Imagine that a salesman must travel to n cities and wants to take the shortest route possible. Assume that the salesman can start from any city on his itinerary and that the distance from city X to city Y is the same as the distance from Y to X (i.e.,...

The travelling salesman problem (TSP) is a problem in discrete or combinatorial optimization. It is a prominent illustration of a class of problems in computational complexity theory which are classified as NP-hard. Mathematical problems related to the...

In this paper we represent a new problem that arises when parts are cut from large plates of metal or glass. We call this problem the plate-cutting traveling salesman problem (P-TSP) because it requires the determination of a minimum-length tour such that exactly one...

The traveling salesman problem has been a very important topic of study for operations researchers and mathematicians for decades. Computer hardware and software advances in recent years have provided multiple alternative approaches to this classic combinatorial challenge. The objective of this paper is to...