Skip to main content
SpringerLink
Log in

Ant Colony Optimization and Its Application to the Vehicle Routing Problem with Pickups and Deliveries

  • Chapter
Natural Intelligence for Scheduling, Planning and Packing Problems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 250))

Abstract

Ant Colony Optimization (ACO) is a population-basedmetaheuristic that can be used to find approximate solutions to difficult optimization problems. It was first introduced for solving the Traveling Salesperson Problem. Since then many implementations of ACO have been proposed for a variety of combinatorial optimization problems. In this chapter, ACO is applied to the Vehicle Routing Problem with Pickups and Deliveries (VRPPD). VRPPD determines a set of vehicle routes originating and ending at a single depot and visiting all customers exactly once. The vehicles are not only required to deliver goods but also to pick up some goods from the customers. The objective is to minimize the total distance traversed. The chapter first provides an overview of the ACO approach. Next, VRPPD is described and the related literature is reviewed. Then, an ACO approach for VRPPD is presented. The approach proposes a new visibility function which attempts to capture the “delivery” and “pickup” nature of the problem. The performance of the approach is tested using well-known benchmark problems from the literature.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Altınel, İ.K., Öncan, T.: A new enhancemant of the Clarke and Wright savings heuristic for the capacitated vehicle routing problem. Journal of the Operational Research Society 56, 954–961 (2005)

    Article  MATH  Google Scholar 

  2. Angelelli, E., Mansini, R.: The vehicle routing problem with time windows and simultaneous pick-up and delivery. In: Klose, A., Speranza, M.G., Van Wassenhove, L.N. (eds.) Quantitative approaches to distribution logistics and supply chain management series. Lecture Notes in Economics and Mathematical Systems, vol. 519, pp. 249–267. Springer, Berlin (2002)

    Google Scholar 

  3. Bianchessi, N., Righini, G.: Heuristic algorithms for the vehicle routing problem with simultaneous pick-up and delivery. Computers and Operations Research 34, 578–594 (2007)

    Article  MATH  Google Scholar 

  4. Brandão, J.: A new tabu search algorithm for the vehicle routing problem with backhauls. European Journal of Operational Research 173, 540–555 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bullnheimer, B., Hartl, R.F., Strauss, C.: Applying the ant system to the vehicle routing problem. In: Voss, S., et al. (eds.) Meta-heuristics: Advances and trends in local search paradigms for optimization, pp. 285–296. Kluwer Academic Publishers, Boston (1998)

    Google Scholar 

  6. Bullnheimer, B., Hartl, R.F., Strauss, C.: An improved ant system algorithm for the vehicle routing problem. Annals of Operations Research 89, 319–328 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  7. Casco, D.O., Golden, B.L., Wasil, E.A.: Vehicle routing with backhauls: models, algorithms, and case studies. In: Golden, B.L., Assad, A.A. (eds.) Vehicle routing: Methods and studies, pp. 127–147. Elsevier, Amsterdam (1988)

    Google Scholar 

  8. Chen, J.F., Wu, T.H.: Vehicle routing problem with simultaneous deliveries and pickups. Journal of the Operational Research Society 57, 579–587 (2006)

    Article  MATH  Google Scholar 

  9. Christofides, N., Mingozzi, A., Toth, P.: The vehicle routing problem. In: Christofides, N., et al. (eds.) Combinatorial optimization, pp. 315–338. Wiley, Chichester (1979)

    Google Scholar 

  10. Clarke, G., Wright, W.: Scheduling of vehicles from a central depot to a number of delivery points. Operations Research 12, 568–581 (1964)

    Article  Google Scholar 

  11. Colorni, A., Dorigo, M., Maniezzo, V., Trubian, M.: Ant system for job-shop scheduling. Belgian Journal of Operations Research, Statistics and Computer Science 34, 39–45 (1994)

    MATH  Google Scholar 

  12. Crispim, J., Brandão, J.: Metaheuristics applied to mixed and simultaneous extensions of vehicle routing problems with backhauls. Journal of the Operational Research Society 56, 1296–1302 (2005)

    Article  MATH  Google Scholar 

  13. Dethloff, J.: Vehicle routing and reverse logistics: the vehicle routing problem with simultaneous delivery and pick-up. OR Spektrum 23, 79–96 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  14. Doerner, K.F., Gronalt, M., Hartl, R.F., Reimann, M., Strauss, C., Stummer, M.: SavingsAnts for the vehicle routing problem. In: Cagnoni, S., Gottlieb, J., Hart, E., Middendorf, M., Raidl, G.R. (eds.) EvoWorkshops 2002. LNCS, vol. 2279, pp. 11–20. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  15. Dorigo, M.: Optimization, learning and natural algorithms (in Italian), PhD Thesis, Dipartimento di Elettronica, Politecnico di Milano, Italy (1992)

    Google Scholar 

  16. Dorigo, M.: Ant colony optimization. Scholarpedia 2(3), 1461 (2008)

    MathSciNet  Google Scholar 

  17. Dorigo, M., Gambardella, L.M.: Ant colony system: A cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation 1, 53–66 (1997)

    Article  Google Scholar 

  18. Dorigo, M., Maniezzo, V., Colorni, A.: The ant system: Optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics-Part B 26, 29–41 (1996)

    Article  Google Scholar 

  19. Dorigo, M., Stützle, T.: Ant colony optimization. MIT Press, Cambridge (2004)

    MATH  Google Scholar 

  20. Doyuran, T., Çatay, B.: Two enhanced savings functions for the Clark-Wright algorithm. In: Blecker, T., Kersten, W., Gertz, C. (eds.) Management in logistics networks and nodes: Concepts, technology and applications. Series on Operations and Technology Management, vol. 8, pp. 245–258. Erich Schmidt Verlag, Berlin (2008)

    Google Scholar 

  21. Gambardella, L.M., Dorigo, M.: Ant colony system hybridized with a new local search for the sequential ordering problem. INFORMS Journal on Computing 12, 237–255 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  22. Gambardella, L.M., Taillard, E., Agazzi, G.: MACS-VRPTW: a multiple ant colony system for vehicle routing problems with time windows. In: Corne, D., Dorigo, M., Glover, F. (eds.) New ideas in optimization, pp. 63–76. McGraw-Hill, London (1999)

    Google Scholar 

  23. Goetschalckx, M., Jacobs-Blecha, C.: The vehicle routing problem with backhauls. European Journal of Operational Research 42, 39–51 (1989)

    Article  MathSciNet  Google Scholar 

  24. Golden, B., Baker, A.J., Schaffer, J.: The vehicle routing problem with backhauling: two approaches. In: Hammesfahr, R.D. (ed.) Proceedings of the 21st Annual Meeting of S.E., TIMS, Myrtle Beach, USA, pp. 90–92 (1985)

    Google Scholar 

  25. Halse, K.: Modeling and solving complex vehicle routing problems. PhD Thesis, Department of Mathematical Modeling, Technical University of Denmark (1992)

    Google Scholar 

  26. Min, H.: The multiple vehicle routing problem with simultaneous delivery and pick-up points. Transportation Research 23A, 377–386 (1989)

    Google Scholar 

  27. Montané, F.A.T., Galvão, R.D.: A tabu search algorithm for the vehicle routing problem with simultaneous pick-up and delivery service. Computers and Operations Research 33, 595–619 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  28. Nagy, G., Salhi, S.: Heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries. European Journal of Operational Research 162, 126–141 (2005)

    Article  MATH  Google Scholar 

  29. Paessens, H.: The savings algorithm for the vehicle routing problem. European Journal of Operational Research 34(3), 336–344 (1988)

    Article  MATH  Google Scholar 

  30. Reimann, M., Doerner, K.F., Hartl, R.F.: Insertion based ants for vehicle routing problems with backhauls and time windows. In: Dorigo, M., Di Caro, G.A., Sampels, M. (eds.) Ant Algorithms 2002. LNCS, vol. 2463, pp. 135–148. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  31. Reimann, M., Doerner, K., Hartl, R.F.: Analyzing a unified ant system for the VRP and some of its variants. In: Raidl, G.R., Cagnoni, S., Cardalda, J.J.R., Corne, D.W., Gottlieb, J., Guillot, A., Hart, E., Johnson, C.G., Marchiori, E., Meyer, J.-A., Middendorf, M. (eds.) EvoWorkshops 2003. LNCS, vol. 2611, pp. 300–310. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  32. Ropke, S., Pisinger, D.: A unified heuristic for vehicle routing problems with backhauls. European Journal of Operational Research 171, 750–775 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  33. Salhi, S., Nagy, G.: A cluster insertion heuristic for single and multiple depot vehicle routing problems with backhauling. Journal of the Operational Research Society 50, 1034–1042 (1999)

    Article  MATH  Google Scholar 

  34. Stützle, T., Dorigo, M.: ACO algorithms for the quadratic assignment problem. In: Corne, D., Dorigo, M., Glover, F. (eds.) New ideas in optimization, pp. 33–50. McGraw-Hill, London (1999)

    Google Scholar 

  35. Stützle, T., Hoos, H.H.: The MAX-MIN ant system and local search for the traveling salesman problem. In: Bäck, T., Michalewicz, Z., Yao, X. (eds.) Proceedings of the 1997 IEEE International Conference on Evolutionary Computation (ICEC 1997), pp. 309–314. IEEE Press, Piscataway (1997)

    Chapter  Google Scholar 

  36. Toth, P., Vigo, D.: An exact algorithm for the vehicle routing problem with backhauls. Transportation Science 31, 372–385 (1997)

    Article  MATH  Google Scholar 

  37. Vural, A.V., Çatay, B., Eksioglu, B.: A dual GA approach to capacitated vehicle routing problem with simultaneous pick-up and deliveries. In: Proceedings of the IIE Research Conference (CD-ROM), Atlanta, GA (2005)

    Google Scholar 

  38. Wade, A., Salhi, S.: An ant system algorithm for the vehicle routing problems with backhauls. In: De Sousa, J.P. (ed.) Proceedings of the 4th Metaheuristics International Conference (MIC 2001), Porto, Portugal, pp. 99–203 (2001)

    Google Scholar 

  39. Wade, A., Salhi, S.: An ant system algorithm for the mixed vehicle routing problem with backhauls. In: Resende, M.G., de Sousa, J.P. (eds.) Metaheuristics: Computer decision-making, pp. 699–719. Kluwer, New York (2003)

    Google Scholar 

  40. Wassan, N.A., Wassan, A.H., Nagy, G.: A reactive tabu search algorithm for the vehicle routing problem with simultaneous pickups and deliveries. Journal of Combinatorial Optimization 15, 368–386 (2008)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Engineering and Natural Sciences, Tuzla, Sabanci University, 34956, Istanbul, Turkey

    Bülent Çatay

Authors
  1. Bülent Çatay
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Computing & Design, Swinburne University of Technology (Sarawak Campus), Jalan Simpang Tiga, 93350, Kuching, Sarawak, Malaysia

    Raymond Chiong  & Sandeep Dhakal  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Çatay, B. (2009). Ant Colony Optimization and Its Application to the Vehicle Routing Problem with Pickups and Deliveries. In: Chiong, R., Dhakal, S. (eds) Natural Intelligence for Scheduling, Planning and Packing Problems. Studies in Computational Intelligence, vol 250. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04039-9_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-04039-9_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04038-2

  • Online ISBN: 978-3-642-04039-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation