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Solving the capacitated clustering problem with variable neighborhood search

  • Advances in Theoretical and Applied Combinatorial Optimization
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Abstract

Variable neighborhood search (VNS) is a proven heuristic framework for finding good solutions to combinatorial and global optimization problems. In this paper two VNS-based heuristics are proposed for solving the capacitated clustering problem. The first follows a standard VNS approach, and the second a skewed VNS that allows moves to inferior solutions. The performance of the two heuristics is assessed on benchmark instances from the literature. We also compare their performance against a recently published iterated VNS procedure. All VNS procedures outperform the state-of-the-art, but the Skewed VNS is best overall. This would suggest that using acceptance criteria before allowing moves to inferior solutions in Skewed VNS is preferable to the random shaking approach that is used in Iterated VNS to move to new regions of the solution space.

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References

  • Brimberg, J., Hansen, P., & Mladenović, N. (2010). Attraction probabilities in variable neighborhood search. 4OR-QJ Operations Research, 8, 181–194.

    Article  Google Scholar 

  • Brimberg, J., Janićijević, S., Mladenović, N., & Urošević, D. (2015a). Solving the clique partitioning problem as a maximally diverse grouping problem. Optimization Letters, 1–13. doi:10.1007/s11590-015-0869-4.

  • Brimberg, J., Mladenović, N., & Urošević, D. (2015b). Solving the maximally diverse grouping problem by skewed general variable neighborhood search. Information Sciences, 295, 650–675.

    Article  Google Scholar 

  • Brimberg, J., Mladenović, N., Todosijević, R., & Urošević, D. (2016). Variable neighborhood descent for the capacitated clustering problem. Lecture Notes in Computer Science, 9869, 336–349.

    Article  Google Scholar 

  • Deng, Y., & Bard, J. F. (2011). A reactive grasp with path relinking for capacitated clustering. Journal of Heuristics, 17(2), 119–152.

    Article  Google Scholar 

  • Duarte, A., & Martí, R. (2007). Tabu search and grasp for the maximum diversity problem. European Journal of Operational Research, 178, 71–84.

    Article  Google Scholar 

  • Fan, Z. P., Chen, Y., Ma, J., & Zeng, S. (2010). A hybrid genetic algorithmic approach to the maximally diverse grouping problem. Journal of Operational Research Society, 62, 92–99.

    Article  Google Scholar 

  • Gallego, M., Laguna, M., Martí, R., & Duarte, A. (2012). Tabu search with strategic oscillation for the maximally diverse grouping problem. Journal of the Operational Research Society, 64(5), 724–734.

    Article  Google Scholar 

  • Lai, X., & Hao, J. K. (2016). Iterated variable neighborhood search for the capacitated clustering problem. Engineering Applications of Artificial Intelligence, 56, 102–120.

    Article  Google Scholar 

  • Martínez-Gavara, A., Campos, V., Gallego, M., Laguna, M., & Martí, R. (2015). Tabu search and grasp for the capacitated clustering problem. Computational Optimization and Applications, 62(2), 589–607.

    Article  Google Scholar 

  • Morán-Mirabal, L., González-Velarde, J., Resende, M. G., & Silva, R. M. (2013). Randomized heuristics for handover minimization in mobility networks. Journal of Heuristics, 19(6), 845–880.

    Article  Google Scholar 

  • Rodriguez, F., Lozano, M., García-Martínez, C., & González-Barrera, J. (2013). An artificial bee colony algorithm for the maximally diverse grouping problem. Inormation Sciences, 230, 183–196.

    Article  Google Scholar 

  • Urošević, D. (2014). Variable neighborhood search for maximum diverse grouping problem. Yugoslav Journal of Operations Research, 24(1), 21–33.

    Article  Google Scholar 

Download references

Acknowledgements

The research has been supported in part by Research Grants 174010 and III 044006 of the Serbian Ministry of Education, Science and Technological Development, and a Natural Sciences and Engineering Research Council of Canada Discovery Grant (NSERC #205041-2014).

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Authors and Affiliations

  1. Royal Military College of Canada, Kingston, ON, Canada

    Jack Brimberg

  2. Mathematical Institute SANU, Belgrade, Serbia

    Nenad Mladenović, Raca Todosijević & Dragan Urošević

Authors
  1. Jack Brimberg
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  2. Nenad Mladenović
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  3. Raca Todosijević
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  4. Dragan Urošević
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Corresponding author

Correspondence to Dragan Urošević.

Appendix

Appendix

See Tables 8, 9, 10, 11, 12, 13, 14, 15, 16, 17.

Table 8 Comparison of different heuristics on RanReal instances with \(N=240\) nodes (\(G=12\)), and \(t_{\max } = N\) s
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Table 9 Comparison of different heuristics on RanReal instances with \(N=480\) nodes (\(G=20\)), and \(t_{\max } = N\) s
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Table 10 Comparison of different heuristics on RanReal instances with \(N=960\) nodes, and \(t_{\max } = N\) s
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Table 11 Comparison of different heuristics on MDG instances with \(N=2000\) nodes (\(G=50\)), and \(t_{\max } = N\) s
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Table 12 Comparison of different heuristics on Handover instances, \(t_{\max } = N\) s
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Table 13 Comparison of different heuristics on handover instances, \(t_{\max } = N\) s
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Table 14 Comparison of different heuristics on RanReal instances with \(N=240\) nodes (\(G=12\)), and \(t_{\max } = 5\times N = 1200\) s
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Table 15 Comparison of different heuristics on RanReal instances with \(N=480\) nodes (\(G=20\)) and \(t_{\max } = 5\times N = 2400\) s
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Table 16 Comparison of different heuristics on RanReal instances with \(N=960\) nodes and \(t_{\max } = 5\times N = 4800\) s
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Table 17 Comparison of different heuristics on MDG instances with \(N=2000\) nodes (\(G=50\)), and \(t_{\max }=5 \times N = 10{,}000\) s
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Brimberg, J., Mladenović, N., Todosijević, R. et al. Solving the capacitated clustering problem with variable neighborhood search. Ann Oper Res 272, 289–321 (2019). https://doi.org/10.1007/s10479-017-2601-5

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  • DOI: https://doi.org/10.1007/s10479-017-2601-5

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