Skip to main content
SpringerLink
Log in

Dynamic programming based metaheuristics for the dial-a-ride problem

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

The organization of a specialized transportation system to perform transports for elderly and handicapped people is usually modeled as dial-a-ride problem. Users place transportation requests with specified pickup and delivery locations and times. The requests have to be completed under user inconvenience considerations by a specified fleet of vehicles. In the dial-a-ride problem, the aim is to minimize the total travel times respecting the given time windows, the maximum user ride times, and the vehicle restrictions. This paper introduces a dynamic programming algorithm for the dial-a-ride problem and demonstrates its effective application in (hybrid) metaheuristic approaches. Compared to most of the works presented in literature, this approach does not make use of any (commercial) solver. We present an exact dynamic programming algorithm and a dynamic programming based metaheuristic, which restricts the considered solution space. Then, we propose a hybrid metaheuristic algorithm which integrates the dynamic programming based algorithms into a large neighborhood framework. The algorithms are tested on a given set of benchmark instances from the literature and compared to a state-of-the-art hybrid large neighborhood search approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Bellman, R. (1962). Dynamic programming treatment of the travelling salesman problem. JACM, 9, 61–63.

    Article  Google Scholar 

  • Bent, R., & Hentenryck, P. V. (2006). A two-stage hybrid algorithm for pickup and delivery vehicle routing problems with time windows. Computers & Operations Research, 33(4), 875–893.

    Article  Google Scholar 

  • Blum, C., Puchinger, J., Raidl, G. R., & Roli, A. (2011). Hybrid metaheuristics in combinatorial optimization: A survey. Applied Soft Computing, 11(6), 4135–4151.

    Article  Google Scholar 

  • Bräysy, O., & Gendreau, M. (2005). Vehicle routing problem with time windows, part II: Metaheuristics. Transportation Science, 39(1), 119–139.

    Article  Google Scholar 

  • Cordeau, J. F., & Laporte, G. (2003). A tabu search heuristic for the static multi-vehicle dial-a-ride problem. Transportation Research Part B: Methodological, 37(6), 579–594.

    Article  Google Scholar 

  • Cordeau, J. F., & Laporte, G. (2007). The dial-a-ride problem: Models and algorithms. Annals of Operations Research, 153, 29–46.

    Article  Google Scholar 

  • Dumas, Y., Desrosiers, J., Gelinas, E., & Solomon, M. M. (1995). An optimal algorithm for the traveling salesman problem with time windows. Operations Research, 43(2), 367–371.

    Article  Google Scholar 

  • Funke, B., Grünert, T., & Irnich, S. (2005). Local search for vehicle routing and scheduling problems: Review and conceptual integration. Journal of Heuristics, 11, 267–306.

    Article  Google Scholar 

  • Gendreau, M., Potvin, J. Y., Brumlaysy, O., Hasle, G., & Løkketangen, A. (2008). Metaheuristics for the vehicle routing problem and its extensions: A categorized bibliography. In B. Golden, S. Raghavan, & E. Wasil (Eds.), The vehicle routing problem: latest advances and new challenges, operations research/computer science interfaces series (Vol. 43, pp. 143–169). New York: Springer.

    Chapter  Google Scholar 

  • Gromicho, J. A. S., van Hoorn, J. J., Kok, A. L., & Schutten, J. M. J. (2012). Restricted dynamic programming: A flexible framework for solving realistic VRPs. Computers & OR, 39(5), 902–909.

    Article  Google Scholar 

  • Gschwind, T., & Irnich, S. (2012). Effective handling of dynamic time windows and synchronization with precedences for exact vehicle routing. Mainz: Chair of Logistics Management, Johannes Gutenberg University Mainz. (Technical Report LM-2012-05).

  • Held, M., & Karp, R. M. (1961). A dynamic programming approach to sequencing problems. In: Proceedings of the 1961 16th ACM national meeting, ACM ’61 (pp. 71.201–71.204). New York: ACM.

  • Malandraki, C., & Dial, R. B. (1996). A restricted dynamic programming heuristic algorithm for the time dependent traveling salesman problem. European Journal of Operational Research, 90(1), 45–55.

    Article  Google Scholar 

  • Maniezzo, V., Stützle, T., & Voß, S. (2009). Matheuristics: Hybridizing metaheuristics and mathematical programming (1st ed.). Heidelberg: Springer.

    Google Scholar 

  • Norvig, P. (1992). Paradigms of artificial intelligence programming: Case studies in common lisp (1st ed.). San Francisco: Morgan Kaufmann Publishers Inc.

    Google Scholar 

  • Parragh, S. N., & Schmid, V. (2013). Hybrid column generation and large neighborhood search for the dial-a-ride problem. Computers & Operations Research, 40(1), 490–497.

    Article  Google Scholar 

  • Parragh, S. N., Doerner, K. F., & Hartl, R. F. (2008). A survey on pickup and delivery problems. Part II. Journal für Betriebswirtschaft, 58, 81–117.

    Article  Google Scholar 

  • Parragh, S. N., Doerner, K. F., & Hartl, R. F. (2010a). Demand responsive transportation. In J. J. Cochran, L. A. Cox, P. Keskinocak, J. P. Kharoufeh, & J. C. Smith (Eds.), Wiley encyclopaedia of operations research and management science. Hoboken, NJ: Wiley.

    Google Scholar 

  • Parragh, S. N., Doerner, K. F., & Hartl, R. F. (2010b). Variable neighborhood search for the dial-a-ride problem. Computers and Operations Research, 37, 1129–1138.

    Article  Google Scholar 

  • Pisinger, D., & Ropke, S. (2010). Large neighborhood search. In M. Gendreau & J. Y. Potvin (Eds.), Handbook of metaheuristics. International series in operations research & management science (Vol. 146, pp. 399–419). New York: Springer.

    Google Scholar 

  • Psaraftis, H. N. (1980). A dynamic programming solution to the single vehicle many-to-many immediate request dial-a-ride problem. Transportation Science, 14(2), 130–154.

    Article  Google Scholar 

  • Ritzinger, U., & Puchinger, J. (2013). Hybrid metaheuristics for dynamic and stochastic vehicle routing. In E. G. Talbi (Ed.), Hybrid metaheuristics. Studies in computational intelligence (Vol. 434, pp. 77–95). Berlin: Springer.

  • Ropke, S., & Pisinger, D. (2006). An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows. Transportation Science, 40(4), 455–472.

    Article  Google Scholar 

  • Ropke, S., Cordeau, J. F., & Laporte, G. (2007). Models and branch-and-cut algorithms for pickup and delivery problems with time windows. Networks, 49(4), 258–272.

    Article  Google Scholar 

  • Schilde, M., Doerner, K. F., & Hartl, R. F. (2011). Metaheuristics for the dynamic stochastic dial-a-ride problem with expected return transports. Computers & Operations Research, 38(12), 1719–1730.

    Article  Google Scholar 

  • Shaw, P. (1998). Using constraint programming and local search methods to solve vehicle routing problems. In M. Maher & J. F. Puget (Eds.), Principles and practice of constraint programming CP98. Lecture notes in computer science (Vol. 1520, pp. 417–431). Berlin: Springer.

    Chapter  Google Scholar 

  • Talbi, E. G. (2013). Hybrid metaheuristics. Studies in computational intelligence (Vol. 434). Berlin: Springer.

    Book  Google Scholar 

  • Toth, P., & Vigo, D. (2001). The vehicle routing problem. Philadelphia, PA: Society for Industrial and Applied Mathematics.

    Google Scholar 

Download references

Acknowledgments

We would like to thank the anonymous referees for their invaluable remarks, helping to improve our paper. We would also like to thank Gerhard Hiermann for many insightful discussions. This work was partially funded by the Austrian Federal Ministry for Transport, Innovation and Technology (BMVIT) within the strategic program FIT-IT ModSim under Grant 822739 (Project HealthLog).

Author information

Authors and Affiliations

  1. Mobility Department, AIT Austrian Institute of Technology GmbH, Giefinggasse 2, 1210 , Vienna, Austria

    Ulrike Ritzinger & Jakob Puchinger

  2. Department of Business Administration, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 , Vienna, Austria

    Richard F. Hartl

Authors
  1. Ulrike Ritzinger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jakob Puchinger
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Richard F. Hartl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ulrike Ritzinger.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ritzinger, U., Puchinger, J. & Hartl, R.F. Dynamic programming based metaheuristics for the dial-a-ride problem. Ann Oper Res 236, 341–358 (2016). https://doi.org/10.1007/s10479-014-1605-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-014-1605-7

Keywords

Search

Navigation