Population-Based Optimization Algorithms for Solving the Travelling 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. For example, given the map shown in figure l, the lowest cost route would be the one written (A, B, C, E, D, A), with the cost 31.