Genetic algorithms and traveling salesman problems

A genetic algorithm (GA) with an asexual reproduction plan through a generalized mutation for an evolutionary operator is developed that can be directly applied to a permutation of n numbers for an approximate global optimal solution of a traveling salesman problem (TSP). Schema analysis of the algorithm shows that a sexual reproduction with the generalized mutation operator preserves the global convergence property of a genetic algorithm thus establishing the fundamental theorem of the GA for the algorithm. Avoiding an intermediate step of encoding through random keys to preserve crossover or permuting n and using “fixing” states for legal crossover are the chief benefits of the innovations reported in this paper. The algorithm has been applied to a number of natural and artificial problems and the results are encouraging.