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Traveling Salesman Problem and Membership in Pedigree Polytope - A Numerical Illustration

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Modelling, Computation and Optimization in Information Systems and Management Sciences (MCO 2008)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 14))

Abstract

Symmetric traveling salesman problem (STSP), a difficult combinatorial problem is formulated as a multistage insertion (MI) decision problem in Arthanari and Usha (2000). MI formulation is a compact 0-1 formulation for STSP. MI has given rise to the definition of a combinatorial object called pedigree. Arthanari (2008) contains a necessary condition for a MI-relaxation solution to be expressible as a convex combination of pedigrees. The existence of a multicommodity flow with the optimum value equal to unity over some layered network is checked for this purpose. This paper walks through an illustrative example to show the construction of such a network and the procedures involved in checking the necessary condition. Another important feature of this example is it brings out the need for discarding some arcs from the network called dummy arcs, for the correctness of the necessary condition for membership.

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Author information

Authors and Affiliations

  1. Department of ISOM, Business School, University of Auckland, Auckland, 1142, New Zealand

    Laleh Haerian Ardekani & Tiru Subramanian Arthanari

Authors
  1. Laleh Haerian Ardekani
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  2. Tiru Subramanian Arthanari
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Editor information

Editors and Affiliations

  1. Laboratory of Theoretical and Applied Computer Science, UFR MIM,, Paul Verlaine University of Metz, Metz, France

    Hoai An Le Thi

  2. Faculty of Sciences, Technology and Communications, University of Luxembourg, Luxembourg

    Pascal Bouvry

  3. Laboratory of Mathematics, National Institute for Applied Sciences, Rouen Mont, Saint Aignan, France

    Tao Pham Dinh

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Haerian Ardekani, L., Subramanian Arthanari, T. (2008). Traveling Salesman Problem and Membership in Pedigree Polytope - A Numerical Illustration. In: Le Thi, H.A., Bouvry, P., Pham Dinh, T. (eds) Modelling, Computation and Optimization in Information Systems and Management Sciences. MCO 2008. Communications in Computer and Information Science, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87477-5_16

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  • DOI: https://doi.org/10.1007/978-3-540-87477-5_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87476-8

  • Online ISBN: 978-3-540-87477-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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