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Scatter search for the bandpass problem

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Abstract

We tackle a combinatorial problem that consists of finding the optimal configuration of a binary matrix. The configuration is determined by the ordering of the rows in the matrix and the objective function value is associated with a value B, the so-called bandpass number. In the basic version of the problem, the objective is to maximize the number of non-overlapping blocks containing B consecutive cells with a value of one in each column of the matrix. We explore variants of this basic problem and use them to test heuristic strategies within the scatter search framework. An existing library of problem instances is used to perform scientific testing of the proposed search procedures to gain insights that may be valuable in other combinational optimization settings. We also conduct competitive testing to compare outcomes with methods published in the literature and to improve upon previous results.

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Notes

  1. The Library of Bandpass Problems can be found here http://sci.ege.edu.tr/~math/BandssProblemsLibrary/.

  2. Problem instances introduced in [19] are found here http://fen.ege.edu.tr/arifgursoy/mopt/.

  3. http://sci.ege.edu.tr/~math/BandpassProblemsLibrary/.

  4. http://fen.ege.edu.tr/arifgursoy/mbpopt/.

References

  1. Babayev, V., Bell, G.I., Nuriyev, U.G.: The bandpass problem: combinatorial optimization and library of problems. J. Combin. Optim. 18(2), 151–172 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. Berberler, M.E., Gürsoy, A.: Genetic algorithm approach for bandpass problem. In: Kasimbeyli R., Dinçer C., Özpeynirci S., Sakalauskas L., (eds.) 24th Mini EURO Conference on Continuous Optimization and Information-Based Technologies in the Financial Sector (MEC EurOPT 2010), pp. 201–206. Vilnius Gediminas Technical University Publishing House Technika, İzmir (2010)

  3. Campos, V., Martí, R., Sánchez-Oro, J., Duarte, A.: GRASP with path relinking for the orienteering problem. J. Oper Res. Soc. 65(2), 1800–1813 (2014)

  4. Das, A., Roberts, M.: Metric distances of permutations. www.cra.org/Activities/craw_archive/dmp/awards/2004/Das/paper.ps. (2004)

  5. Duarte, A., Martí, R., Glover, F., Gortázar, F.: Hybrid scatter tabu search for unconstrained global optimization. Ann. Oper. Res. 183(1), 95–123 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Duarte, A., Sánchez-Oro, J., Resende, M.G.C., Glover, F., Martí, R.: GRASP with exterior path relinking for differential dispersion minimization. Inf. Sci. 296(1), 46–60 (2015)

  7. Duarte, A., Martí, R.: Tabu search and grasp for the maximum diversity problem. Eur. J. Oper. Res. 178(1), 71–84 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Feo, T.A., Resende, M.G.C.: A probabilistic heuristic for a computationally difficult set covering problem. Oper. Res. Lett. 8, 67–71 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  9. Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. J. Glob. Optim. 6, 109–133 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  10. Gallego, M., Duarte, A., Laguna, M., Martí, R.: Hybrid heuristics for the maximum diversity problem. Comput. Optim. Appl. 44(3), 411–426 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gallego, M., Laguna, M., Martí, R., Duarte, A.: Tabu search with strategic oscillation for the maximally diverse grouping problem. J. Oper. Res. Soc. 64(5), 724–734 (2013)

  12. Glover, F.: Heuristics for integer programming using surrogate constraints. Decis. Sci. 8(1), 156–166 (1977)

    Article  Google Scholar 

  13. Glover, F.: A template for scatter search and path relinking. Lecture Notes in Computer Science, 1363, 1–51 (1998)

  14. Glover, F.: Exterior path relinking for zero-one optimization. Int. J. Appl. Metaheur. Comput. 5(3), 1–8

  15. Glover, F., Laguna, M.: Tabu Search. Springer, New York (1997)

    Book  MATH  Google Scholar 

  16. Goralski, W.J.: SONET, a Guide to Synchronous Optical Networks. McGraw-Hill, New York (1997)

    Google Scholar 

  17. Gürsoy, A., Nuriyev, U.G.: Genetic algorithm for multi bandpass problem and library of problems. In: Proceedings of the IV International Conference on Problems of Cybernetics and Informatics (PCI), Section I, Information and Communication Technologies, Baku, Azerbaijan, Sept 12–14, 134–138 (2012)

  18. Kaminow, I.P., Saleh, A.A.M., Thomas, R.E., Chan, V.W.S., Stevens, M.L.: A wideband all-optical WDM network. IEEE J. Sel. Areas Commun. 14(5), 780–799 (1996)

    Article  Google Scholar 

  19. Kurt, M., Kutucu, H., Gürsoy, A., Nuriyev, U.: The optimization of the bandpass lengths in the multi-bandpass problem. In: Proceedings of the Seventh International Conference on Management Science and Engineering Management: Focused on Electrical and Information Technology, Xu, J., Fry, J. A., Lev, B., Hajiyev, A. (eds.) (1): 115–123. Springer, Berlin (2014)

  20. Laguna, M., Martí, R.: Scatter Search: Methodology and Implementations in C. Kluwer, Boston (2003)

    Book  MATH  Google Scholar 

  21. Li, Z., Lin, G.: The three column bandpass problem is solvable in linear time. Theor. Comput. Sci. 412(4–5), 281–299 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  22. Lin, G.: On the bandpass problem. J. Combin. Optim. 22(1), 71–77 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. Martí, R., Duarte, A., Laguna, M.: Advanced scatter search for the max-cut problem. INFORMS J. Comput. 21(1), 26–38 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  24. Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  25. Nuriyev, U.G., Kutucu, H., Kurt, M.: Mathematical models of the bandpass problem and OrderMatic computer game. Math. Comput. Model. 53, 1282–1288 (2011)

    Article  MATH  Google Scholar 

  26. Pantrigo, J.J., Martí, R., Duarte, A., Pardo, E.G.: Scatter search for the cutwidth minimization problem. Ann. Oper. Res. 199(1), 285–304 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  27. Ramaswami, R., Sivarajan, K., Sasaki, G.: Optical Networks: A Practical Perspective. Morgan Kaufmann, San Francisco (1998)

    Google Scholar 

  28. Resende, M., Martí, R., Gallego, M., Duarte, A.: GRASP and path relinking for the max–min diversity problem. Comput. Oper. Res. 37, 498–508 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  29. Sánchez-Oro, J., Laguna, M., Duarte, A., Martí, R.: Scatter search for the profile minimization problem. Networks. 65(1), 10–21 (2015)

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Acknowledgments

This research was partially supported by the Ministerio de Economía y Competitividad of Spain (Project Number TIN2015-65460-C2-P) and the Comunidad de Madrid (Project Number S2013/ICE-2894).

Author information

Authors and Affiliations

  1. Departamento de Ciencias de la Computación, Universidad Rey Juan Carlos, Madrid, Spain

    Jesús Sánchez-Oro & Abraham Duarte

  2. Leeds School of Business, University of Colorado at Boulder, Boulder, CO, USA

    Manuel Laguna

  3. Departamento de Estadística e Investigación Operativa, Universidad de Valencia, Valencia, Spain

    Rafael Martí

Authors
  1. Jesús Sánchez-Oro
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  2. Manuel Laguna
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  3. Rafael Martí
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  4. Abraham Duarte
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Corresponding author

Correspondence to Abraham Duarte.

Appendices

Appendix 1

Table 7 shows the objective function values of the new best-known solutions for the BKS instances. A dash indicates that no solution better than the current best known was found in our experimentation.

Table 7 New best solutions found during the scientific experimentation for SS1
Full size table

Appendix 2

LocalSolver input and model functions for the experiments with BP2.

figure d

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Sánchez-Oro, J., Laguna, M., Martí, R. et al. Scatter search for the bandpass problem. J Glob Optim 66, 769–790 (2016). https://doi.org/10.1007/s10898-016-0446-0

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