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Nonlinear resolving functions for the travelling salesman problem

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Abstract

We propose two approaches to finding lower bounds in the traveling salesman problem (TSP). The first approach, based on a linear specification of the resolving function φ(t, y), uses a two-index TSP model in its solution. This model has many applications. The second approach, based on a nonlinear specification of the resolving function φ(t, y), uses a single-index TSP model. This model is original and lets us significantly reduce the branching procedure in the branch-and-bound method for exact TSP solution. One cannot use the two-index TSP model here due to the nonlinear specification of the resolving function φ(t, y).

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Authors and Affiliations

  1. Moscow State University of Economics, Statistics, and Informatics, Moscow, Russia

    S. I. Sergeev

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  1. S. I. Sergeev
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Original Russian Text © S.I. Sergeev, 2013, published in Avtomatika i Telemekhanika, 2013, No. 6, pp. 101–120.

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Sergeev, S.I. Nonlinear resolving functions for the travelling salesman problem. Autom Remote Control 74, 978–994 (2013). https://doi.org/10.1134/S0005117913060088

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