Traveling Salesman Problem

The Travelling Salesman Problem or the TSP is a representative of a large class of problems known as combinatorial optimization problems. In the ordinary form of the TSP, a map of cities is given to the salesman and he has to visit all the cities only once to complete a tour such that the length of the tour is the shortest among all possible tours for this map. The data consist of weights assigned to the edges of a finite complete graph, and the objective is to find a Hamiltonian cycle, a cycle passing through all the vertices, of the graph while having the minimum total weight. In the TSP context, Hamiltonian cycles are commonly called tours.