Although the m-ATSP (or multi traveling salesman problem) is well known for its importance in scheduling and vehicle routing, it has, to the best of our knowledge, never been studied polyhedraly, i.e., it has always been transformed to the standard ATSP. This transformation is valid only if the cost of an arc from node i to node j is the same for all machines. In many practical applications thi...

We consider the probabilistic relationship between the value of a random asymmetric traveling salesman problem ATSP (M) and the value of its assignment relaxation AP (M). We assume here that the costs are given by an n × n matrix M whose entries are independently and identically distributed. We focus on the relationship between Pr(ATSP (M) = AP (M)) and the probability pn that any particular en...

The asymmetric traveling salesman problem (ATSP) is one of the most fundamental problems in combinatorial optimization. An instance of ATSP is a directed complete graph G = (V,E) with edge weights w : E → N that satisfy the triangle inequality, i. e., w(a, c) ≤ w(a, b) +w(b, c) for all distinct vertices a, b, c ∈ V . The goal is to find a Hamiltonian cycle of minimum weight. The weight of a Ham...

The railway capacity optimization problem deals with the maximization of the number of trains running on a given network per unit time. In this study, we frame this problem as a typical asymmetrical Travelling Salesman Problem (ATSP), with the ATSP nodes representing the train arrival /departure events and the ATSP total cost representing the total time-interval of the schedule. The application...

The Generalized Traveling Salesman Problem (GTSP) is stated as follows. Given a weighted complete digraph K∗ n and a partition V1, . . . , Vk of its vertices, find a minimum weight cycle containing exactly one vertex from each set Vi, i = 1, . . . , k. We study transformations from GTSP to TSP. The ’exact’ Noon-Bean transformation is investigated in computational experiments. We study the ’non-...

The only metric that had existed so far to determine the best algorithm for solving an general Asymmetric Traveling Salesman Problem (ATSP) instance is based on the number of cities; nevertheless, it is not sufficiently adequate for discriminating the best algorithm for solving an ATSP instance, thus the necessity for devising a new metric through the use of data-mining techniques. In this pape...