Hybrid meta-heuristics with VNS and exact methods: application to large unconditional and conditional vertex \(p\)-centre problems
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Large-scale unconditional and conditional vertex \(p\)-centre problems are solved using two meta-heuristics. One is based on a three-stage approach whereas the other relies on a guided multi-start principle. Both methods incorporate Variable Neighbourhood Search, exact method, and aggregation techniques. The methods are assessed on the TSP dataset which consist of up to 71,009 demand points with \(p\) varying from 5 to 100. To the best of our knowledge, these are the largest instances solved for unconditional and conditional vertex \(p\)-centre problems. The two proposed meta-heuristics yield competitive results for both classes of problems.
KeywordsLarge unconditional and conditional vertex \(p\)-centre Aggregation Variable neighbourhood search Exact method
The authors would like to thank both referees for their useful suggestions that improved both the content as well as the presentation of the paper. We are also grateful to the Indonesian Government and Department of Industrial Engineering—ITENAS Bandung, Indonesia for the sponsorship of the first author.
- Barua, S., Sander, J.: Mining statistically sound co-location patterns at multiple distances. In: Proceedings of the 26th International Conference on Scientific and Statistical Database Management, Article No. 7 (2014)Google Scholar
- Casillas, P.: Aggregation problems in location-allocation modeling. In: Gosh, A., Rushton, G. (eds.) Spatial analysis and location-allocation models, pp. 327–344. Van Nostrand Reinhold, New York (1987)Google Scholar
- Daskin, M.S.: A new approach to solving the vertex \(p\)-center problem to optimality: algorithm and computational results. Commun. Oper. Res. Soc. Jpn. 45, 428–436 (2000)Google Scholar
- Dongarra, J.J.: Performance of various computers using standard linear equation software. http://www.netlib.org/benchmark/performance.pdf. Accessed 15 April 2013
- Ilhan, T., Pinar, M.: An efficient exact algorithm for the vertex \(p\)-center problem (2001). http://www.ie.bilkent.edu.tr/~mustafap/pubs/
- Irawan, C.A., Salhi, S.: Solving large p-median problems by a multistage hybrid approach using demand points aggregation and variable neighbourhood search. J. Glob. Optim. (2013). doi: 10.1007/s10898-013-0080-z
- Liu, S., Liu, Y., Ni, L. M., Fan, J., Li, M.: Towards Mobility-based Clustering. In: Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 919–928 (2010)Google Scholar
- Qu, Q., Liu, S., Yang, B. Jensen, C.S.: Integrating non-spatial preferences into spatial location queries. In: Proceedings of the 26th International Conference on Scientific and Statistical Database Management, Article No. 8 (2014)Google Scholar
- Tansel, B.C., Francis, R.L., Lowe, T.J.: State of the art-location on network: a survey. Part I: the \(p\)-center and \(p\)-median problems. Manag. Sci. 29, 482–497 (1983a)Google Scholar
- Tansel, B.C., Francis, R.L., Lowe, T.J.: State of the art-location on network: a survey. Part II: exploiting tree network structure. Manag. Sci. 29, 498–511 (1983b)Google Scholar