Abstract
The 2-Peripatetic Salesman Problem (2-PSP) minimizes the total length of 2 edge-disjoint Hamiltonian cycles. This type of problems arises in designing communication or computer networks, or whenever one aims to increase network reliability using disjoint tours. The NP-hardness of the 2-PSP is shown. Lower bound values are obtained by generalizing the 1 -tree approach for the TSP to a 2 edge-disjoint 1-trees approach for the 2-PSP. One can construct 2 edge-disjoint 1-trees using a greedy algorithm, into which a partitioning procedure is incorporated that runs in O(n2logn) time. Upper bound solutions are obtained by two heuristics based on a lower bound solution and by a modified Savings heuristic for problems up to 140 cities.
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© 1992 Springer-Verlag Berlin · Heidelberg
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De Kort, J.B.J.M. (1992). Upper and Lower Bounds for the Symmetric 2-Peripatetic Salesman Problem. In: Bühler, W., Feichtinger, G., Hartl, R.F., Radermacher, F.J., Stähly, P. (eds) Papers of the 19th Annual Meeting / Vorträge der 19. Jahrestagung. Operations Research Proceedings, vol 1990. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77254-2_34
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DOI: https://doi.org/10.1007/978-3-642-77254-2_34
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