On the high multiplicity traveling salesman problem

On the high multiplicity traveling salesman problem

This paper considers a version of the traveling salesman problem where the cities are to be visited multiple times. Each city has its own required number of visits. We investigate how the optimal solution and its objective value change when the numbers of visits are increased by a common multiplicator. In addition, we derive lower bounds on values of the multiplicator beyond which further incre...

The traveling salesman problem

The Traveling Salesman Problem

The Traveling Salesman Problem (TSP) is perhaps the most studied discrete optimization problem. Its popularity is due to the facts that TSP is easy to formulate, difficult to solve, and has a large number of applications. It appears that K. Menger [31] was the first researcher to consider the Traveling Salesman Problem (TSP). He observed that the problem can be solved by examining all permutati...

An Approach for Solving Traveling Salesman Problem

In this paper, we introduce a new approach for solving the traveling salesman problems (TSP) and provide a solution algorithm for a variant of this problem. The concept of the proposed method is based on the Hungarian algorithm, which has been used to solve an assignment problem for reaching an optimal solution. We introduced a new fittest criterion for crossing over such problems, and illu...

On the Discretized Dubins Traveling Salesman Problem

This research deals with a variation of the traveling salesman problem in which the cost of a tour, during which a kinematically constrained vehicle visits a set of targets, has to be minimized. We are motivated by scenarios that include motion planning for unmanned aerial, marine, and ground vehicles, just to name a few possible application outlets. We discretize the original continuous proble...