A genetic algorithm with a mixed region search for the asymmetric traveling salesman problem

This paper presents a genetic algorithm to solve the asymmetric traveling salesman problem. The genetic algorithm proposed in this study extends search space by purposefully generating and including infeasible solutions in the population. Instead of trying to maintain feasibility with crossover operations, it searches through both feasible and infeasible regions for good quality solutions. It is also shown in the article that the size of the infeasible region defined by solutions with subtours dominates that of a feasible region in the asymmetric traveling salesman problem. A comparative computational study using benchmark problems shows that the proposed genetic algorithm is a viable option for hard asymmetric traveling salesman problems.