IDEAS home Printed from https://ideas.repec.org/a/eee/transe/v126y2019icp87-102.html
   My bibliography  Save this article

Mixed steepest descent algorithm for the traveling salesman problem and application in air logistics

Author

Listed:
  • Muren,
  • Wu, Jianjun
  • Zhou, Li
  • Du, Zhiping
  • Lv, Ying

Abstract

In this paper, a new mixed steepest descent algorithm which has short computation time and stable solution is provided. Comparisons and case studies based on different traffic network and distance are made with other intelligent and exact algorithms. The large-scale experiment shows that the possibility of securing the optimal solution is greater than 99.5% and the average computation time is lower than 0.06 s when the node scales are less than 50. The proposed algorithm can not only be applied in emergency logistics problems but is also useful for solving other real-world problems.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:transe:v:126:y:2019:i:c:p:87-102
    DOI: 10.1016/j.tre.2019.04.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1366554518312808
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.tre.2019.04.004?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. Huang, Kai & Jiang, Yiping & Yuan, Yufei & Zhao, Lindu, 2015. "Modeling multiple humanitarian objectives in emergency response to large-scale disasters," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 75(C), pages 1-17.
    2. W. Qin & J. Zhang & D. Song, 2018. "An improved ant colony algorithm for dynamic hybrid flow shop scheduling with uncertain processing time," Journal of Intelligent Manufacturing, Springer, vol. 29(4), pages 891-904, April.
    3. 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.
    4. Volgenant, Ton & Jonker, Roy, 1982. "A branch and bound algorithm for the symmetric traveling salesman problem based on the 1-tree relaxation," European Journal of Operational Research, Elsevier, vol. 9(1), pages 83-89, January.
    5. Gerhard Reinelt, 1991. "TSPLIB—A Traveling Salesman Problem Library," INFORMS Journal on Computing, INFORMS, vol. 3(4), pages 376-384, November.
    6. Kara, Imdat & Bektas, Tolga, 2006. "Integer linear programming formulations of multiple salesman problems and its variations," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1449-1458, November.
    7. Gouveia, Luis & Leitner, Markus & Ruthmair, Mario, 2017. "Extended formulations and branch-and-cut algorithms for the Black-and-White Traveling Salesman Problem," European Journal of Operational Research, Elsevier, vol. 262(3), pages 908-928.
    8. Sheu, Jiuh-Biing, 2014. "Post-disaster relief–service centralized logistics distribution with survivor resilience maximization," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 288-314.
    9. Loree, Nick & Aros-Vera, Felipe, 2018. "Points of distribution location and inventory management model for Post-Disaster Humanitarian Logistics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 116(C), pages 1-24.
    10. Lu, Chung-Cheng & Ying, Kuo-Ching & Chen, Hui-Ju, 2016. "Real-time relief distribution in the aftermath of disasters – A rolling horizon approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 93(C), pages 1-20.
    11. 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.
    12. Kulkarni, R. V. & Bhave, P. R., 1985. "Integer programming formulations of vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 20(1), pages 58-67, April.
    13. Harlan Crowder & Manfred W. Padberg, 1980. "Solving Large-Scale Symmetric Travelling Salesman Problems to Optimality," Management Science, INFORMS, vol. 26(5), pages 495-509, May.
    14. He, Yuxuan & Liu, Nan, 2015. "Methodology of emergency medical logistics for public health emergencies," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 79(C), pages 178-200.
    15. Gabriela Ochoa & Nadarajen Veerapen, 2018. "Mapping the global structure of TSP fitness landscapes," Journal of Heuristics, Springer, vol. 24(3), pages 265-294, June.
    16. Diao, Xudong & Chen, Chun-Hsien, 2018. "A sequence model for air traffic flow management rerouting problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 110(C), pages 15-30.
    17. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
    18. Jon Jouis Bentley, 1992. "Fast Algorithms for Geometric Traveling Salesman Problems," INFORMS Journal on Computing, INFORMS, vol. 4(4), pages 387-411, November.
    19. Voudouris, Christos & Tsang, Edward, 1999. "Guided local search and its application to the traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 113(2), pages 469-499, March.
    20. Zahra Beheshti & Siti Shamsuddin & Siti Yuhaniz, 2013. "Binary Accelerated Particle Swarm Algorithm (BAPSA) for discrete optimization problems," Journal of Global Optimization, Springer, vol. 57(2), pages 549-573, October.
    21. Gilbert Laporte, 2009. "Fifty Years of Vehicle Routing," Transportation Science, INFORMS, vol. 43(4), pages 408-416, November.
    22. Haitao Li & Bahram Alidaee, 2016. "Tabu search for solving the black-and-white travelling salesman problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(8), pages 1061-1079, August.
    23. Xiao, Mingming & Cai, Kaiquan & Abbass, Hussein A., 2018. "Hybridized encoding for evolutionary multi-objective optimization of air traffic network flow: A case study on China," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 115(C), pages 35-55.
    24. Matteo Fischetti & Juan José Salazar González & Paolo Toth, 1997. "A Branch-and-Cut Algorithm for the Symmetric Generalized Traveling Salesman Problem," Operations Research, INFORMS, vol. 45(3), pages 378-394, June.
    25. Wang, Haijun & Du, Lijing & Ma, Shihua, 2014. "Multi-objective open location-routing model with split delivery for optimized relief distribution in post-earthquake," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 69(C), pages 160-179.
    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. 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.
    2. Bibi Aamirah Shafaa Emambocus & Muhammed Basheer Jasser & Angela Amphawan & Ali Wagdy Mohamed, 2022. "An Optimized Discrete Dragonfly Algorithm Tackling the Low Exploitation Problem for Solving TSP," Mathematics, MDPI, vol. 10(19), pages 1-24, October.
    3. Scianna, Marco, 2024. "The AddACO: A bio-inspired modified version of the ant colony optimization algorithm to solve travel salesman problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 357-382.

    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. Gianpaolo Ghiani & Gilbert Laporte & Frédéric Semet, 2006. "The Black and White Traveling Salesman Problem," Operations Research, INFORMS, vol. 54(2), pages 366-378, April.
    2. Burger, M. & Su, Z. & De Schutter, B., 2018. "A node current-based 2-index formulation for the fixed-destination multi-depot travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 265(2), pages 463-477.
    3. 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.
    4. Ferrer, José M. & Martín-Campo, F. Javier & Ortuño, M. Teresa & Pedraza-Martínez, Alfonso J. & Tirado, Gregorio & Vitoriano, Begoña, 2018. "Multi-criteria optimization for last mile distribution of disaster relief aid: Test cases and applications," European Journal of Operational Research, Elsevier, vol. 269(2), pages 501-515.
    5. 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.
    6. 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.
    7. Jamal Ouenniche & Prasanna K. Ramaswamy & Michel Gendreau, 2017. "A dual local search framework for combinatorial optimization problems with TSP application," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(11), pages 1377-1398, November.
    8. Gorka Kobeaga & María Merino & Jose A. Lozano, 2021. "On solving cycle problems with Branch-and-Cut: extending shrinking and exact subcycle elimination separation algorithms," Annals of Operations Research, Springer, vol. 305(1), pages 107-136, October.
    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. Bernardino, Raquel & Paias, Ana, 2018. "Solving the family traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 267(2), pages 453-466.
    11. Aardal, K.I. & van Hoesel, S., 1995. "Polyhedral Techniques in Combinatorial Optimization," Other publications TiSEM ed028a07-eb6a-4c8d-8f21-d, Tilburg University, School of Economics and Management.
    12. Zhou, Yawen & Liu, Jing & Zhang, Yutong & Gan, Xiaohui, 2017. "A multi-objective evolutionary algorithm for multi-period dynamic emergency resource scheduling problems," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 99(C), pages 77-95.
    13. Zang, Xiaoning & Jiang, Li & Liang, Changyong & Fang, Xiang, 2023. "Coordinated home and locker deliveries: An exact approach for the urban delivery problem with conflicting time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).
    14. Bruce Golden & Zahra Naji-Azimi & S. Raghavan & Majid Salari & Paolo Toth, 2012. "The Generalized Covering Salesman Problem," INFORMS Journal on Computing, INFORMS, vol. 24(4), pages 534-553, November.
    15. Chris Walshaw, 2002. "A Multilevel Approach to the Travelling Salesman Problem," Operations Research, INFORMS, vol. 50(5), pages 862-877, October.
    16. 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.
    17. Rahma Lahyani & Leandro C. Coelho & Jacques Renaud, 2018. "Alternative formulations and improved bounds for the multi-depot fleet size and mix vehicle routing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 125-157, January.
    18. 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.
    19. Paredes-Belmar, Germán & Montero, Elizabeth & Lüer-Villagra, Armin & Marianov, Vladimir & Araya-Sassi, Claudio, 2022. "Vehicle routing for milk collection with gradual blending: A case arising in Chile," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1403-1416.
    20. Pop, Petrică C. & Cosma, Ovidiu & Sabo, Cosmin & Sitar, Corina Pop, 2024. "A comprehensive survey on the generalized traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 314(3), pages 819-835.

    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:transe:v:126:y:2019:i:c:p:87-102. 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/wps/find/journaldescription.cws_home/600244/description#description .

    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.