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A discrete particle swarm optimization algorithm for the generalized traveling salesman problem

Dividing the set of nodes into clusters in the well-known traveling salesman problem results in the generalized traveling salesman problem which seeking a tour with minimum cost passing through only a single node from each cluster. In this paper, a discrete particle swarm optimization is presented to solve the problem on a set of benchmark instances. The discrete particle swarm optimization algorithm exploits the basic features of its continuous counterpart. It is also hybridized with a local search, variable neighborhood descend algorithm, to further improve the solution quality. In addition, some speed-up methods for greedy node insertions are presented. The discrete particle swarm optimization algorithm is tested on a set of benchmark instances with symmetric distances up to 442 nodes from the literature. Computational results show that the discrete particle optimization algorithm is very promising to solve the generalized traveling salesman problem.