【作者】 黄磊；

【导师】 梁青槐；

【作者基本信息】 北京交通大学 ， 道路与铁道工程， 2025， 硕士

【摘要】 城市轨道交通线网的形态与布局是线网规划的核心内容,直接影响到网络的运行效率、服务水平、以及应对运营风险的能力。目前线网规划工程实践中,线网形态和布局通常采用定性分析的方法,线网规划方案受人为主观因素影响较大,特别是在网络较大时,更是难以准确、系统、科学地把握网络整体性能。本文用拓扑网络表征线网的形态与布局,基于复杂网络理论构建了一种城市轨道交通拓扑线网生成数学模型,引入多目标优化算法进行求解,得到城市轨道交通拓扑网络自动量化生成方法。论文主要研究内容和成果如下:(1)构建了拓扑线网评价指标体系。从结构性、连通性、鲁棒性与服务能力四个维度,选取了拓扑线网整体性能评价的七项指标,其中,空间匹配度与网络延伸性为结构性指标,分别衡量线网覆盖范围与居民人口空间分布的契合程度、线网在拓扑空间的疏密程度;网络效率为连通性指标,用以刻画站点间的通达程度;圈数率、结构熵、最大连通子图为鲁棒性指标,分别量化线网的路径冗余量、拓扑复杂性及网络在随机攻击下的稳定性;线网单位长度客流吸引量为服务能力指标,从客流吸引能力与成本效益的角度衡量线网效益。(2)提出了基础网络构建和客流分析的方法。基于城市主次干道交叉口、大型客流集散点分布及城市交通总体规划,构建候选站点集,按照主次干道走向及最短路径原则构建候选链路集,构建了基础网络。基于城市人口、用地数据,采用Logit可达性模型计算候选站点乘客出行总量,运用基于用地特征的双约束重力模型预测候选站点的OD矩阵,以迭代比例拟合法对OD矩阵进行修正,得到了客流OD矩阵。构建的基础网络和OD矩阵作为拓扑网络生成模型的输入。(3)构建了城市轨道交通拓扑线网自动生成数学模型。模型用链路组合(链路集)表示拓扑网络。以候选链路集为决策变量,以网络规模、锚固节点、锚固链路、连通性、无标度特性为约束,以拓扑线网评价指标为目标优化函数,将拓扑线网生成问题转化为了多目标组合优化问题。模型中引入无标度网络约束控制换乘站、中间站和终点站比例,而多目标建模策略能规避引入主观性。(4)设计了多目标多约束优化求解算法。基于NSGA-Ⅲ框架,采用基于贪心算法的双策略初始化方法,解决了多目标多约束优化问题可行域稀疏导致的初始化难的问题;针对拓扑网络无向性特征,设计两类交叉算子,保障了子代的拓扑连通性,引入自适应交叉策略动态调整交叉概率,提升了算法的搜索效率与全局探索能力;基于约束偏离度,引入分类选择机制对不可行个体的修复潜力进行评估,将具备可行性补偿能力的解优选进入下一代种群,提升了多约束环境下算法的稳定性和解集质量。(5)以F市为案例对模型和算法进行了验证。生成的线网方案在结构形态上呈现出十字形、环状等多样特征,展现良好的多样性。性能对比结果表明,F市既有线网在鲁棒性方面具备一定优势,而生成方案在服务能力与结构性能方面表现突出,单位长度客流吸引量、空间匹配度与网络延伸性指标分别平均提升23.8%、61.4%与74.4%。此外,生成网络在空间分布上呈现向北集聚趋势,与F市“北密南疏”的人口格局高度一致。对比实验显示,仅在引入双策略初始化与双交叉机制的前提下,NSGA-Ⅲ才能有效生成满足约束的可行解并实现稳定收敛,且所得到的帕累托解在目标空间上对NSGA-Ⅱ生成的解形成全面支配。更多还原

【Abstract】 The morphology and layout of urban rail transit networks are central to network planning,directly influencing operational efficiency,service level,and the ability to respond to operational risks.In current engineering practice,network morphology and layout are often analyzed qualitatively,and planning schemes are significantly affected by subjective judgment.This issue becomes particularly pronounced in large-scale networks,making it difficult to evaluate overall performance in a systematic and scientific manner.In this study,the morphology and layout of transit networks are represented using topological graphs.A mathematical model for the automatic generation of urban rail transit topological networks is developed based on complex network theory.A multi-objective optimization algorithm is introduced to solve the model,forming a data-driven method for generating urban rail topologies.The main contributions and findings are as follows:(1)A comprehensive evaluation index system for topological networks is constructed.Seven indicators are selected from four dimensions—structural characteristics,connectivity,robustness,and service capability.Specifically,spatial matching degree and network extensibility are used to characterize structural properties,measuring the alignment between network coverage and population distribution,and the density of the network in topological space,respectively.Network efficiency serves as the connectivity indicator,quantifying accessibility between stations.Loop rate,structural entropy,and maximum connected subgraph are robustness indicators,measuring path redundancy,topological complexity,and the network’s stability under random attacks.Passenger attraction per unit length is used as the serviceability indicator,reflecting cost-effectiveness from the perspective of passenger demand.(2)A method for base network construction and passenger flow estimation is proposed.Candidate station sets are generated based on major and minor road intersections,key passenger hubs,and urban transportation planning.Candidate link sets are constructed according to road alignment and shortest path principles,forming the base network.Using population and land use data,a Logit accessibility model is used to estimate the travel demand at each candidate station.A doubly constrained gravity model incorporating land use characteristics is applied to predict the OD matrix,which is further refined via an iterative proportional fitting procedure.(3)A mathematical model for automatic generation of topological transit networks is developed.The model represents a topological network as a combination of candidate links.The link set serves as the decision variable,with constraints on network size,anchor nodes,anchor links,connectivity,and scale-free characteristics.The objective functions are defined by the aforementioned performance indicators.The formulation converts the generation problem into a multi-objective combinatorial optimization task.The inclusion of a scale-free constraint allows control over the proportions of transfer,intermediate,and terminal stations,while the multi-objective formulation avoids bias from subjective weighting.(4)A tailored multi-objective,multi-constraint optimization algorithm is designed.Based on the NSGA-Ⅲ framework,a dual-strategy initialization method grounded in greedy heuristics is proposed to address the difficulty of generating feasible initial solutions due to sparse feasible regions.Two types of crossover operators are designed to ensure the topological connectivity of offspring,and an adaptive crossover strategy dynamically adjusts the crossover probability to enhance search efficiency and global exploration.A classification selection mechanism is introduced based on constraint deviation to evaluate and retain infeasible individuals with high repair potential,thereby improving solution quality and algorithmic robustness under multiple constraints.(5)The model and algorithm are validated using a real-world case in F City.The generated network schemes exhibit diverse structural forms,including cross-shaped and ring-shaped patterns,demonstrating strong solution diversity.Performance comparison shows that while the existing F City network has advantages in robustness,the generated schemes outperform in service capacity and structural performance,with improvements of 23.8%,61.4%,and 74.4%in passenger attraction per unit length,spatial matching degree,and network extensibility,respectively.Moreover,the generated networks exhibit a spatial aggregation trend toward the north,aligning with the city’s“dense north,sparse south”population distribution.Experimental results confirm that only when both dual-strategy initialization and dual crossover mechanisms are adopted can NSGA-Ⅲ stably generate feasible solutions and achieve convergence.The resulting Pareto front dominates that of NSGA-Ⅱ across all objectives.更多还原