{"title":"利用两阶段稳健优化进行基于对称性的城市轨道交通网络规划","authors":"Zhaoguo Huang, Changxi Ma","doi":"10.3390/sym16091149","DOIUrl":null,"url":null,"abstract":"To address the symmetry-related resilience issues of stations and lines in urban rail transit networks, we propose a two-stage robust optimization-based approach for urban rail transit network planning. In this context, resilience is conceptualized as the ability of the network to maintain its operational symmetry under normal and disruptive conditions. Firstly, we used passenger flow distributions as decision variables to construct a two-stage symmetry-based urban rail transit network planning model, aiming to simultaneously minimize the total cost and total operating time of the network while preserving its functional symmetry. Secondly, we designed a hybrid evolutionary algorithm with chromosomes having a two-layer encoding structure, where the Niched Pareto Genetic Algorithm served as the main algorithmic framework, and a Large Neighborhood Search mechanism was designed to optimize the connectivity gene layer of individuals, ensuring the symmetry of network connectivity. Finally, we conducted computational verification on randomly generated instances to confirm the effectiveness of the model and algorithm. The experimental results demonstrated that our method could find two sets of Pareto optimal solutions for cost preference and time preference, thereby preserving the operational symmetry of the network under normal and damaged conditions, as well as reducing the total operating time. This effectively improved the overall efficiency and resilience of the network. Our designed hybrid evolutionary algorithm converged to satisfactory objective values in the early iterations, exhibiting strong search and optimization performance and effectively solving the two-stage symmetry-based urban rail transit network planning model.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Symmetry-Based Urban Rail Transit Network Planning Using Two-Stage Robust Optimization\",\"authors\":\"Zhaoguo Huang, Changxi Ma\",\"doi\":\"10.3390/sym16091149\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"To address the symmetry-related resilience issues of stations and lines in urban rail transit networks, we propose a two-stage robust optimization-based approach for urban rail transit network planning. In this context, resilience is conceptualized as the ability of the network to maintain its operational symmetry under normal and disruptive conditions. Firstly, we used passenger flow distributions as decision variables to construct a two-stage symmetry-based urban rail transit network planning model, aiming to simultaneously minimize the total cost and total operating time of the network while preserving its functional symmetry. Secondly, we designed a hybrid evolutionary algorithm with chromosomes having a two-layer encoding structure, where the Niched Pareto Genetic Algorithm served as the main algorithmic framework, and a Large Neighborhood Search mechanism was designed to optimize the connectivity gene layer of individuals, ensuring the symmetry of network connectivity. Finally, we conducted computational verification on randomly generated instances to confirm the effectiveness of the model and algorithm. The experimental results demonstrated that our method could find two sets of Pareto optimal solutions for cost preference and time preference, thereby preserving the operational symmetry of the network under normal and damaged conditions, as well as reducing the total operating time. This effectively improved the overall efficiency and resilience of the network. Our designed hybrid evolutionary algorithm converged to satisfactory objective values in the early iterations, exhibiting strong search and optimization performance and effectively solving the two-stage symmetry-based urban rail transit network planning model.\",\"PeriodicalId\":501198,\"journal\":{\"name\":\"Symmetry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Symmetry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3390/sym16091149\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symmetry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/sym16091149","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Symmetry-Based Urban Rail Transit Network Planning Using Two-Stage Robust Optimization
To address the symmetry-related resilience issues of stations and lines in urban rail transit networks, we propose a two-stage robust optimization-based approach for urban rail transit network planning. In this context, resilience is conceptualized as the ability of the network to maintain its operational symmetry under normal and disruptive conditions. Firstly, we used passenger flow distributions as decision variables to construct a two-stage symmetry-based urban rail transit network planning model, aiming to simultaneously minimize the total cost and total operating time of the network while preserving its functional symmetry. Secondly, we designed a hybrid evolutionary algorithm with chromosomes having a two-layer encoding structure, where the Niched Pareto Genetic Algorithm served as the main algorithmic framework, and a Large Neighborhood Search mechanism was designed to optimize the connectivity gene layer of individuals, ensuring the symmetry of network connectivity. Finally, we conducted computational verification on randomly generated instances to confirm the effectiveness of the model and algorithm. The experimental results demonstrated that our method could find two sets of Pareto optimal solutions for cost preference and time preference, thereby preserving the operational symmetry of the network under normal and damaged conditions, as well as reducing the total operating time. This effectively improved the overall efficiency and resilience of the network. Our designed hybrid evolutionary algorithm converged to satisfactory objective values in the early iterations, exhibiting strong search and optimization performance and effectively solving the two-stage symmetry-based urban rail transit network planning model.