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Combinatorial optimization tolerances calculated in linear time

Author

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  • Goldengorin, Boris
  • Sierksma, Gerard

    (Groningen University)

Abstract

For a given optimal solution to a combinatorial optimization problem, we show, under very natural conditions, the equality of the minimal values of upper and lower tolerances, where the upper tolerances are calculated for the given optimal solution and the lower tolerances outside the optimal solution. As a consequence, the calculation of such tolerances can now be done in linear time, while all current methods use quadratic time.

Suggested Citation

  • Goldengorin, Boris & Sierksma, Gerard, 2003. "Combinatorial optimization tolerances calculated in linear time," Research Report 03A30, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    • Handle: RePEc:gro:rugsom:03a30
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    File URL: http://irs.ub.rug.nl/ppn/252306341
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    1. repec:dgr:rugsom:05a11 is not listed on IDEAS
    2. Vyacheslav Chistyakov & Boris Goldengorin & Panos Pardalos, 2012. "Extremal values of global tolerances in combinatorial optimization with an additive objective function," Journal of Global Optimization, Springer, vol. 53(3), pages 475-495, July.
    3. Jäger, G. & Goldengorin, B., 2005. "How to make a greedy heuristic for the asymmetric traveling salesman problem competitive," Research Report 05A11, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    4. Marcel Turkensteen & Dmitry Malyshev & Boris Goldengorin & Panos M. Pardalos, 2017. "The reduction of computation times of upper and lower tolerances for selected combinatorial optimization problems," Journal of Global Optimization, Springer, vol. 68(3), pages 601-622, July.

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