[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Log in

The band collocation problem

  • Published:
Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

In order to reduce costs in the telecommunication sector, many mathematical models have been developed. Over time, these models either fall out out of use or are revised according to new technological developments. The Bandpass Problem (BP) is an optimization problem introduced in 2004 to reduce hardware costs in communication networks. However, over time, technological advances in fiber-optic networks have caused the BP to lose functionality and usability. Major changes should be made to the model to make the BP functional again. It is necessary to define the problem after having made these changes as a new problem, not as a revised problem. In this paper, we first review the BP. We then discuss the notion that the BP has become unusable due to technological developments. We introduce a new problem called the Band Collocation Problem (BCP), which fixes the issues in the BP. We also develop several mathematical models of the BCP. Furthermore, we prove that the BCP is NP-hard. In order to encourage further research, we develop a Library of Band Collocation Problems. Finally, we present heuristic and meta-heuristic methods to solve the BCP and compare the computational results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Babayev D, Nuriyev U, Bell G, Berberler M, Kutucu H, Gürsoy A, Kurt M (2008) Mathematical modelling of a telecommunication packing problem and a heuristic approach for finding a solution. In: International conference on control and optimization with industrial applications, Baku, Azerbaijan, June, pp 2–4

  • Babayev DA, Bell GI, Nuriyev UG (2009) The bandpass problem: combinatorial optimization and library of problems. J Comb Opt 18(2):151–172. https://doi.org/10.1007/s10878-008-9143-3

    Article  MathSciNet  MATH  Google Scholar 

  • Babayev DA, Nuriyev UG, Bell GI, Berberler ME, Gursoy A, Kurt M (2007) Library of bandpass problems (Accessed December 25 2019). http://fenfak.ege.edu.tr/~arifgursoy/BandpassProblemsLibrary/

  • Bell G, Babayev D (2004) Bandpass problem. In: Annual INFORMS meeting, October, Denver, CO, USA

  • Berberler M, Gürsoy A (2010) Genetic algorithm approach for bandpass problem. In: 24th Mini EURO conference on continuous optimization and information-based technologies in the financial sector (MEC EurOPT 2010) pp 201–206

  • Chen ZZ, Wang L (2012) An improved approximation algorithm for the bandpass-2 problem. In: International conference on combinatorial optimization and applications, Springer, Heidelberg, pp 188–199

  • Cheng MX, Li Y, Du DZ (2006) Combinatorial optimization in communication networks, vol 18. Springer, Heidelberg

    Book  MATH  Google Scholar 

  • Croes GA (1958) A method for solving traveling-salesman problems. Oper Res 6(6):791–812

    Article  MathSciNet  MATH  Google Scholar 

  • Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. WH Freman and Co, New York

    MATH  Google Scholar 

  • Goraliski WJ (1997) SONET: a guide to synchronous optical networks. McGraw-Hill Inc., New York

    Google Scholar 

  • Gursoy A, Kurt M, Kutucu H, Nuriyev U (2016) A heuristic algorithm for the band collocation problem. In: Proceeding of the 10th IEEE international conference on application of information and communication technologies (AICT-2016), Azerbaijan, Baku, October 12–14, pp 473–476

  • Gursoy A, Kurt M, Kutucu H, Nuriyev U (2017) New heuristics and meta-heuristics for the bandpass problem. Eng Sci Technol Int J 20(6):1531–1539

    Google Scholar 

  • Gursoy A, Tekin A, Keserlioğlu S, Kutucu H, Kurt M, Nuriyev U (2017) An improved binary integer programming model of the band collocation problem. J Mod Technol Eng 2(1):34–42

    Google Scholar 

  • Huang L, Tong W, Goebel R, Liu T, Lin G (2015) A 0.5358-approximation for bandpass-2. J Comb Opt 30(3):612–626

    Article  MathSciNet  MATH  Google Scholar 

  • Iannone E (2016) Telecommunication networks. CRC Press, Boca Raton

    Google Scholar 

  • Karaboga D (2005) An idea based on honey bee swarm for numerical optimization, vol 200, pp 1–10. Technical report-tr06, Erciyes University, Engineering Faculty, Computer Engineering Department

  • Karaboga D, Basturk B (2008) On the performance of artificial bee colony (abc) algorithm. Appl Soft Comput 8(1):687–697

    Article  Google Scholar 

  • Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680

    Article  MathSciNet  MATH  Google Scholar 

  • Kumar S, Deen MJ (2014) Fiber optic communications: fundamentals and applications. John Wiley & Sons, New Jersey

    Book  Google Scholar 

  • Kurt M, Kutucu H, Gursoy A, Nuriyev U (2014) The optimization of the bandpass lengths in the multi-bandpass problem. In: Proceedings of the seventh international conference on management science and engineering management, Springer, pp 115–123

  • Kutucu H, Gursoy A, Kurt M, Nuriyev U (2019) On the solution approaches of the band collocation problem. TWMS J Appl Eng Math 9(4):724

    Google Scholar 

  • Kutucu H, Gursoy A, Kurt M, Nuriyev UG (2016) The band collocation problem: a library of problems and a metaheuristic approach. In: Proceeding of the international conference on discrete optimization and operations research (DOOR-2016), vol 1623, Vladivostok, Russia, September 19–23, pp 464–476. http://ceur-ws.org/Vol-1623/paperls6.pdf

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

    Article  MathSciNet  MATH  Google Scholar 

  • Lin G (2011) On the bandpass problem. J Comb Opt 22(1):71–77

    Article  MathSciNet  MATH  Google Scholar 

  • Nuriyev U, Kurt M, Kutucu H, Gursoy A (2015) The band collocation problem and its combinatorial model. In: The international conference mathematical and computational modelling in science and technology(ICMCMST 2015), pp 140–141

  • Nuriyev UG, Kurt M, Kutucu H, Gursoy A (2019) Band collocation problem online library (bcplib). http://fenfak.ege.edu.tr/~arifgursoy/bps/ (Accessed December 25 2019)

  • Nuriyev UG, Kutucu H, Kurt M (2011) Mathematical models of the bandpass problem and ordermatic computer game. Math Comput Modell 53(5–6):1282–1288

    Article  MATH  Google Scholar 

  • Nuriyeva F (2016) On a generalized sequential partially covering problem. Appl Comput Math 15(2):239–242

    MathSciNet  MATH  Google Scholar 

  • Osman IH, Christofides N (1994) Capacitated clustering problems by hybrid simulated annealing and tabu search. Int Trans Oper Res 1(3):317–336

    Article  MATH  Google Scholar 

  • Optical multiplexers. http://shop.fiber24.net/index.php/en/Optical-Multiplexers/l-OPTIC-MUX (2018 (Accessed 25 May 2018))

  • Resende MG, Pardalos PM (2008) Handbook of optimization in telecommunications. Springer, Berlin

    MATH  Google Scholar 

  • Sánchez-Oro J, Laguna M, Martí R, Duarte A (2016) Scatter search for the bandpass problem. J Global Optim 66(4):769–790

    Article  MathSciNet  MATH  Google Scholar 

  • Tong W, Goebel R, Liu T, Lin G (2014) Approximating the maximum multiple rna interaction problem. Theoret Comput Sci 556:63–70

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors are grateful to the anonymous referees for their constructive comments and valuable suggestions which have helped us very much to improve the quality of the paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Arif Gursoy.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kutucu, H., Gursoy, A., Kurt, M. et al. The band collocation problem. J Comb Optim 40, 454–481 (2020). https://doi.org/10.1007/s10878-020-00576-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10878-020-00576-2

Keywords

Mathematics Subject Classification

Navigation