Vulnerability-based Network Optimization Model Research

Urban rail transit is the backbone system of public transportation in metropolises,of which the increasing network level tends to be a central issue for alleviating traffic jam and promoting urban development,gradually becoming one of the major guarantees for the steady operation of cities.Despite its contribution to travel efficiency,it also brings new challenges to ensure the integrity and safety of the network.For example,the damage of few stations or line sections under emergent incidents may significantly lead to structure and function reduction of the whole network.The term “vulnerability”of complex network theory is usually used to describe this problem,to represent the degree of loss of network structure and function after being attacked.Several measures like security protection,emergency deployment,and peak flow limitation are often used to prevent and handle the vulnerability problems.However,some of the vulnerability issues are structural and originate from unreasonable transfer station settings and line layout,which can only be effectively solved by adjusting the network scheme during the planning stage.Therefore,it is necessary to carry out quantitative research from supply side and optimize the line network on the basis of accurately identifying the significantly vulnerable key links in the urban rail transit network under emergencies.The vulnerability-based network optimization research is conducted,which seeks to address the following questions:(1)The research paradigm of urban rail transit network vulnerability was systematically sorted out.By defining the basic assumptions,measurement indicators,research objectives,and attack strategies,two research objectives were clarified.On one hand,after the failure of a single station,there was no node in the network that caused significant damage to the network structure and function;on the other hand,after all station failed continuously,the proportion of nodes removed as high as possible when the network structure and function reduction reached the "crash threshold".(2)The analysis of the evolution of network vulnerability was carried out by taking Beijing Metro operating network from 2000 to 2020 as an example.The loss degree of network structure and function under a single station failure and continuous failure of all stations was calculated separately in order to obtain the network vulnerability characterization and changes.The correlation between network vulnerability and network robustness index was further studied through the bivariate Pearson test.The results showed that the vulnerability and robustness index were significant positive correlated under continuous failures,which meant the potential using as the objective function for subsequent optimization due to the strong analytical ability of robustness index.For the failure of single station,the two are not related,so it was necessary to construct an objective function that can be used for optimization.(3)A network optimization model was established,of which the comprehensive consideration was given to the optimization goals of improving network vulnerability both under single station failure and continuous failures of all stations.For the former,an index that may accurately characterize the existence of significant vulnerable nodes in the network was constructed as the optimized objective function.Aiming at the latter,natural connectivity was selected as the optimized objective function.The optimization model took the investment cost as the constraint,used the simulated annealing algorithm to solve the key connection,and then adjusted the network planning scheme.(4)The optimization model was verified by taking the planned network scheme of Beijing Metro as an example.The results suggested that the optimized scheme eliminated the original significant vulnerable nodes under a single station failure and also increased the proportion of nodes removal when the reduction of network structure and function reached the "collapse threshold" under continuous failure.This showed that the optimization model established in this paper can significantly improve the vulnerability problem of urban rail network.Our work provides a quantitative optimization method for urban rail transit network planning practitioners based on network vulnerability,which can adjust the network plan accordingly,and improve the theoretical research of urban rail network planning.This work improves the theoretical research of network planning,which is of positive significance for promoting the scientific and in-depth development of urban rail network planning.