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A Heuristic Search Approach for a Nonstationary Stochastic Shortest Path Problem with Terminal Cost

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  • James L. Bander

    (Industrial Engineering and Operations Research, Norfolk Southern Corporation, 600 West Peachtree Street NW, Suite 900, Atlanta, Georgia 30308)

  • Chelsea C. White

    (Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

Abstract

We present a best-first heuristic search approach for determining an optimal policy for a stochastic shortest path problem. A vehicle is to travel from an origin, starting at time t 0 , to a destination, where once the destination is reached a terminal cost is accrued. The terminal cost depends on the time of arrival. Travel time along each arc in the network is modeled as a random variable with a distribution dependent on the time that travel along the arc is begun. The objective is to determine a routing policy that minimizes expected total cost. A routing policy is a rule that assigns the next arc to traverse, given the current node and time.The heuristic search algorithm that we specialize to this stochastic problem is AO * . We demonstrate the significant computational advantages of AO * , relative to dynamic programming, on the basis of run time and storage, using a 131-intersection network of the major roads in Cleveland, Ohio. Further computational experience is based on grid networks that were randomly generated to have characteristics similar to transportation networks, and on randomly generated unstructured networks.

Suggested Citation

  • James L. Bander & Chelsea C. White, 2002. "A Heuristic Search Approach for a Nonstationary Stochastic Shortest Path Problem with Terminal Cost," Transportation Science, INFORMS, vol. 36(2), pages 218-230, May.
    • Handle: RePEc:inm:ortrsc:v:36:y:2002:i:2:p:218-230
    DOI: 10.1287/trsc.36.2.218.562
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    References listed on IDEAS

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    1. Dimitri P. Bertsekas & John N. Tsitsiklis, 1991. "An Analysis of Stochastic Shortest Path Problems," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 580-595, August.
    2. H. Frank, 1969. "Shortest Paths in Probabilistic Graphs," Operations Research, INFORMS, vol. 17(4), pages 583-599, August.
    3. Randolph W. Hall, 1986. "The Fastest Path through a Network with Random Time-Dependent Travel Times," Transportation Science, INFORMS, vol. 20(3), pages 182-188, August.
    4. Amir Eiger & Pitu B. Mirchandani & Hossein Soroush, 1985. "Path Preferences and Optimal Paths in Probabilistic Networks," Transportation Science, INFORMS, vol. 19(1), pages 75-84, February.
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    Cited by:

    1. N Shi & R K Cheung & H Xu & K K Lai, 2011. "An adaptive routing strategy for freight transportation networks," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 799-805, April.
    2. Gao, Song & Chabini, Ismail, 2006. "Optimal routing policy problems in stochastic time-dependent networks," Transportation Research Part B: Methodological, Elsevier, vol. 40(2), pages 93-122, February.
    3. Thomas, Barrett W. & White III, Chelsea C., 2007. "The dynamic shortest path problem with anticipation," European Journal of Operational Research, Elsevier, vol. 176(2), pages 836-854, January.
    4. Häme, Lauri & Hakula, Harri, 2013. "Dynamic journeying under uncertainty," European Journal of Operational Research, Elsevier, vol. 225(3), pages 455-471.
    5. Azadian, Farshid & Murat, Alper E. & Chinnam, Ratna Babu, 2012. "Dynamic routing of time-sensitive air cargo using real-time information," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(1), pages 355-372.
    6. Levering, Nikki & Boon, Marko & Mandjes, Michel & Núñez-Queija, Rudesindo, 2022. "A framework for efficient dynamic routing under stochastically varying conditions," Transportation Research Part B: Methodological, Elsevier, vol. 160(C), pages 97-124.
    7. Vural Aksakalli & O. Furkan Sahin & Ibrahim Ari, 2016. "An AO* Based Exact Algorithm for the Canadian Traveler Problem," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 96-111, February.

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