Traveling Salesman Problem Methods of Solution Survey

In this paper, a full review of the Travelling Salesman problem (TSP) is given. In general, TSP is considered an important area of research in the field of the applied mathematics. The problem has started in the 19th century by the well-known mathematician ((Hamilton)). The idea of TSP is to find the shortest Hamiltonian cycle that covers all the nodes in a graph. Later, researchers started to work on this problem using a variety of techniques to obtain an optimal solution. In fact, solutions of TSP are divided into two main types. The exact solutions that do not require a long time to be processed and the heuristic solutions that give approximate results. The main idea of this paper is to review a collection of successful methods that deal with TSP. In addition, this paper contains some examples with different databases size and comparison of multiple methods. Furthermore, a mathematical model of this problem with complexity analysis are given.