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Green, Smart and Connected Transportation Systems pp 141–160Cite as

Dynamic Programming Approaches for Solving Shortest Path Problem in Transportation: Comparison and Application

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Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 617))

Abstract

This paper seeks to investigate the performance of two different dynamic programming approaches for shortest path problem of transportation road network in different context, including the Bellman’s dynamic programming approach and the Dijkstra’s algorithm. The procedures to implement the two algorithms are discussed in detail in this study. The application of the Bellman’s approach shows that it is computationally expensive due to a lot of repetitive calculations. In comparison, the Dijkstra’s algorithm can effectively improve the computational efficiency of the backward dynamic programming approach. According to whether the shortest path from the node to the original node has been found, the Dijkstra’s algorithm marked the node with permanent label and temporal label. In each step, it simultaneously updates both the permanent label and temporal label to avoid the repetitive calculations in the backward dynamic programming approach. In addition, we also presented an algorithm using dynamic programming theory to solve the K shortest path problem. The K shortest path algorithm is particular useful to find the possible paths for travelers in real-world. The computational performance of the three approaches in large network is explored. This study will be useful for transportation engineers to choose the approaches to solve the shortest path problem for different needs.

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Acknowledgements and Conflict of Interest Statement

This research is supported by the Natural Science Foundation of Zhejiang province (LQ17E080007), National Natural Science Foundation of China (71501009) and (51408323) and Sponsored by K. C. Wong Magna Fund in Ningbo University. The authors are very grateful to the anonymous reviewers for their valuable suggestions and comments. The author(s) declare(s) that there is no conflict of interest regarding the publication of this paper.

Author information

Authors and Affiliations

  1. Faculty of Maritime and Transportation, Ningbo University, Ningbo, China

    Xuan Li, Xiaofei Ye & Lili Lu

  2. National Traffic Management Engineering & Technology Research Centre Ningbo University Sub-centre, Ningbo, China

    Xuan Li, Xiaofei Ye & Lili Lu

Authors
  1. Xuan Li
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  2. Xiaofei Ye
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  3. Lili Lu
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Corresponding author

Correspondence to Xuan Li .

Editor information

Editors and Affiliations

  1. Beijing Institute of Technology, Beijing, China

    Wuhong Wang

  2. Ulm, Baden-Württemberg, Germany

    Martin Baumann

  3. Beijing Institute of Technology, Beijing, China

    Xiaobei Jiang

Appendix

Appendix

Matlab code for dynamic programming approach and Dijkstra’s algorithm to solving the shortest path problem on Sioux Fall network and Borman network.

figure a
figure b

Matlab code for solving the K shortest path problem

figure c

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Li, X., Ye, X., Lu, L. (2020). Dynamic Programming Approaches for Solving Shortest Path Problem in Transportation: Comparison and Application. In: Wang, W., Baumann, M., Jiang, X. (eds) Green, Smart and Connected Transportation Systems. Lecture Notes in Electrical Engineering, vol 617. Springer, Singapore. https://doi.org/10.1007/978-981-15-0644-4_12

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  • DOI: https://doi.org/10.1007/978-981-15-0644-4_12

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-0643-7

  • Online ISBN: 978-981-15-0644-4

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