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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116896When 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.13 pages, 4 figuresComputational PhysicsData Analysis, Statistics and ProbabilityOn the exact number of possibilities for cutting and reconnecting the tour of a traveling salesman with Lin-$k$-Optstext