于随机森林的模型 公路交通网络（交通事故） 鲁棒性 资源分配优化、修复调度优化 Zang等[41] 结合深度学习和图神经网络的具有预测性的、实时的韧性评估方法 公路交通网络（降雨） 鲁棒性、恢复性 修复调度优化 Zang等[42] 基于动态多粒度图神经网络的实时的道路韧性评估方法 公路交通网络（暴雨） 鲁棒性、恢复性 修复调度优化 Zhang等[43] 基于众包数据的多维脆弱性评估框架 公路交通网络（地震） 鲁棒性 网络结构优化、资源分配优化 Wang等[44] 基于扩散图卷积递归神经网络的端到端深度学习框架 公路/高速公路交通网络（极端天气） 鲁棒性、恢复性 资源分配优化 Ghadami等[45] 基于早期预警信号的方法 高速公路网络（拥堵） 鲁棒性 网络结构优化 Tang等[46] 基于系统思维的层次化贝叶斯网络模型 城市交通系统 鲁棒性 网络结构优化 Wang等[47] 多维动态贝叶斯网络模型 城市交通系统 恢复性 网络结构优化、修复调度优化 基于多指标评估方法 Yin等[48] 交通流模拟、中断模拟、回归模型 公路交通网络（不良事件） 鲁棒性 修复调度优化、资源分配优化 Fang等[49] 基于多阶段模型的交通系统韧性评估方法，使用蒙特卡洛模拟和历史数据来生成台风情景 高铁/民航交通网络（台风） 恢复性 修复调度优化、资源分配优化 Yang等[50] 利用InfoWorks ICM水动力模型模拟的数据，以及Geodetector模型 公路交通网络（内涝） 鲁棒性 网络结构优化、资源分配优化 Nickdoost等[51] 复合指数开发框架 公路交通网络（风灾、水灾） 鲁棒性 资源分配优化、修复调度优化 Nan等[52] 综合韧性指标、混合复合维度建模方法 基础设施系统（电力系统） 鲁棒性、恢复性 资源分配优化 Ganin等[53] 基于图论，采用重力模型分配交通流，再模拟随机链路失效，从而评估韧性 公路交通网络（灾害） 恢复性 资源分配优化、修复调度优化 徐鹏程等[54] 综合了图论、复杂网络理论、数据驱动和物理模型的多维度评估方法 高速公路网络（拥堵） 恢复性 网络结构优化 Liu等[55] 基于乘客出行的网络性能指标与韧性三角形 多式联运网络（公交-轨道网络） 鲁棒性、恢复性 网络结构优化、资源分配 Du等[56] 基于启发式算法求解韧性优化模型，综合网络结构和功能进行评估 多式联运系统（公交-轨道网络） 鲁棒性、恢复性 网络结构优化、资源分配 Wang等[57] 考虑乘客行为的级联失效模型，综合需求与设施供应的韧性评估 多式联运系统（公交-轨道网络） 恢复性 网络结构优化、资源分配 
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表 2 四类韧性评估方法的综合比较
Table 2. Comprehensive comparison of four types of resilience assessment methods
方法类别 核心评估维度 主要优势 主要局限 拟优化路径 基于图和复杂网络的方法 侧重静态鲁棒性与结构脆弱性评估，对恢复性动态过程刻画能力有限 计算效率高、数据依赖性低（仅需拓扑数据），适用于大规模网络宏观静态分析 忽略交通流动态特性，难以精细刻画系统性能的动态下降与恢复过程 结构性优化：为网络加固、冗余设计等策略提供关键节点识别与拓扑优化依据 基于概率统计
模型的方法鲁棒性与恢复性评估兼顾，通过刻画不确定性为两者提供量化基础 擅长处理不确定性，评估维度相对均衡，能够为风险评估提供概率输入 对先验知识和模型假设的准确性要求高，计算复杂度较高，实时性较弱 不确定性优化：为鲁棒/随机优化模型提供扰动概率分布，将韧性转化为优化约束或目标 基于数据驱动的方法 侧重于动态恢复性的实时评估与预测，也能通过历史数据分析鲁棒性表现 适应性强，能利用实时数据精准刻画动态过程，具备预测能力 对数据质量和数量要求高，模型可解释性（黑箱问题）和泛化能力是挑战 动态与自适应优化：通过实时预测与状态反馈，支持应急资源调度、动态交通控制等策略 基于多指标评估方法 致力于整合鲁棒性与恢复性，构建单一或多维度的综合韧性指标，实现整体性衡量 评估全面性最高，能够提供系统韧性的整体性、综合性视图 构建过程复杂，需多领域知识；指标权重主观性强，可解释性和易用性较低 多目标优化：其综合指数可直接作为优化的目标函数，或作为评估不同方案优劣的评价器
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表 3 单维度韧性优化研究
Table 3. Studies on single-dimensional resilience optimization
方法 作者 研究对象 优化目标 关键模型 核心约束 决策变量 求解算法 优化指标 面向网络结构的韧性优化方法 Ma等[58] 省际区域网络 最小化出行时间 多模式交通分配模型 链路流约束、成本约束、预设恢复计划约束 各路径的交通流量 梯度投影算法 恢复力 路庆昌等[59] 城市轨道交通网络 最小化累积性能损失和最小化延误时间 双层优化模型 恢复时间约束、预算约束、用户均衡约束 地铁站点的保护状态 遗传算法和Frank-Wolfe算法 恢复力、抵抗力 Yin等[60] 省内区域交通网络 最小化操作成本和最坏情况下的恢复成本 两阶段可恢复鲁棒优化模型 设施-需求预分配约束、灾后供需覆盖约束、容量约束 救援设施位置、救援物资分配、灾后恢复行动决策 两阶段分解算法 恢复力 Wang等[61] 城市道路交通网络 最小化恢复时间 基于紧急水平的多层韧性分析模型 列车载客量上限约束、路径通行能力约束、拥挤阈值 受损车道数、车道变向数、救援车辆路线 遗传算法和集成重配置策略 恢复力 程驰尧等[62] 城市轨道交通网络 最大化路网韧性 基于后向加边的网络优化模型 连通度约束、成本约束、换乘节点优先约束 核心节点的连接关系 模拟退火算法 抵抗力/鲁棒性 面向资源分配优化的方法 Li等[63] 城市轨道交通网络 最小化恢复时间 混合整数非线性规划模型 最小追踪约束、满载率上限、容量约束、停站时间动态调整约束 列车重新调度时间、是否取消服务、是否使用备用列车 两阶段迭代优化方法 恢复力 Tao等[64] 城市道路交通网络 最小化出行时间 交通信号优化模型 溢出约束以及交通均衡约束 交通信号的周期长度和绿灯时间 基于贪婪策略和梯度下降的两级算法 恢复力、抵抗力 Hosseini等[65] 城市道路交通网络 最小化恢复时间和性能损失 基于概率的综合模型 资源分配约束、恢复序列约束 资源的数量、位置、容量及任务序列 模拟退火算法 恢复力 Sun等[66] 城市道路交通网络 最大化路网韧性和最小化操作成本 基于贝叶斯网络和多目标优化模型 设施状态转移概率、个体行为状态转移概率 节点状态 多目标非支配排序遗传算法 恢复力、抵抗力 马飞等[67] 城市轨道交通网络 最小化人员接触，最大化集成韧性指标 基于复杂网络以及传染病传播模型 客流容量约束、网络结构约束、时间资源约束 客流限制水平、网络运行效率 仿真模拟与参数扫描 恢复力 Zamanifar等[68] 城市道路网络 最大化运输网络的性能、恢复过程的效率和效果 基于多属性决策三阶段框架 可操作、可区分、非冗余 候选决策属性（如访问服务节点级别等） 多属性值理论 恢复力 面向修复策略优化的方法 Sasai等[69] 城市道路交通网络 最小化用户成本和运维成本 动态规划模型 成本平衡约束、恢复时间约束、马尔科夫决策过程 每个时间步采取的最佳维护和修复行动序列 动态规划马尔可夫决策算法 恢复力 Wu等[70] 城市道路交通网络 最大化路网韧性 韧性评估和恢复优先级模型 路段交通性能建模、随机修复时间约束 桥梁修复优先级和交通网络恢复状态 用户均衡算法和Frank-Wolfe算法 恢复力 Pei等[71] 城市道路交通网络 最小化性能损失 最优修复策略模型 修复团队数量限制约束、桥梁功能随时间变化约束 交通和医疗设施的恢复顺序 模拟退火算法 恢复力、抵抗力 Zhang等[72] 农村交通网络 最小化恢复时间和最大化累积效益率 路桥交通系统优化模型 资源限制约束、修复时间约束、经济权衡约束 桥梁的修复开始时间 多目标遗传算法 恢复力 Zou等[73] 省内区域交通网络 最大化道路恢复速度 深度集成辅助的主动学习模型 资源限制约束、修复时间随机分布约束 交通道路恢复顺序 深度卷积神经网络和全局优化算法 恢复性 毛新华等[74] 城市道路交通网络 最大化路网韧性和最小化恢复时间 最优修复调度模型 修复预算上限约束、抢修队数量约束、最长工期约束 修复路段的选择和修复先后顺序 禁忌搜索算法和Frank-Wolfe算法 恢复力、抵抗力 Yaibok等[75] 城市道路交通网络 最小化出行时间 基础路径交通分配模型 洪水风险动态映射、高峰OD需求约束 疏散路线选择和交通流量分配 基于路径的流量分配方法 恢复性 Liu等[76] 城市道路交通网络 最小化出行时间和燃油消耗 混合整数非线性模型 流量守恒约束、最小残差、节点流量平衡 各节点的交通流量 基于多智能体的分布式优化算法 恢复性 郝新军等[77] 城市道路交通网络 最大化路网连通度 动态规划模型 协同修复约束、路由协同约束 维修队的修复调度和路由 马尔科夫决策和强化学习 恢复性
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表 4 复合维度网络韧性的协同优化方法
Table 4. Multi-dimensional network resilience collaborative optimization methods
类型 作者 研究对象 优化目标 关键模型 核心约束 决策变量 求解算法 优化指标 恢复次序 Du等[56] 城市轨道交通-地面公交 最大化联运系统的韧性度量函数、恢复能力 双层网络韧性优化模型 修复资源约束、修复时间约束、性能完全恢复约束 损坏站点的恢复顺序 遗传算法 恢复力、抵抗力 Zou等[81] 省内道路交通-电力系统网络 最大化预期的系统韧性提升 双层混合整数优化模型 预算限制、地理耦合、动态交通流约束、不确定性约束 灾前缓解和修复行动的资源分配以及灾后修复 二进制粒子群优化结合背包问题的启发式初始化算法 恢复力、
抵抗力Zou等[82] 城市交通网络-能源枢纽 最小化极端事件下整个能源枢纽的电力和热负荷削减总量 混合整数线性规划模型 电池SOC约束、交通时间动态性约束、多能源耦合约束 电动汽车预定位置，不同能源枢纽之间实时调度和
路由。基于场景的随机规划、求解器Gurobi 恢复性 应急疏散 Zhang等[83] 城市轨道交通-地面公交 量化公交服务中断后的故障影响 改进的耦合映射格 耦合站点覆盖半径约束、信号传递强度约束、需求点覆盖约束 交通节点状态演化函数 无 鲁棒性/抵抗力 Guo等[84] 跨省区域铁路-道路-航空 最小化救援成本、最大化需求点覆盖；最小化从需求点到救援设施的时间 应急设施分配、合作覆盖
模型设施覆盖半径约束、建设成本约束、需求点覆盖约束 应急救援设施位置选择 混合型启发
算法恢复性 Yang等[85] 城市道路交通-轨道交通 最小化系统总疏散时间（总旅行时间和等待时间） 点队列、双队列流动动力学疏散模型 流量守恒方程、避难所容量限制、排队动力学约束、交互过程约束 疏散计划（路径、换乘等） 连续平均法顺序优化 恢复性 Gan等[86] 城市道路交通-电力网络 最小化交通网络的总运行成本以及电力网络中未服务的电力负荷成本 混合整数二次约束规划 用户均衡、电网潮流平衡、充电站容量限制、调度约束、路径流量约束 电动汽车的充电重新调度策略（路由和重新选择策略） 线性化技术、求解器 恢复性 交通效率 Abbasi等[87] 海港地区道路交通-轨道交通 最小化运输成本、最小化气体排放等 混合整数多目标优化模型 流量守恒约束、容量约束、吞吐量限制、转运时间窗约束 路径流量、链路流量等 IBM商业
求解器恢复性 Guo等[88] 国家之间的多式联运运输方式 最小化多周期多模态运输的总运营成本（运输成本、中转成本和仓库建设存储成本） 考虑不确定性的鲁棒优化
模型路径流量可行性、仓库存储容量限制、多周期运输时间协调约束、换乘成本约束 仓库建设、货物存储、运输模式等 混合型启发式算法 恢复性 Zhang等[89] 货运系统中的多式联运枢纽网络 最小化枢纽网络建设和运输成本 两阶段鲁棒优化
模型单商品流约束、枢纽建设预算限制、旅行时间限制、容量协调限制 枢纽位置、
运输路径等改进的Benders分解算法 恢复力、
抵抗力Zhang等[90] 城市交通网络-电力网络 最小化最坏情况下的总运营成本、最小化交通网络的总旅行拥堵时间等 三层优化的混合整数线性
模型配电网络结构重构约束、网络流量平衡约束、用户均衡约束、维修时间约束 线路加固、发电机放置、交通灯状态等 列约束生成算法、子问题
分解恢复性
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表 5 韧性评估方法与优化提升策略的对应关系
Table 5. Corresponding relationship between resilience assessment methods and optimization strategies
韧性评估方法 核心评估指标 优化策略类型 应用场景 核心指导维度 内在指导逻辑 基于图和复杂网络的方法 识别关键节点（节点度，交通需求）[30] 网络结构优化、修复策略优化[56] 网络抗毁性设计与加固
界定决策变量评估识别的关键节点集合将整个交通网络的搜索空间降维至子集层面进行优化，明确了网络加固或修复序列算法中的核心决策变量与搜索权重 识别网络瓶颈（容量加权谱分析）[27] 网络结构优化[62] 关键链路增容与备份 约束解空间 利用谱分析定位的瓶颈环节，在数学上约束了拓扑优化问题的解空间，使针对性的增边/扩容策略成为可能 节点/边故障模型；网络结构脆弱性[23, 26] 网络结构优化、修复策略优化[61] 有限资源下的修复排序 确立优先次序 拓扑脆弱性指标提供了量化的适应度函数依据，指导优化算法在有限资源约束下优先处理高价值目标，实现计算效率最大化 级联失效模型（CML）；多式联运脆弱性[33] 修复策略优化[83-84] 防止跨区域级联崩溃 划定拓扑边界 级联失效评估划定了故障传播的拓扑边界，为多模态网络中的阻断策略提供了空间约束条件 基于概率统计模型的方法 贝叶斯网络评估韧性[46-47] 资源分配优化[66] 不确定扰动下的资源分配 构建机会约束 评估量化的贝叶斯风险分布，将不确定性转化为优化模型中的概率约束或机会约束，确保资源分配方案满足鲁棒性要求 刻画不确定性如随机用户行为、随机恢复时间[35] 修复策略优化[70, 73] 最坏情景防御 界定鲁棒
可行域随机参数的评估结果为修复调度模型划定了鲁棒可行域，指导策略寻找在最坏情景下的最优解 基于数据驱动的方法 基于深度学习预测时空韧性[41-42, 44] 修复策略优化[73] 突发事件短时应急响应 重构决策时域 基于深度学习的短时预测提供了系统状态的先验认知，支持优化模型采用滚动时框架进行主动干预 多源众包数据（OD数据）、交通流分析[39, 43] 修复策略优化[75] 实时交通流疏导与管控 生成动态
状态流实时流数据分析将优化决策从静态规划转变为动态闭环控制，使得疏散路径规划能够实时响应交通流的演变 基于多指标评估方法 韧性三角形；性能损失积分；累积效益[22, 52] 网络结构优化[59] 全周期恢复方案制定 构建目标函数 基于韧性三角理论定义了性能损失，并将其作为双层优化模型的目标函数 韧性三角形；性能损失；累积效益[22, 52] 修复策略优化[72, 74] 多策略比选与综合评价 统一评价标尺 性能损失积分与累积效益率为多目标优化提供了标准化的数学形式，解决了修复调度中不同策略优劣难以量化比较的理论难题 多指标（乘客需求、基础设施供应）[57] 网络结构优化（复合维度）[58] 供需失衡下的流量分配 参数化
约束供需耦合评估将多维指标转化为交通分配模型中的广义成本函数或阻抗参数，实现了从指标到模型参数的直接映射 轨道交通-地面公交网络耦合；乘客旅行换乘行为[29, 55] 应急疏散（复合维度）[85] 大规模人群/车辆疏散 提供微观反馈 基于多智能体的微观行为评估为宏观疏散优化提供了底层反馈逻辑，通过迭代修正实现系统最优与用户均衡的统一
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