Traveling salesman problem is quite known in the field of combinatorial optimization. Through this research describe how the traveling salesman problem is solved by the heuristic method of genetic algorithms. This research to find the most approximate solution that gives us the least distance, which is the shortest route for traverse the cities given in the data set such that each city is passed through just once and the traveling salesman comes back to the initial city from where he started. I accomplish this by carrying out the algorithm through generating a fitness formula and with the help of genetic operators like selection, crossover and mutation. The main purpose of this study is to propose a new representation method of chromosomes using binary matrix and new fittest criteria to be used as method for finding the optimal solution for TSP. The proposed method is taken from genetic algorithm of artificial inelegance as a basic ingredient which has been used as search algorithm to find the near-optimal solutions. This research introducing the new fittest criteria for crossover, and also applying the algorithm on symmetric as well as asymmetric TSP.