A genetic algorithm for the generalized traveling salesman problem

In a traveling salesman problem, if the set of nodes is divided into clusters so that a single node from each cluster can be visited, then the problem is known as the generalized traveling salesman problem where the objective is to find a tour with minimum cost passing through only a single node from each cluster. In this paper, a genetic algorithm is presented to solve the problem on a set of benchmark instances. The genetic algorithm is hybridized with an iterated local search to further improve the solution quality. Some speed-up methods are presented to accelerate the greedy node insertions. The genetic algorithm is tested on a set of benchmark instances with symmetric distances ranging from 51 to 442 nodes from the literature. Computational results show that the proposed genetic algorithm is the best performing algorithm so far in the literature in terms of solution quality.