New Genetic Algorithm for the Travelling Salesman Problem

Given a collection of cities and the cost of travel between each pair of them, the traveling salesman problem is to find the cheapest way of visiting all of the cities and returning to starting point. The simplicity of the statement of the problem is deceptive, the traveling salesman problem is one of the most intensely studied problems in computational mathematics and yet no effective solution method is known for the general case. This problem is one of the most difficult problems in the NP-hard class, which implies that finding a polynomial time algorithm to solve it is unlikely. There are different methods ranging from exact to heuristic and metaheuristics. It takes a long time to have an optimum solution with exact algorithms, so several heuristics have been proposed for handling near optimum solutions. In this study, a genetic algorithm as a heuristic optimization technique and neighborhood approximation is developed. This new algorithm’s solvability in benchmark and symmetric traveling salesman problem instances is tested problems in the sense that traveling from city X to city Y costs just as much as traveling from Y to X, and results are listed.