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An exact algorithm for the clustered travelling salesman problem

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Abstract

We consider the clustered travelling salesman problem in which vertices (except the starting vertex) of the network are divided into some prespecified clusters. The problem is to find a least cost Hamiltonian cycle (tour) in which vertices of any cluster are visited contiguously and the clusters are visited in the prespecified order. The problem is NP-hard and it arises in practical transportation and sequencing problems. This paper develops a lexisearch algorithm for obtaining exact optimal solution to the problem. The efficiency of the algorithm against an existing algorithm to the problem has been examined for asymmetric TSPLIB instances of various sizes and clusters. Finally, we present solutions to some symmetric TSPLIB instances.

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Acknowledgments

The author is thankful to the honourable anonymous reviewer for his constructive comments and suggestions, which helped the author to improve this paper.

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Authors and Affiliations

  1. Department of Computer Science, Al-Imam Muhammad Ibn Saud Islamic University, P.O. Box 5701, Riyadh, 11432, Kingdom of Saudi Arabia

    Zakir Hussain Ahmed

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  1. Zakir Hussain Ahmed
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Correspondence to Zakir Hussain Ahmed.

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Ahmed, Z.H. An exact algorithm for the clustered travelling salesman problem. OPSEARCH 50, 215–228 (2013). https://doi.org/10.1007/s12597-012-0107-0

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