A*-guided heuristic for a multi-objective bus passenger Trip Planning Problem

  • Sylvain M. R. FournierEmail author
  • Eduardo Otte Hülse
  • Éder Vasco Pinheiro
Original Paper


The Bus Passenger Trip Planning Problem is the decision problem the bus passenger faces when he has to move around the city using the bus network: how and when can he reach his destination? Or possibly: given a fixed time to get to the destination, what should be his departure time? We show that both questions are computationally equivalent and can be answered using an A*-guided and Pareto dominance-based heuristic. The A* procedure drives the search estimating the arrival time at the target node, even in intermediate nodes. Dominance is triggered each time a new label is generated, in order to prune out labels defining subpaths with high values for the objectives we focus on: arrival time at destination, number of transfers and total walking distance. We discuss the tradeoff between processing time and solution quality through a parameter called A* speed. The tool is available for transit users on a day-to-day basis in Brazilian cities of up to 800,000 inhabitants and returns a variety of solutions within a couple of seconds.


Trip Planning Problem Pareto dominance A* algorithm 



  1. Attanasi A, De Cristofaro S, Meschini L, Gentile G (2013) Hyperpath journey planner: a dynamic shortest pathfinder for multimodal transportation networks. In: Proceedings of the 26th European Conference on Operational Research (EURO INFORM 2013, Rome, Italy)Google Scholar
  2. Bast H, Delling D, Goldberg A, Müller-Hannemann M, Pajor T, Sanders P, Wagner D, Werneck RF (2015) Route planning in transportation networks. Microsoft Research Technical Report, Redmond, pp 1–65Google Scholar
  3. Berger A, Delling D, Gebhardt A, Müller-Hannemann M (2009) Accelerating Time-Dependent Multi-Criteria Timetable Information is Harder Than Expected. In: Clausen J, Stefano GD (eds) 9th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS’09), Schloss Dagstuhl–Leibniz-Zentrum für Informatik, Dagstuhl, Germany, vol 12.
  4. Brodal GS, Jacob R (2004) Time-dependent networks as models to achieve fast exact time-table queries. Electron Notes Theor Comput Sci 92:3–15CrossRefGoogle Scholar
  5. Comi A, Nuzzolo A, Crisalli U, Rosati L (2017) A new generation of individual real-time transit information systems. In: Lam WHK (ed) Modelling intelligent multi-modal transit systems. CRC Press, Boca Raton, pp 80–107Google Scholar
  6. Cooke KL, Halsey E (1966) The shortest route through a network with time-dependent internodal transit times. J Math Anal Appl 14(3):493–498CrossRefGoogle Scholar
  7. Delling D, Pajor T, Werneck RF (2012) Round-Based Public Transit Routing. In: Proceedings of the 14th meeting on algorithm engineering and experiments (ALENEX’12) pp 130–140Google Scholar
  8. Dreyfus SE (1969) An appraisal of some shortest path algorithms. Oper Res 17(3):395–412CrossRefGoogle Scholar
  9. Gentile G (2017) Time-dependent shortest hyperpaths for dynamic routing on transit networks. In: Nuzzolo A, Lam WHK (eds) Modelling intelligent multi-modal transit systems. CRC Press, Boca Raton, pp 174–230Google Scholar
  10. Idri A, Oukarfi M, Boulmakoul A, Zeitouni K, Masri A (2017) A new time-dependent shortest path algorithm for multimodal transportation network. Proc Comput Sci 109:692–697CrossRefGoogle Scholar
  11. Jariyasunant J, Work DB, Kerkez B, Sengupta R, Bayen AM, Glaser S (2010) Mobile transit trip planning with real-time data. In: Transportation research board 89th annual meeting (September). pp 1–17Google Scholar
  12. Mandow L, De La Cruz JLP (2010) Multiobjective A* search with consistent heuristics. J ACM 57(5):1–25CrossRefGoogle Scholar
  13. Nannicini G, Delling D, Schultes D, Liberti L (2011) Bidirectional A* search on time-dependent road networks. Networks 59(2):240–251CrossRefGoogle Scholar
  14. Pyrga E, Schulz F, Wagner D, Zaroliagis C (2008) Efficient models for timetable information in public transportation systems. J Exp Algorithmics 12(2):2.4Google Scholar
  15. Sanders P, Mandow L (2013) Parallel label-setting multi-objective shortest path search. In: Proceedings—IEEE 27th international parallel and distributed processing symposium. IPDPS, pp 215–224Google Scholar
  16. Spiess H, Florian M (1989) Optimal strategies: a new assignment model for transit networks. Transp Res Part B 23(2):83–102CrossRefGoogle Scholar
  17. Wang S, Lin W, Yang Y, Xiao X, Zhou S (2015) Efficient route planning on public transportation networks. In: Proceedings of the 2015 ACM SIGMOD international conference on management of data—SIGMOD ’15 pp 967–982Google Scholar
  18. Wu Q, Hartley J (2004) Accommodating user preferences in the optimization of public transport travel. Int J Simul 5(3–4):12–25Google Scholar
  19. Yang Y, Wang S, Hu X, Li J, Xu B (2012) A modified K-shortest paths algorithm for solving the earliest arrival problem on the time-dependent model of transportation systems. In: Proceedings of the international multiconference of engineers and computer scientists II:1562–1567Google Scholar
  20. Zhao L, Ohshima T, Nagamochi H (2008) A* algorithm for the time-dependent shortest path problem. In: The 11th Japan-Korea joint workshop on algorithms and computation (WAAC08) pp 36–43Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.WPLEX Software Ltda.FlorianópolisBrazil

Personalised recommendations