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A Note on the Separation of Subtour Elimination Constraints in Asymmetric Routing Problems

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  • Michael Drexl

    (Johannes Gutenberg University Mainz)

Abstract

This note proposes an alternative procedure for identifying violated subtour elimination constraints (SECs) in branch-and-cut algorithms for routing problems, such as variants of travelling salesman, shortest Hamiltonian path, or elementary shortest path problems, on directed graphs. The proposed procedure is based on computing the strong components of the support graph. The procedure possesses a better worst-case time complexity than the standard way of separating SECs, which uses minimum cut algorithms, and is easier to implement.

Suggested Citation

  • Michael Drexl, 2012. "A Note on the Separation of Subtour Elimination Constraints in Asymmetric Routing Problems," Working Papers 1205, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    • Handle: RePEc:jgu:wpaper:1205
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    File URL: https://download.uni-mainz.de/RePEc/pdf/Discussion_Paper_1205.pdf
    File Function: First version, 2012
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    References listed on IDEAS

    as
    1. Matteo Fischetti & Paolo Toth, 1997. "A Polyhedral Approach to the Asymmetric Traveling Salesman Problem," Management Science, INFORMS, vol. 43(11), pages 1520-1536, November.
    2. Vansteenwegen, Pieter & Souffriau, Wouter & Oudheusden, Dirk Van, 2011. "The orienteering problem: A survey," European Journal of Operational Research, Elsevier, vol. 209(1), pages 1-10, February.
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