IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v211y2011i3p427-441.html
   My bibliography  Save this article

Traveling salesman problem heuristics: Leading methods, implementations and latest advances

Author

Listed:
  • Rego, César
  • Gamboa, Dorabela
  • Glover, Fred
  • Osterman, Colin

Abstract

Heuristics for the traveling salesman problem (TSP) have made remarkable advances in recent years. We survey the leading methods and the special components responsible for their successful implementations, together with an experimental analysis of computational tests on a challenging and diverse set of symmetric and asymmetric TSP benchmark problems. The foremost algorithms are represented by two families, deriving from the Lin-Kernighan (LK) method and the stem-and-cycle (S&C) method. We show how these families can be conveniently viewed within a common ejection chain framework which sheds light on their similarities and differences, and gives clues about the nature of potential enhancements to today's best methods that may provide additional gains in solving large and difficult TSPs.

Suggested Citation

  • Rego, César & Gamboa, Dorabela & Glover, Fred & Osterman, Colin, 2011. "Traveling salesman problem heuristics: Leading methods, implementations and latest advances," European Journal of Operational Research, Elsevier, vol. 211(3), pages 427-441, June.
    • Handle: RePEc:eee:ejores:v:211:y:2011:i:3:p:427-441
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00606-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Gamboa, Dorabela & Rego, Cesar & Glover, Fred, 2005. "Data structures and ejection chains for solving large-scale traveling salesman problems," European Journal of Operational Research, Elsevier, vol. 160(1), pages 154-171, January.
    2. Jon Jouis Bentley, 1992. "Fast Algorithms for Geometric Traveling Salesman Problems," INFORMS Journal on Computing, INFORMS, vol. 4(4), pages 387-411, November.
    3. Rego, Cesar, 1998. "Relaxed tours and path ejections for the traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 522-538, April.
    4. S. Lin & B. W. Kernighan, 1973. "An Effective Heuristic Algorithm for the Traveling-Salesman Problem," Operations Research, INFORMS, vol. 21(2), pages 498-516, April.
    5. Helsgaun, Keld, 2000. "An effective implementation of the Lin-Kernighan traveling salesman heuristic," European Journal of Operational Research, Elsevier, vol. 126(1), pages 106-130, October.
    6. Paris-C. Kanellakis & Christos H. Papadimitriou, 1980. "Local Search for the Asymmetric Traveling Salesman Problem," Operations Research, INFORMS, vol. 28(5), pages 1086-1099, October.
    7. César Rego & Fred Glover, 2010. "Ejection chain and filter-and-fan methods in combinatorial optimization," Annals of Operations Research, Springer, vol. 175(1), pages 77-105, March.
    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. Zhang, Zhe & Gong, Xue & Song, Xiaoling & Yin, Yong & Lev, Benjamin & Zhou, Xiaoyang, 2024. "An effective two phase heuristic for synchronized seru production scheduling and 3PL transportation problems," International Journal of Production Economics, Elsevier, vol. 268(C).
    2. Luca Cicala & Francesco Gargiulo & Sara Parrilli & Donato Amitrano & Gianpaolo Pigliasco, 2024. "Progressive Monitoring of Micro-Dumps Using Remote Sensing: An Applicative Framework for Illegal Waste Management," Sustainability, MDPI, vol. 16(13), pages 1-24, July.
    3. Jana, R.K. & Mitra, Subrata K. & Sharma, Dinesh K., 2018. "Software vendors travel management decisions using an elitist nonhomogeneous genetic algorithm," International Journal of Production Economics, Elsevier, vol. 202(C), pages 123-131.
    4. Wang, Zutong & Guo, Jiansheng & Zheng, Mingfa & Wang, Ying, 2015. "Uncertain multiobjective traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 241(2), pages 478-489.
    5. Thomas Weise & Yuezhong Wu & Raymond Chiong & Ke Tang & Jörg Lässig, 2016. "Global versus local search: the impact of population sizes on evolutionary algorithm performance," Journal of Global Optimization, Springer, vol. 66(3), pages 511-534, November.
    6. Xu, Liang & Xu, Zhou & Xu, Dongsheng, 2013. "Exact and approximation algorithms for the min–max k-traveling salesmen problem on a tree," European Journal of Operational Research, Elsevier, vol. 227(2), pages 284-292.
    7. Scholz, André & Henn, Sebastian & Stuhlmann, Meike & Wäscher, Gerhard, 2016. "A new mathematical programming formulation for the Single-Picker Routing Problem," European Journal of Operational Research, Elsevier, vol. 253(1), pages 68-84.
    8. Pawel Sitek & Jarosław Wikarek, 2019. "Capacitated vehicle routing problem with pick-up and alternative delivery (CVRPPAD): model and implementation using hybrid approach," Annals of Operations Research, Springer, vol. 273(1), pages 257-277, February.
    9. Sleegers, Joeri & Olij, Richard & van Horn, Gijs & van den Berg, Daan, 2020. "Where the really hard problems aren’t," Operations Research Perspectives, Elsevier, vol. 7(C).
    10. Muren, & Wu, Jianjun & Zhou, Li & Du, Zhiping & Lv, Ying, 2019. "Mixed steepest descent algorithm for the traveling salesman problem and application in air logistics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 126(C), pages 87-102.
    11. Dongyun Wang & Qiwei Yu & Yu Zhang, 2015. "Research on Laser Marking Speed Optimization by Using Genetic Algorithm," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-10, May.
    12. Mladenović, Nenad & Urošević, Dragan & Hanafi, Saı¨d & Ilić, Aleksandar, 2012. "A general variable neighborhood search for the one-commodity pickup-and-delivery travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 220(1), pages 270-285.
    13. Taillard, Éric D. & Helsgaun, Keld, 2019. "POPMUSIC for the travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 272(2), pages 420-429.
    14. Aliyev, Denis A. & Zirbel, Craig L., 2023. "Seriation using tree-penalized path length," European Journal of Operational Research, Elsevier, vol. 305(2), pages 617-629.
    15. Heber F. Amaral & Sebastián Urrutia & Lars M. Hvattum, 2021. "Delayed improvement local search," Journal of Heuristics, Springer, vol. 27(5), pages 923-950, October.
    16. Saïd Hanafi & Raca Todosijević, 2017. "Mathematical programming based heuristics for the 0–1 MIP: a survey," Journal of Heuristics, Springer, vol. 23(4), pages 165-206, August.
    17. Gary R. Waissi & Pragya Kaushal, 2020. "A polynomial matrix processing heuristic algorithm for finding high quality feasible solutions for the TSP," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 73-87, March.
    18. Taillard, Éric D., 2022. "A linearithmic heuristic for the travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 297(2), pages 442-450.
    19. Lancia, Giuseppe & Vidoni, Paolo, 2020. "Finding the largest triangle in a graph in expected quadratic time," European Journal of Operational Research, Elsevier, vol. 286(2), pages 458-467.
    20. Jiang, Zhongzhou & Liu, Jing & Wang, Shuai, 2016. "Traveling salesman problems with PageRank Distance on complex networks reveal community structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 293-302.
    21. Kalliopi Kastampolidou & Christos Papalitsas & Theodore Andronikos, 2022. "The Distributed Kolkata Paise Restaurant Game," Games, MDPI, vol. 13(3), pages 1-21, April.
    22. Kalliopi Kastampolidou & Christos Papalitsas & Theodore Andronikos, 2021. "DKPRG or how to succeed in the Kolkata Paise Restaurant gamevia TSP," Papers 2101.07760, arXiv.org.
    23. Shengbin Wang & Weizhen Rao & Yuan Hong, 2020. "A distance matrix based algorithm for solving the traveling salesman problem," Operational Research, Springer, vol. 20(3), pages 1505-1542, September.
    24. Martin Bichler, 2020. "Comments on: Shared resources in collaborative vehicle routing," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 21-24, April.
    25. Sebastian Henn & André Scholz & Meike Stuhlmann & Gerhard Wäscher, 2015. "A New Mathematical Programming Formulation for the Single-Picker Routing Problem in a Single-Block Layout," FEMM Working Papers 150005, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.

    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. Gary R. Waissi & Pragya Kaushal, 2020. "A polynomial matrix processing heuristic algorithm for finding high quality feasible solutions for the TSP," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 73-87, March.
    2. César Rego & Fred Glover, 2010. "Ejection chain and filter-and-fan methods in combinatorial optimization," Annals of Operations Research, Springer, vol. 175(1), pages 77-105, March.
    3. Colin Osterman & César Rego, 2016. "A k-level data structure for large-scale traveling salesman problems," Annals of Operations Research, Springer, vol. 244(2), pages 583-601, September.
    4. Chen, Yu-Wang & Zhu, Yao-Jia & Yang, Gen-Ke & Lu, Yong-Zai, 2011. "Improved extremal optimization for the asymmetric traveling salesman problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4459-4465.
    5. K Sang-Ho & G Young-Gun & K Maing-Kyu, 2003. "Application of the out-of-kilter algorithm to the asymmetric traveling salesman problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(10), pages 1085-1092, October.
    6. G Babin & S Deneault & G Laporte, 2007. "Improvements to the Or-opt heuristic for the symmetric travelling salesman problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(3), pages 402-407, March.
    7. Nikolakopoulos, Athanassios & Sarimveis, Haralambos, 2007. "A threshold accepting heuristic with intense local search for the solution of special instances of the traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1911-1929, March.
    8. Jean Bertrand Gauthier & Stefan Irnich, 2020. "Inter-Depot Moves and Dynamic-Radius Search for Multi-Depot Vehicle Routing Problems," Working Papers 2004, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    9. Jeanette Schmidt & Stefan Irnich, 2020. "New Neighborhoods and an Iterated Local Search Algorithm for the Generalized Traveling Salesman Problem," Working Papers 2020, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    10. David Applegate & William Cook & André Rohe, 2003. "Chained Lin-Kernighan for Large Traveling Salesman Problems," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 82-92, February.
    11. Mutsunori Yagiura & Toshihide Ibaraki & Fred Glover, 2004. "An Ejection Chain Approach for the Generalized Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 133-151, May.
    12. Luca Maria Gambardella & Marco Dorigo, 2000. "An Ant Colony System Hybridized with a New Local Search for the Sequential Ordering Problem," INFORMS Journal on Computing, INFORMS, vol. 12(3), pages 237-255, August.
    13. Ghosh, Diptesh, 2016. "Exploring Lin Kernighan neighborhoods for the indexing problem," IIMA Working Papers WP2016-02-13, Indian Institute of Management Ahmedabad, Research and Publication Department.
    14. Pan-Li Zhang & Xiao-Bo Sun & Ji-Quan Wang & Hao-Hao Song & Jin-Ling Bei & Hong-Yu Zhang, 2022. "The Discrete Carnivorous Plant Algorithm with Similarity Elimination Applied to the Traveling Salesman Problem," Mathematics, MDPI, vol. 10(18), pages 1-34, September.
    15. Rego, César & Duarte, Renato, 2009. "A filter-and-fan approach to the job shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 194(3), pages 650-662, May.
    16. Jiang, Zhongzhou & Liu, Jing & Wang, Shuai, 2016. "Traveling salesman problems with PageRank Distance on complex networks reveal community structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 293-302.
    17. Henke, Tino & Speranza, M. Grazia & Wäscher, Gerhard, 2015. "The multi-compartment vehicle routing problem with flexible compartment sizes," European Journal of Operational Research, Elsevier, vol. 246(3), pages 730-743.
    18. Lamb, John D., 2012. "Variable neighbourhood structures for cycle location problems," European Journal of Operational Research, Elsevier, vol. 223(1), pages 15-26.
    19. William Cook & André Rohe, 1999. "Computing Minimum-Weight Perfect Matchings," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 138-148, May.
    20. Luc Muyldermans & Patrick Beullens & Dirk Cattrysse & Dirk Van Oudheusden, 2005. "Exploring Variants of 2-Opt and 3-Opt for the General Routing Problem," Operations Research, INFORMS, vol. 53(6), pages 982-995, December.

    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:211:y:2011:i:3:p:427-441. 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.