Abstract
The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly one city from each group. The recent studies on this subject consider different variations of a memetic algorithm approach to the GTSP. The aim of this paper is to present a new memetic algorithm for GTSP with a powerful local search procedure. The experiments show that the proposed algorithm clearly outperforms all of the known heuristics with respect to both solution quality and running time. While the other memetic algorithms were designed only for the symmetric GTSP, our algorithm can solve both symmetric and asymmetric instances.
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Notes
We assume that s i+M = s i for the solution (s 1 s 2 ... s M ) and for any 1 ≤ i ≤ M.
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Acknowledgments
We would like to thank Natalio Krasnogor for numerous useful discussions of earlier versions of the paper and Michael Basarab for helpful advice on memetic algorithms.
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This is a modified version of the paper “A Memetic Algorithm for the Generalized Traveling Salesman Problem” by G. Gutin, D. Karapetyan and N. Krasnogor published in the proceedings of NICSO 2007.
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Gutin, G., Karapetyan, D. A memetic algorithm for the generalized traveling salesman problem. Nat Comput 9, 47–60 (2010). https://doi.org/10.1007/s11047-009-9111-6
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DOI: https://doi.org/10.1007/s11047-009-9111-6