IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v265y2018i3p843-859.html
   My bibliography  Save this article

A simulated annealing algorithm for the capacitated vehicle routing problem with two-dimensional loading constraints

Author

Listed:
  • Wei, Lijun
  • Zhang, Zhenzhen
  • Zhang, Defu
  • Leung, Stephen C.H.

Abstract

This paper studies the well-known capacitated vehicle routing problem with two-dimensional loading constraints (2L-CVRP). It requires designing a set of min-cost routes, starting and terminating at the central depot, to satisfy customer demands which involve a set of two-dimensional, rectangular, weighted items. A simulated annealing algorithm with a mechanism of repeatedly cooling and rising the temperature is proposed to solve the four versions of this problem, with or without the LIFO constraint, and allowing rotation of goods or not. An open space based heuristic is employed to identify the feasible loading patterns. In addition, the data structure Trie is used to accelerate the procedure by keeping track of the packing feasibility information of routes examined, and also by controlling the effort spent on different routes. The proposed algorithm is tested on the widely used instances of 2L-CVRP. The results show that our approach outperforms all existing algorithms on the four problem versions, and reaches or improves the best-known solutions for most instances. Furthermore, we compared the impact of different loading constraints, and observed some interesting results.

Suggested Citation

  • Wei, Lijun & Zhang, Zhenzhen & Zhang, Defu & Leung, Stephen C.H., 2018. "A simulated annealing algorithm for the capacitated vehicle routing problem with two-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 265(3), pages 843-859.
    • Handle: RePEc:eee:ejores:v:265:y:2018:i:3:p:843-859
    DOI: 10.1016/j.ejor.2017.08.035
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037722171730766X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2017.08.035?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Stefan Ropke & David Pisinger, 2006. "An Adaptive Large Neighborhood Search Heuristic for the Pickup and Delivery Problem with Time Windows," Transportation Science, INFORMS, vol. 40(4), pages 455-472, November.
    2. G. B. Dantzig & J. H. Ramser, 1959. "The Truck Dispatching Problem," Management Science, INFORMS, vol. 6(1), pages 80-91, October.
    3. Fuellerer, Guenther & Doerner, Karl F. & Hartl, Richard F. & Iori, Manuel, 2010. "Metaheuristics for vehicle routing problems with three-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 201(3), pages 751-759, March.
    4. Michel Gendreau & Manuel Iori & Gilbert Laporte & Silvano Martello, 2006. "A Tabu Search Algorithm for a Routing and Container Loading Problem," Transportation Science, INFORMS, vol. 40(3), pages 342-350, August.
    5. Wei, Lijun & Oon, Wee-Chong & Zhu, Wenbin & Lim, Andrew, 2013. "A goal-driven approach to the 2D bin packing and variable-sized bin packing problems," European Journal of Operational Research, Elsevier, vol. 224(1), pages 110-121.
    6. Defu Zhang & Lijun Wei & Stephen C. H. Leung & Qingshan Chen, 2013. "A Binary Search Heuristic Algorithm Based on Randomized Local Search for the Rectangular Strip-Packing Problem," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 332-345, May.
    7. Oscar Dominguez & Angel Juan & Barry Barrios & Javier Faulin & Alba Agustin, 2016. "Using biased randomization for solving the two-dimensional loading vehicle routing problem with heterogeneous fleet," Annals of Operations Research, Springer, vol. 236(2), pages 383-404, January.
    8. José Oliveira, 2010. "Comments on: Routing problems with loading constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 31-33, July.
    9. Manuel Iori & Juan-José Salazar-González & Daniele Vigo, 2007. "An Exact Approach for the Vehicle Routing Problem with Two-Dimensional Loading Constraints," Transportation Science, INFORMS, vol. 41(2), pages 253-264, May.
    10. Oscar Dominguez & Angel A. Juan & Barry Barrios & Javier Faulin & Alba Agustin, 2016. "Using biased randomization for solving the two-dimensional loading vehicle routing problem with heterogeneous fleet," Annals of Operations Research, Springer, vol. 236(2), pages 383-404, January.
    11. G. Clarke & J. W. Wright, 1964. "Scheduling of Vehicles from a Central Depot to a Number of Delivery Points," Operations Research, INFORMS, vol. 12(4), pages 568-581, August.
    12. Zachariadis, Emmanouil E. & Tarantilis, Christos D. & Kiranoudis, Christos T., 2009. "A Guided Tabu Search for the Vehicle Routing Problem with two-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 195(3), pages 729-743, June.
    13. Manuel Iori & Silvano Martello, 2010. "Routing problems with loading constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 4-27, July.
    14. Leung, Stephen C.H. & Zhang, Zhenzhen & Zhang, Defu & Hua, Xian & Lim, Ming K., 2013. "A meta-heuristic algorithm for heterogeneous fleet vehicle routing problems with two-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 225(2), pages 199-210.
    15. Manuel Iori & Silvano Martello, 2010. "Rejoinder on: Routing problems with loading constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 41-42, July.
    16. Zachariadis, Emmanouil E. & Tarantilis, Christos D. & Kiranoudis, Chris T., 2013. "Integrated distribution and loading planning via a compact metaheuristic algorithm," European Journal of Operational Research, Elsevier, vol. 228(1), pages 56-71.
    17. Zhang, Zhenzhen & Wei, Lijun & Lim, Andrew, 2015. "An evolutionary local search for the capacitated vehicle routing problem minimizing fuel consumption under three-dimensional loading constraints," Transportation Research Part B: Methodological, Elsevier, vol. 82(C), pages 20-35.
    18. Van Breedam, Alex, 1995. "Improvement heuristics for the Vehicle Routing Problem based on simulated annealing," European Journal of Operational Research, Elsevier, vol. 86(3), pages 480-490, November.
    19. Wei, Lijun & Zhang, Zhenzhen & Zhang, Defu & Lim, Andrew, 2015. "A variable neighborhood search for the capacitated vehicle routing problem with two-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 243(3), pages 798-814.
    20. Silvano Martello & Daniele Vigo, 1998. "Exact Solution of the Two-Dimensional Finite Bin Packing Problem," Management Science, INFORMS, vol. 44(3), pages 388-399, March.
    21. Renaud Masson & Fabien Lehuédé & Olivier Péton, 2013. "An Adaptive Large Neighborhood Search for the Pickup and Delivery Problem with Transfers," Transportation Science, INFORMS, vol. 47(3), pages 344-355, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alonso, M.T. & Martinez-Sykora, A. & Alvarez-Valdes, R. & Parreño, F., 2022. "The pallet-loading vehicle routing problem with stability constraints," European Journal of Operational Research, Elsevier, vol. 302(3), pages 860-873.
    2. Xiang Song & Dylan Jones & Nasrin Asgari & Tim Pigden, 2020. "Multi-objective vehicle routing and loading with time window constraints: a real-life application," Annals of Operations Research, Springer, vol. 291(1), pages 799-825, August.
    3. Chang, Ximing & Wu, Jianjun & Correia, Gonçalo Homem de Almeida & Sun, Huijun & Feng, Ziyan, 2022. "A cooperative strategy for optimizing vehicle relocations and staff movements in cities where several carsharing companies operate simultaneously," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 161(C).
    4. Yaoting Huang & Boyu Chen & Wenlian Lu & Zhong-Xiao Jin & Ren Zheng, 2022. "Asynchronous optimization of part logistics routing problem," Journal of Global Optimization, Springer, vol. 82(4), pages 803-834, April.
    5. Amine Masmoudi, M. & Mancini, Simona & Baldacci, Roberto & Kuo, Yong-Hong, 2022. "Vehicle routing problems with drones equipped with multi-package payload compartments," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 164(C).
    6. Yan, Xiaoyuan & Xu, Min & Xie, Chi, 2023. "Local container drayage problem with improved truck platooning operations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 169(C).
    7. Eren Atsiz & Burcu Balcik & Dilek Gunnec & Busra Uydasoglu Sevindik, 2022. "A coordinated repair routing problem for post-disaster recovery of interdependent infrastructure networks," Annals of Operations Research, Springer, vol. 319(1), pages 41-71, December.
    8. Qiuping Ni & Yuanxiang Tang, 2023. "A Bibliometric Visualized Analysis and Classification of Vehicle Routing Problem Research," Sustainability, MDPI, vol. 15(9), pages 1-37, April.
    9. Zheng Zhang & Bin Ji & Samson S. Yu, 2023. "An Adaptive Tabu Search Algorithm for Solving the Two-Dimensional Loading Constrained Vehicle Routing Problem with Stochastic Customers," Sustainability, MDPI, vol. 15(2), pages 1-23, January.
    10. Moshref-Javadi, Mohammad & Lee, Seokcheon & Winkenbach, Matthias, 2020. "Design and evaluation of a multi-trip delivery model with truck and drones," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 136(C).
    11. Ji, Chenlu & Mandania, Rupal & Liu, Jiyin & Liret, Anne, 2022. "Scheduling on-site service deliveries to minimise the risk of missing appointment times," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).
    12. Zhang, Xiangyi & Chen, Lu & Gendreau, Michel & Langevin, André, 2022. "A branch-and-cut algorithm for the vehicle routing problem with two-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 302(1), pages 259-269.
    13. Shaojun Lu & Jun Pei & Xinbao Liu & Panos M. Pardalos, 2020. "Robust parallel-batching scheduling with fuzzy deteriorating processing time and variable delivery time in smart manufacturing," Fuzzy Optimization and Decision Making, Springer, vol. 19(3), pages 333-357, September.
    14. Chang, Ximing & Wu, Jianjun & Sun, Huijun & Correia, Gonçalo Homem de Almeida & Chen, Jianhua, 2021. "Relocating operational and damaged bikes in free-floating systems: A data-driven modeling framework for level of service enhancement," Transportation Research Part A: Policy and Practice, Elsevier, vol. 153(C), pages 235-260.
    15. Peng Xu & Qixing Liu & Yuhu Wu, 2023. "Energy Saving-Oriented Multi-Depot Vehicle Routing Problem with Time Windows in Disaster Relief," Energies, MDPI, vol. 16(4), pages 1-15, February.
    16. Vincent F. Yu & Winarno & Achmad Maulidin & A. A. N. Perwira Redi & Shih-Wei Lin & Chao-Lung Yang, 2021. "Simulated Annealing with Restart Strategy for the Path Cover Problem with Time Windows," Mathematics, MDPI, vol. 9(14), pages 1-22, July.
    17. Yongji Jia & Wang Zeng & Yanting Xing & Dong Yang & Jia Li, 2020. "The Bike-Sharing Rebalancing Problem Considering Multi-Energy Mixed Fleets and Traffic Restrictions," Sustainability, MDPI, vol. 13(1), pages 1-15, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Carlos A. Vega-Mejía & Jairo R. Montoya-Torres & Sardar M. N. Islam, 2019. "Consideration of triple bottom line objectives for sustainability in the optimization of vehicle routing and loading operations: a systematic literature review," Annals of Operations Research, Springer, vol. 273(1), pages 311-375, February.
    2. Xiang Song & Dylan Jones & Nasrin Asgari & Tim Pigden, 2020. "Multi-objective vehicle routing and loading with time window constraints: a real-life application," Annals of Operations Research, Springer, vol. 291(1), pages 799-825, August.
    3. Côté, J.F. & Guastaroba, G. & Speranza, M.G., 2017. "The value of integrating loading and routing," European Journal of Operational Research, Elsevier, vol. 257(1), pages 89-105.
    4. Mahdi Alinaghian & Komail Zamanlou & Mohammad S. Sabbagh, 2017. "A bi-objective mathematical model for two-dimensional loading time-dependent vehicle routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(11), pages 1422-1441, November.
    5. Zhang, Zhenzhen & Wei, Lijun & Lim, Andrew, 2015. "An evolutionary local search for the capacitated vehicle routing problem minimizing fuel consumption under three-dimensional loading constraints," Transportation Research Part B: Methodological, Elsevier, vol. 82(C), pages 20-35.
    6. Männel, Dirk & Bortfeldt, Andreas, 2016. "A hybrid algorithm for the vehicle routing problem with pickup and delivery and three-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 254(3), pages 840-858.
    7. Jean-François Côté & Michel Gendreau & Jean-Yves Potvin, 2020. "The Vehicle Routing Problem with Stochastic Two-Dimensional Items," Transportation Science, INFORMS, vol. 54(2), pages 453-469, March.
    8. Zachariadis, Emmanouil E. & Tarantilis, Christos D. & Kiranoudis, Chris T., 2016. "The Vehicle Routing Problem with Simultaneous Pick-ups and Deliveries and Two-Dimensional Loading Constraints," European Journal of Operational Research, Elsevier, vol. 251(2), pages 369-386.
    9. Wei, Lijun & Zhang, Zhenzhen & Zhang, Defu & Lim, Andrew, 2015. "A variable neighborhood search for the capacitated vehicle routing problem with two-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 243(3), pages 798-814.
    10. Schmid, Verena & Doerner, Karl F. & Laporte, Gilbert, 2013. "Rich routing problems arising in supply chain management," European Journal of Operational Research, Elsevier, vol. 224(3), pages 435-448.
    11. Vidal, Thibaut & Crainic, Teodor Gabriel & Gendreau, Michel & Prins, Christian, 2013. "Heuristics for multi-attribute vehicle routing problems: A survey and synthesis," European Journal of Operational Research, Elsevier, vol. 231(1), pages 1-21.
    12. Henriette Koch & Andreas Bortfeldt & Gerhard Wäscher, 2017. "A hybrid solution approach for the 3L-VRP with simultaneous delivery and pickups," FEMM Working Papers 170005, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    13. Cherkesly, Marilène & Gschwind, Timo, 2022. "The pickup and delivery problem with time windows, multiple stacks, and handling operations," European Journal of Operational Research, Elsevier, vol. 301(2), pages 647-666.
    14. Leung, Stephen C.H. & Zhang, Zhenzhen & Zhang, Defu & Hua, Xian & Lim, Ming K., 2013. "A meta-heuristic algorithm for heterogeneous fleet vehicle routing problems with two-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 225(2), pages 199-210.
    15. Zhang, Xiangyi & Chen, Lu & Gendreau, Michel & Langevin, André, 2022. "A branch-and-cut algorithm for the vehicle routing problem with two-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 302(1), pages 259-269.
    16. Manuel Iori & Silvano Martello, 2010. "Routing problems with loading constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 4-27, July.
    17. Manuel Ostermeier & Sara Martins & Pedro Amorim & Alexander Hübner, 2018. "Loading constraints for a multi-compartment vehicle routing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(4), pages 997-1027, October.
    18. Emmanouil E. Zachariadis & Christos D. Tarantilis & Chris T. Kiranoudis, 2017. "Vehicle routing strategies for pick-up and delivery service under two dimensional loading constraints," Operational Research, Springer, vol. 17(1), pages 115-143, April.
    19. Emmanouil E. Zachariadis & Christos D. Tarantilis & Chris T. Kiranoudis, 2012. "The Pallet-Packing Vehicle Routing Problem," Transportation Science, INFORMS, vol. 46(3), pages 341-358, August.
    20. Oscar Dominguez & Angel Juan & Barry Barrios & Javier Faulin & Alba Agustin, 2016. "Using biased randomization for solving the two-dimensional loading vehicle routing problem with heterogeneous fleet," Annals of Operations Research, Springer, vol. 236(2), pages 383-404, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:265:y:2018:i:3:p:843-859. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.