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TSPInfrastructure for the Traveling Salesperson Problem

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  • Hahsler, Michael
  • Hornik, Kurt

Abstract

The traveling salesperson (or, salesman) problem (TSP) is a well known and important combinatorial optimization problem. The goal is to find the shortest tour that visits each city in a given list exactly once and then returns to the starting city. Despite this simple problem statement, solving the TSP is difficult since it belongs to the class of NP-complete problems. The importance of the TSP arises besides from its theoretical appeal from the variety of its applications. Typical applications in operations research include vehicle routing, computer wiring, cutting wallpaper and job sequencing. The main application in statistics is combinatorial data analysis, e.g., reordering rows and columns of data matrices or identifying clusters. In this paper, we introduce the R package TSP which provides a basic infrastructure for handling and solving the traveling salesperson problem. The package features S3 classes for specifying a TSP and its (possibly optimal) solution as well as several heuristics to find good solutions. In addition, it provides an interface to Concorde, one of the best exact TSP solvers currently available.

Suggested Citation

  • Hahsler, Michael & Hornik, Kurt, 2007. "TSPInfrastructure for the Traveling Salesperson Problem," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i02).
    • Handle: RePEc:jss:jstsof:v:023:i02
    DOI: http://hdl.handle.net/10.18637/jss.v023.i02
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    References listed on IDEAS

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    1. Lawrence Hubert & Frank Baker, 1978. "Applications of combinatorial programming to data analysis: The traveling salesman and related problems," Psychometrika, Springer;The Psychometric Society, vol. 43(1), pages 81-91, March.
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    Cited by:

    1. Maria Michela Dickson & Yves Tillé, 2016. "Ordered spatial sampling by means of the traveling salesman problem," Computational Statistics, Springer, vol. 31(4), pages 1359-1372, December.
    2. Wittek, Peter, 2013. "Two-way incremental seriation in the temporal domain with three-dimensional visualization: Making sense of evolving high-dimensional datasets," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 193-201.
    3. Kemal Ihsan Kilic & Leonardo Mostarda, 2022. "Novel Concave Hull-Based Heuristic Algorithm For TSP," SN Operations Research Forum, Springer, vol. 3(2), pages 1-45, June.
    4. Hahsler, Michael & Hornik, Kurt & Buchta, Christian, 2008. "Getting Things in Order: An Introduction to the R Package seriation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 25(i03).
    5. Thomas Kirschstein & Christian Bierwirth, 2018. "The selective Traveling Salesman Problem with emission allocation rules," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 97-124, January.
    6. 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.
    7. Doppstadt, C. & Koberstein, A. & Vigo, D., 2016. "The Hybrid Electric Vehicle – Traveling Salesman Problem," European Journal of Operational Research, Elsevier, vol. 253(3), pages 825-842.

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