A fuzzy approach for designing of subway lines, case study: development of the Tehran subway network

Document Type : Research Article


1 Transportation Planning Department, Faculty of Civil and Environmental Engineering, Tarbiat Modares University, Tehran, Iran

2 Associate Professor, Faculty of Civil and Environmental Engineering, Tarbiat Modares University

3 Groove School of Engineering, City College of New York, United States of America


Subway network design can be classified as one of the most challenging problems in transportation planning, where different deterministic or non-deterministic approaches have been utilized for optimal design. Non-deterministic methods, having fewer limitations and representing reality with its intrinsic uncertainty, have thus been the focus of less research. This paper incorporates concepts of fuzzy set theory into the optimal design of subway networks to the case of Tehran. Two binary mathematical programming models with different objective functions are developed. The first model maximizes the covered population while minimizing construction cost, whereas the second maximizes the ratio of the covered population to construction cost. These objective functions are modeled in both a fuzzy and a deterministic state. In the fuzzy model, we use a fuzzy penalty factor instead of edge length constraints and propose a Sugeno fuzzy inference system for calculating the covered population. Results indicate that the total length of designed lines with the linear and nonlinear fuzzy approach is equal to 139.3 km (477000 billion Iranian Rials) and 144.6 km (494000 billion Iranian Rials), respectively. Considering topology improvement per construction cost index, designed lines with the linear fuzzy model are better than the nonlinear fuzzy model. In comparison to the classic deterministic approach, the proposed fuzzy approach can improve topology improvement per construction cost index by 23 percent.


Main Subjects

[1] D. Pulido, G. Darido, R. Munoz-Raskin, J. Moody. The urban rail development handbook. World Bank Group Press, (2018).
[2] G. Laporte, J. A. Mesa, F. A. Ortega, F. Perea. Planning rapid transit networks. Socio-Economic Planning Sciences45(3) (2011) 95-104.
[3] H. Dufourd, M. Gendreau, G. Laporte. Locating a transit line using tabu search. Location Science4(1-2) (1996) 1-19.
[4] G. Bruno, M. Gendreau, G. Laporte. A heuristic for the location of a rapid transit line. Computers & Operations Research29(1) (2002) 1-12.
[5] M. Labbé, G. Laporte, I.R. Martín, J.J.S. González. The ring star problem: Polyhedral analysis and exact algorithm. Networks: An International Journal43(3) (2004) 177-189.
[6] A. Marín. An extension to rapid transit network design problem. Top15(2) (2007) 231-241.
[7] A. Marin, P. Jaramillo. Urban rapid transit network capacity expansion. European Journal of Operational Research191(1) (2008) 45-60.
[8] A. Marín, P. Jaramillo. Urban rapid transit network design: accelerated Benders decomposition. Annals of Operations Research169(1) (2009) 35-53.
[9] S. Kermansshahi, M. Shafahi, Y. Mollanejad, M. Zangui. Rapid transit network design using simulated annealing. In 12th World conference of transportation research (2010) 11-15.
[10] G. Laporte, A. Marin, J.A. Mesa, F. Perea. Designing robust rapid transit networks with alternative routes. Journal of advanced transportation, 45(1) (2011) 54-65.
[11] S. Afandizadeh, M. Ahmadinejad, M. Hashemi. A genetic algorithm approach to metro design problem. Journal of transportation research, 8(1) (2011) 1-10 (In Persian).
[12] G. Gutiérrez-Jarpa, C. Obreque, G. Laporte, V. Marianov. Rapid transit network design for optimal cost and origin–destination demand capture. Computers & Operations Research40(12) (2013) 3000-3009.
[13]G. Laporte, M.M. Pascoal. Path based algorithms for metro network design. Computers & Operations Research, 62 (2015) 78-94.
[14] E.M. de Sá, I. Contreras, J.F. Cordeau. Exact and heuristic algorithms for the design of hub networks with multiple lines. European Journal of Operational Research246(1) (2015) 186-198.
[15] D. Canca, A. De-Los-Santos, G. Laporte, J.A. Mesa. A general rapid network design, line planning and fleet investment integrated model. Annals of Operations Research246(1-2) (2016) 127-144.
[16] L. Cadarso, A. Marín. Rapid transit network design considering risk aversion. Electronic Notes in Discrete Mathematics52 (2016) 29-36.
[17] D. Canca, A. De-Los-Santos, G. Laporte, J.A. Mesa. An adaptive neighborhood search metaheuristic for the integrated railway rapid transit network design and line planning problem. Computers & Operations Research, 78 (2017) 1-14.
[18] G. Gutiérrez-Jarpa, G. Laporte, V. Marianov, L. Moccia. Multi-objective rapid transit network design with modal competition: The case of Concepción, Chile. Computers & Operations Research78 (2017) 27-43
[19] L. Cadarso, A. Marín. Improved rapid transit network design model: considering transfer effects. Annals of Operations Research258(2) (2017) 547-567.
[20] G. Gutiérrez-Jarpa, G. Laporte, V. Marianov. Corridor-based metro network design with travel flow capture. Computers & Operations Research89, (2018) 58-67.
[21] Y. Wei, J.G. Jin, J. Yang, L. Lu. Strategic network expansion of urban rapid transit systems: A bi‐objective programming model. Computer‐Aided Civil and Infrastructure Engineering, 34(5) (2019) 431-441.
[22] A.R. Mahdavi, A.R. Mamdoohi, M. Allahviranloo, Application of a mathematical programming model for development of Tehran metro network, 6th International Conference on Recent Advances in Rail Engineering, (2019) 1-10 (In Persian).
[23] A.R. Mahdavi. An evaluation and development model of Urban Rail Transit Network case study: Tehran metropolitan area, MSc Thesis, Tarbiat Modares University, (2019) (In Persian)
[24] A.R. Mahdavi, A.R. Mamdoohi, M. Allahviranloo, Topology Evaluation of Tehran metro network utilizing a mixed index for metro networks ranking, Amirkabir Journal of Civil Engineering, Online Published (2019) (DOI: 10.22060/CEEJ.2019.16436.6226) (In Persian).
[25] S. Saidi. Long Term Planning and Modeling of Ring-Radial Urban Rail Transit Networks. PhD Dissertation, University of Calgary (2016).
[26] S. Saidi, S. Wirasinghe, L. Kattan. Rail Transit: Exploration with Emphasis on Networks with Ring Lines. Transportation Research Record: Journal of the Transportation Research Board, 2419 (2014) 23-32.
[27] J. Zhang, M. Zhao, H. Liu, X. Xu. Networked characteristics of the urban rail transit networks. Physica A: Statistical Mechanics and its Applications392(6) (2013) 1538-1546.
[28] N. Sharav, S. Bekhor, Y. Shiftan. Network Analysis of the Tel Aviv Mass Transit Plan. Urban Rail Transit4(1) (2018) 23-34.
[29] J. Mahdianpoor, H. Saremi. Analysis of quantitative and economic indicators of housing and forecasting of population structure, housing prices and houses required till 1410 in Tehran, Urban management studies, 9(31) (2017) 37-57 (In Persian).