GENETIC ALGORITHMS AND TRAVELING SALESMAN PROBLEMS

A genetic algorithm (GA) with an asexual reproduction plan through a g eneralized 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 ge neralized mutation operator preserves the global convergence property of a genetic algorithm thus establishing the fundamental theorem of th e GA for the algorithm. Avoiding an intermediate step of encoding thro ugh random keys to preserve crossover or permuting n and using ''fixin g'' states for legal crossover are the chief benefits of the innovatio ns reported in this paper. The algorithm has been applied to a number of natural and artificial problems and the results are encouraging.