Ant colony Optimization Algorithm to Expand the Traveling Salesman Problem

The traveler salesman problem (TSP) is such a problem in which a salesman starts from a desirable knot and after meeting other knots, finally returns to the first knot. The target in this problem is finding a net with minimum cost between all the knots. In this problem, the salesman meets each knot only once except the first one which is met twice, one in start and the other in the end of travel. This problem has very important applications in other problems such as timing and navigation. It is sort of NP-completeness problems and precise optimization algorithms are not competent for solving this problem in large dimensions.In this paper, an extension of this problem is represented in which it is assumed the first knot is different from the last (Open Traveling Salesman Problem). Then a mathematical planning model is recommended and finally the ant algorithm method is used for solving the problem.