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A path-based greedy algorithm for multi-objective transit routes design with elastic demand

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Abstract

This paper is concerned with the problem of finding optimal sub-routes from a set of predefined candidate transit routes with the objectives of maximizing transit ridership as well as minimizing operational costs. The main contributions of this paper are: (1) considering transit ridership maximization in a multi-objective bi-level optimization framework; (2) proposing a greedy algorithm for the multi-objective design problem; (3) applying an efficient path-based algorithm to solve the lower level multi-modal traffic assignment problem. Numerical experiments indicate that the proposed algorithm is not only able to approximate the Pareto-optimal solutions with satisfactory accuracy, but also achieves a fast performance even for problems of real-world scale.

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Notes

  1. In a more general setting, several sub-routes may be selected from a candidate route. However, this extension is left for a future study.

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Acknowledgments

The authors would like to thank the editor and two anonymous reviewers for their constructive comments which helped improve this paper. The research is partially funded by the United States National Science Foundation under the award number CMMI-1402911.

Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Tarbiat Modares University, Tehran, Iran

    Amirali Zarrinmehr, Mahmoud Saffarzadeh & Seyedehsan Seyedabrishami

  2. Department of Civil and Environmental Engineering, Northwestern University, Evanston, USA

    Yu Marco Nie

Authors
  1. Amirali Zarrinmehr
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  2. Mahmoud Saffarzadeh
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  3. Seyedehsan Seyedabrishami
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  4. Yu Marco Nie
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Corresponding author

Correspondence to Mahmoud Saffarzadeh.

Appendix

Appendix

1.1 The information of candidate routes in the Chicago Sketch network

Table 4 shows the sequence of transit nodes for each of 55 candidate routes adopted in the Chicago Sketch network.

Table 4 Candidate transit routes used in the Chicago Sketch network
Full size table

1.2 Finding the greedy solutions in the Chicago Sketch network

To illustrate how the algorithm finds 61 greedy solutions in the Chicago Sketch network, as in Table 2 of the paper, Table 5 reports transit links that are removed from the configuration as the algorithm proceeds. For brevity, the following notations are used in this table to show the removed links:

Table 5 The performance of the algorithm in finding 61 greedy solutions in the Chicago Sketch network
Full size table
kB:

The beginning link of the kth sub-route

kE:

The ending link of the kth sub-route

[k]:

All links of the kth sub-route

The removed transit links, in each iteration, are listed in ascending order of their D/L values.

1.3 Configuration of sub-routes for solutions A, B, C, and D

Table 6 reports the configuration associated with four solutions A, B, C, and D, depicted in Fig. 7 of the paper. In this table, we use either k(N 1,N 2) or k(Ø) to show the kth sub-route. The former notation stands for a sub-route starting from node N 1 and ending in node N 2 of the kth sub-route. The latter also means that the kth sub-route is empty.

Table 6 The configuration of sub-routes from four solutions depicted in Fig. 7
Full size table

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Zarrinmehr, A., Saffarzadeh, M., Seyedabrishami, S. et al. A path-based greedy algorithm for multi-objective transit routes design with elastic demand. Public Transp 8, 261–293 (2016). https://doi.org/10.1007/s12469-016-0131-1

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