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The Traveling Salesman Problem: A Survey

Author

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  • M. Bellmore

    (The Johns Hopkins University, Baltimore, Maryland)

  • G. L. Nemhauser

    (The Johns Hopkins University, Baltimore, Maryland)

Abstract

A survey and synthesis of research on the traveling salesman problem is given. We begin by defining the problem and presenting several theorems. This is followed by a general classification of the solution techniques and a detailed description of some of the proven methods. Finally a summary of computational results is given.

Suggested Citation

  • M. Bellmore & G. L. Nemhauser, 1968. "The Traveling Salesman Problem: A Survey," Operations Research, INFORMS, vol. 16(3), pages 538-558, June.
    • Handle: RePEc:inm:oropre:v:16:y:1968:i:3:p:538-558
    DOI: 10.1287/opre.16.3.538
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    Citations

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    Cited by:

    1. Srour, F.J. & Zuidwijk, R.A., 2008. "How Much is Location Information Worth? A Competitive Analysis of the Online Traveling Salesman Problem with Two Disclosure Dates," ERIM Report Series Research in Management ERS-2008-075-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    2. French, Ben C., 1977. "PART II. The Analysis of Productive Efficiency in Agricultural Marketing: Models, Methods, and Progress," AAEA Monographs, Agricultural and Applied Economics Association, number 337214, january.
    3. Khan, W. A. & Hayhurst, D. R. & Cannings, C., 1999. "Determination of optimal path under approach and exit constraints," European Journal of Operational Research, Elsevier, vol. 117(2), pages 310-325, September.
    4. Gharehgozli, Amir Hossein & Yu, Yugang & de Koster, René & Udding, Jan Tijmen, 2014. "An exact method for scheduling a yard crane," European Journal of Operational Research, Elsevier, vol. 235(2), pages 431-447.
    5. Thomas L. Morin & Roy E. Marsten, 1974. "Brand-and-Bound Strategies for Dynamic Programming," Discussion Papers 106, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Delavernhe, Florian & Jaillet, Patrick & Rossi, André & Sevaux, Marc, 2021. "Planning a multi-sensors search for a moving target considering traveling costs," European Journal of Operational Research, Elsevier, vol. 292(2), pages 469-482.
    7. Bismark Singh & Lena Oberfichtner & Sergey Ivliev, 2023. "Heuristics for a cash-collection routing problem with a cluster-first route-second approach," Annals of Operations Research, Springer, vol. 322(1), pages 413-440, March.
    8. Kusum Deep & Hadush Mebrahtu & Atulya K. Nagar, 2018. "Novel GA for metropolitan stations of Indian railways when modelled as a TSP," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 9(3), pages 639-645, June.
    9. Aura Hernández-Sabaté & Lluís Albarracín & F. Javier Sánchez, 2020. "Graph-Based Problem Explorer: A Software Tool to Support Algorithm Design Learning While Solving the Salesperson Problem," Mathematics, MDPI, vol. 8(9), pages 1-20, September.
    10. Manerba, Daniele & Mansini, Renata & Riera-Ledesma, Jorge, 2017. "The Traveling Purchaser Problem and its variants," European Journal of Operational Research, Elsevier, vol. 259(1), pages 1-18.

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