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.
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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)
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 1–65
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. https://doi.org/10.4230/OASIcs.ATMOS.2009.2148
Brodal GS, Jacob R (2004) Time-dependent networks as models to achieve fast exact time-table queries. Electron Notes Theor Comput Sci 92:3–15
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 80–107
Cooke KL, Halsey E (1966) The shortest route through a network with time-dependent internodal transit times. J Math Anal Appl 14(3):493–498
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 130–140
Dreyfus SE (1969) An appraisal of some shortest path algorithms. Oper Res 17(3):395–412
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 174–230
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 109:692–697
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 1–17
Mandow L, De La Cruz JLP (2010) Multiobjective A* search with consistent heuristics. J ACM 57(5):1–25
Nannicini G, Delling D, Schultes D, Liberti L (2011) Bidirectional A* search on time-dependent road networks. Networks 59(2):240–251
Pyrga E, Schulz F, Wagner D, Zaroliagis C (2008) Efficient models for timetable information in public transportation systems. J Exp Algorithmics 12(2):2.4
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 215–224
Spiess H, Florian M (1989) Optimal strategies: a new assignment model for transit networks. Transp Res Part B 23(2):83–102
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 967–982
Wu Q, Hartley J (2004) Accommodating user preferences in the optimization of public transport travel. Int J Simul 5(3–4):12–25
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:1562–1567
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 36–43
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Fournier, S.M.R., Hülse, E.O. & Pinheiro, É.V. A*-guided heuristic for a multi-objective bus passenger Trip Planning Problem. Public Transp (2019). https://doi.org/10.1007/s12469-019-00204-1
- Trip Planning Problem
- Pareto dominance
- A* algorithm