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On the exact number of possibilities for cutting and reconnecting the tour of a traveling salesman with Lin-$k$-Opts

Guenther Stattenberger·Markus Dankesreiter·Florian Baumgartner·Johannes J. Schneider
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Abstract

When trying to find approximate solutions for the Traveling Salesman Problem with heuristic optimization algorithms, small moves called Lin-$k$-Opts are often used. In our paper, we provide exact formulas for the numbers of possible tours into which a randomly chosen tour can be changed with a Lin-$k$-Opt.

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Guenther Stattenberger, Markus Dankesreiter, Florian Baumgartner, Johannes J. Schneider. 2006-08-27. On the exact number of possibilities for cutting and reconnecting the tour of a traveling salesman with Lin-$k$-Opts. https://arxiv.org/abs/physics/0608269

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