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An Ant System application to the Bus Network Design Problem: an algorithm and a case study

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Abstract

Bus system design is a difficult problem, and hence is usually decomposed into a series of sub-problems solved sequentially. Bus network design is foremost in this series of problems. The bus network design problem in this study is the problem of choosing a subset of interconnected bus routes from among a given set of such routes, which minimizes the total travel time of the users of the network, while being feasible in fleet requirements. The Ant System concept has been exploited to solve this problem. The algorithm has been applied to the problem and calibrated based on the network of Sioux Falls. For this purpose, several fleet assignment routines have been tested, some sensitivity analyses are made to estimate suitable parameter values, and alternative ways of laying pheromone on bus routes have been examined.

Experiments are conducted to investigate the performance of the solution algorithm when the number of routes, or bus fleet size, increases. Moreover, other experiments help to determine the number of algorithmic iterations. These experiments prepared the algorithm to be applied to design the bus network of the City of Mashhad, with a population of over 2 million. The results have been compared with those of another solution to the same problem, obtained by another meta-heuristic, namely a Genetic Algorithm.

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References

  • Aashtiani HZ, Poorzahedy H, Kermanshah M, Tabatabaee N (1997) Bus systems for the City of Mashhad. Mashhad comprehensive transportation studies. Report No. 76-12, The Institute for Transportation Studies and Research, Sharif Univ. of Technology, Tehran, Iran (in Farsi)

  • Baaj MH, Mahmassani HS (1991) An AI-based approach for transit route systems planning and design. J Adv Transp 25(2):187–210

    Google Scholar 

  • Bansal AN (1981) Optimization of bus route network for a fixed spatial distribution. In: Jaiswal NK (ed) Scientific management of transport systems. North-Holland, Amsterdam

    Google Scholar 

  • Borndorfer R, Grotschel M, Pfetsch M (2007) A column generation approach to line planning in public transport. Transp Sci 41(1):123–132

    Article  Google Scholar 

  • Byrne B (1976) Cost minimizing positions, lengths and headways for parallel public transit lines having different speeds. Transp Res 10:209–214

    Article  Google Scholar 

  • Ceder A, Wilson HM (1986) Bus network design. Transp Res 20B(4):331–344

    Article  Google Scholar 

  • Dorigo M, Stützle T (2005) Ant colony optimization. Prentice-Hall of India, New Delhi. (Also, MIT Press, 2004)

    Google Scholar 

  • Dubios D, Bell G, Libre M (1979) A set of methods in transportation network synthesis and analysis. J Oper Res Soc 30:797–808

    Google Scholar 

  • Dufourd H, Gendreau M, Laporte G (1996) Locating a transit line using tabu search. Location Sci 4(1–2):1–19

    Article  Google Scholar 

  • Fan W, Machemehl RB (2004) Optimal transit route network design problem: algorithms, implementations, and numerical results. Center for Transportation Research, University of Texas at Austin

  • Gwo-Hshiung T, An Shiau T (1988) Multiple objective programming for bus operation: a case study for Taipei city. Transp Res, Part B, Methodol 22(3):195–206

    Article  Google Scholar 

  • Hsselstrom D (1981) Public transportation planning: a mathematical programming approach. Dissertation, Department of Business Administration, University of Gothenburg, Sweden

  • Hurdle G (1973) Minimum cost location for parallel public transportation lines. Transp Sci 7:90–172

    Google Scholar 

  • INRO consultants Inc (1989–1999) EMME/2 user’s manual. Montréal, Canada. Chapter 4, pp 349–351

  • Israeli Y, Ceder A (1995) Transit route design using scheduling and multi-objective programming techniques. In: Daduna J, Branco I, Paixao JP (eds) Computer-aided transit scheduling: proceedings of the sixth international work-shop on computer-aided scheduling of public transport. Lecture notes in economics and mathematical systems. Springer, Berlin, pp 56–57

    Google Scholar 

  • Jiang H, Yu Q, Huang Y (2010) An improved Ant Colony algorithm for urban transit network optimization. In: Sixth international conference on natural computation, vol 5, pp 2739–2743. ISBN:978-1-4244-5958-2. doi:10.1109/ICNC.2010.582661

    Chapter  Google Scholar 

  • Kocur G, Hendrickson C (1982) Design of local bus service with demand equilibrium. Transp Sci 16:149–170

    Article  Google Scholar 

  • Lampkin W, Saalman PD (1978) The design of routes service frequencies and schedules for municipal bus undertaking: a case study. Oper Res Q 18:375–397

    Article  Google Scholar 

  • LeBlanc LJ (1975) An algorithm for discrete network design problem. Transp Sci 9:183–199

    Article  Google Scholar 

  • LeBlanc LJ (1988) Transit system network design. Transp Res, Part B, Methodol 22(5):383–390

    Article  Google Scholar 

  • Lee YJ, Vuchic VR (2000) Transit network design with variable demand. In: 79th annual meeting of TRB, Washington, DC

    Google Scholar 

  • Lines AH, Lampkin W, Saalman PD (1966) The design of routes and service frequency for a municipal bus company. Business Operation Research Ltd., London

    Google Scholar 

  • Mandl CE (1980) Evaluation and optimization of urban public transport networks. Eur J Oper Res 6:31–56

    Google Scholar 

  • Martins CL, Pato MV (1998) Search strategies for the feeder bus network design problem. Eur J Oper Res 106(2–3):425–440

    Article  Google Scholar 

  • Mauttone A, Urquhart ME (2009) A multi-objective metaheuristic approach for the transit network design problem. Public Transp 1(4):253–273

    Article  Google Scholar 

  • Newell G (1979) Some issues relating to the optimal design of bus routes. Transp Sci 13:20–35

    Article  Google Scholar 

  • Ngamchai S, Lovell DJ (2003) Optimal time transfer in bus transit route network design using a genetic algorithm. Journal of Transportation Engineering, ASCE, pp 510–521

  • Pattnaik SB, Mohan S, Tom VM (1998) Urban bus transit network design using genetic algorithm. J Transp Eng 124(4):368–375

    Article  Google Scholar 

  • Poorzahedy H, Abulghasemi F (2005) Application of ant system to network design problem. Transportation 32:251–273

    Article  Google Scholar 

  • Poorzahedy H, Rouhani OM (2007) Hybrid meta-heuristic algorithms for solving network design problem. Eur J Oper Res 182:578–596

    Article  Google Scholar 

  • Rea JC (1971) Designing urban transit system: an approach to the route technology selection problem. PB 204, University of Washington, Seattle, WA

  • Sadrossadat H (2003) Bus network design using Genetic Algorithm: Case of Mashhad. MSc Thesis, Dept. of CE, Sharif, University of Technology (in Farsi)

  • Schöbel A, Scholl S (2005) Line planning with minimal traveling time. In: Kroon LG, Möhring RH (eds) Fifth workshop on algorithmic methods and models for optimization of railways

    Google Scholar 

  • Sheffi Y (1985) Urban transportation network: equilibrium analysis with mathematical programming methods. Prentice-Hall, New York

    Google Scholar 

  • Shih MC, Mahmassani HS (1994) A vehicle sizing model for bus transit systems. Presented at the 73rd annual meeting of the Transportation Research Board, Washington, DC

  • Silman LA, Barazily Z, Passy U (1974) Planning the route system for urban buses. Oper Res 1:201–211

    Google Scholar 

  • Spiess H, Florian M (1989) Optimal strategies: A new assignment model for transit networks. Transp Res, Part B, Methodol 23B(2):83–102

    Article  Google Scholar 

  • Tom VM, Mohan S (2003) Transit route network design using frequency coded genetic algorithm. J Transp Eng 186–195

  • Van Nes R, Hamerslag R, Immer BH (1988) The design of public transport networks. Transportation Research Record 1202, Transportation Research Board, Washington, DC, pp 74–83

  • Yang Z, Yu B, Cheng C (2007) A parallel Ant Colony algorithm for Bus Network Optimization. Comput-Aided Civ Infrastruct Eng 22(1):44–55

    Article  Google Scholar 

  • Zhao F, Ubaka I (2004) Transit network optimization, minimizing transfers and optimizing route directness. J Public Transp 7(1):63–82

    Google Scholar 

  • Zhao F, Zeng X (2008) Optimization of transit route network, vehicle headways and timetables for large scale transit networks. Eur J Oper Res 186:841–855

    Article  Google Scholar 

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Acknowledgements

The authors would like to thank the Institute for Transportation Studies and Research of Sharif University of Technology, for the financial as well as informational support of this study. They also appreciate the highly careful remarks and recommendations made by the anonymous referees, which enhanced the presentation of the paper significantly.

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Authors and Affiliations

  1. The Institute for Transportation Studies and Research, Sharif Univ. of Technology, Tehran, Iran

    Hossain Poorzahedy & Farshid Safari

  2. Dept. of Civil Eng., Sharif Univ. of Technology, Tehran, Iran

    Hossain Poorzahedy & Farshid Safari

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  1. Hossain Poorzahedy
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  2. Farshid Safari
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Correspondence to Hossain Poorzahedy.

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Poorzahedy, H., Safari, F. An Ant System application to the Bus Network Design Problem: an algorithm and a case study. Public Transp 3, 165–187 (2011). https://doi.org/10.1007/s12469-011-0046-9

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