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A minimum spanning tree based heuristic for the travelling salesman tour

Author

Listed:
  • Santosh Kumar

    (University of Melbourne)

  • Elias Munapo

    (North West University, Mafikeng Campus)

  • ‘Maseka Lesaoana

    (University of Limpopo)

  • Philimon Nyamugure

    (National University of Science and Technology)

Abstract

This paper presents a heuristic to find the travelling salesman tour (TST) in a connected network. The approach first identifies a node and two associated arcs that are desirable for inclusion in the required TST. If we let this node be denoted by $$p$$ p and two selected arcs emanating from this node be denoted by $$\left( {p,q} \right)\,{\text{and}}\,\left( {p,k} \right),$$ p , q and p , k , then we find a path joining the two nodes $$q\,{\text{and}}\, k$$ q and k passing through all the remaining nodes of the given network. A sum of these lengths, i.e. length of the links $$\left( {p,q} \right)\,{\text{and}}\,\left( {p,k} \right)$$ p , q and p , k along with the length of the path that joins the nodes $$q\,{\text{and}}\, k$$ q and k passing through all the remaining nodes will result in a feasible TST, hence gives an upper bound on the TST. A simple procedure is outlined to identify: (1) the node $$p$$ p , (2) the two corresponding links $$\left( {p,q} \right)\,{\text{and}}\,\left( {p,k} \right),$$ p , q and p , k , and (3) the path joining the nodes $$q\,{\text{and}}\, k$$ q and k passing through all the remaining nodes. The approach is based on the minimum spanning tree; hence the complexity of the TST is reduced. The network in the present context has been assumed to be a connected network with at least two arcs emanating from each node.

Suggested Citation

  • Santosh Kumar & Elias Munapo & ‘Maseka Lesaoana & Philimon Nyamugure, 2018. "A minimum spanning tree based heuristic for the travelling salesman tour," OPSEARCH, Springer;Operational Research Society of India, vol. 55(1), pages 150-164, March.
    • Handle: RePEc:spr:opsear:v:55:y:2018:i:1:d:10.1007_s12597-017-0318-5
    DOI: 10.1007/s12597-017-0318-5
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    References listed on IDEAS

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    1. WOLSEY, Laurence A., 1980. "Heuristic analysis, linear programming and branch and bound," LIDAM Reprints CORE 407, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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