On Solving Travelling Salesman Problem with Vertex Requisitions

Abstract

We consider the Travelling Salesman Problem with Vertex Requisitions, where each position of the tour is given at most two possible vertices to pass. The problem is known to be strongly NP-hard. The proposed algorithm for this problem has smaller time complexity compared to the previously known one. In particular, almost all instances of the problem are solvable in O(n) time using the new  algorithm, n being the number of vertices. The developed approach also helps in fast enumeration of a neighborhood in the local search and yields an integer programming model with O(n) binary variables for the problem under consideration.