Abstract: Genetic algorithms are inspired by the process of natural evolution and are one of the most widely used optimization algorithms. This study deals with analyzing the convergence behavior of a new variant of the genetic algorithms involving a modified version of the ternary crossover operator. To compare the performance of the proposed variant of genetic algorithms with that of the traditional genetic algorithms both of these are applied to two benchmark datasets of the Travelling Salesman Problem (TSP) taken from TSPLIB. The convergence behavior of both these algorithms is analyzed for 100 iterations with tournament size as 30 and 50. The results indicate that the proposed variant of genetic algorithm involving a modified ternary crossover operator converges to a better solution as compared to that of the traditional genetic algorithms.