A minimum spanning tree based heuristic for the travelling salesman tour

Santosh Kumar (), Elias Munapo (), ‘Maseka Lesaoana () and Philimon Nyamugure ()
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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

OPSEARCH, 2018, vol. 55, issue 1, No 8, 150-164

Abstract: 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.

Keywords: Connected network; Minimum spanning tree path; Travelling salesman tour (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s12597-017-0318-5

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