SpringerLink
Log in

Multi-objective Flower Pollination Algorithm and Its Variants to Find Optimal Golomb Rulers for WDM Systems

  • Chapter
  • First Online:
Applications of Flower Pollination Algorithm and its Variants

Part of the book series: Springer Tracts in Nature-Inspired Computing ((STNIC))

  • 150 Accesses

Abstract

The high degree of complexities, inhomogeneity, and nonlinearities makes multi-objective engineering and industrial design problems very complex and time-consuming. The nature-inspired multi-objective algorithms (MOAs) are the best choice to deal with such design problems. This chapter presents a comparative study of the multi-objective flower pollination algorithm (MOFPA) and its hybrid variants to produce the optimal Golomb ruler (OGR) sequences. One of the main applications of OGR sequence is an unequally spaced bandwidth-efficient channel-allocation approach to suppress one of the major nonlinear four-wave mixing (FWM) crosstalk signals generated in an optical wavelength division multiplexing (WDM) system. Thus, the OGRs approach in an optical WDM system offers a bandwidth-efficient scheme, then the uniformly spaced channel-allocation approach. To explore the search space of the MOFPA, this chapter proposes an improved hybrid MOFPA variants based on multiple populations and fitness (cost) values-based differential evolution mutation features. The algorithms solve the bi-objective, one is ruler length and the other is a total unequally spaced channel bandwidth occupied by OGRs in the optical WDM system. The presented MOAs are compared with other existing classical computing approaches and nature-inspired optimization algorithms to find OGRs in terms of the length of the ruler, the total occupied channel bandwidth, the bandwidth expansion factor, the computational complexity, and computational time. The idea of computational complexity for the proposed algorithms is represented through the Big O notation. In order to validate the proposed MOAs, the non-parametric statistical Wilcoxon analysis is being considered. This comparative study also concludes that for large mark values, the hybrid algorithm potentially performs better than other approaches.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
EUR 29.95
Price includes VAT (Germany)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 117.69
Price includes VAT (Germany)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 160.49
Price includes VAT (Germany)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info
Hardcover Book
EUR 160.49
Price includes VAT (Germany)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Yang XS, Karamanoglu M, He X (2014) Flower pollination algorithm: a novel approach for multiobjective optimization. Eng Optim 46:1222–1237

    Article  MathSciNet  Google Scholar 

  2. Abbass HA, Sarker R (2002) The Pareto differential evolution algorithm. Int J Artif Intell Tools 11:531–552

    Article  Google Scholar 

  3. Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, NewYork

    MATH  Google Scholar 

  4. Bansal S, Singh AK, Gupta N (2017) Optimal Golomb ruler sequences generation: a novel parallel hybrid multi-objective bat algorithm. J Inst Eng (India) Ser B 98:43–64

    Google Scholar 

  5. Bansal S, Gupta N, Singh AK (2017) Nature-inspired metaheuristic algorithms to find near-OGR sequences for WDM channel allocation and their performance comparison. Open Math 15:520–547

    Article  MathSciNet  Google Scholar 

  6. Bansal S, Sharma K (2017) Nature-inspired based modified multi-objective BB-BC algorithm to find near-OGRs for optical WDM systems and its performance comparison. In: Hamou RM (ed) Handbook of research on biomimicry in information retrieval and knowledge management. IGI Global, pp 1–25

    Google Scholar 

  7. Bansal S (2017) Nature-inspired based multi-objective hybrid algorithms to find near-OGRs for optical WDM systems and their comparison. In: Hamou RM (ed) Advanced metaheuristic methods in big data retrieval and analytics. IGI Global, pp 175–211

    Google Scholar 

  8. Yang XS (2013) Optimization and metaheuristic algorithms in engineering. In: Yang XS, Gandomi AH, Talatahari S, Alavi AH (eds) Metaheursitics in water, geotechnical and transport engineering. Elsevier, pp 1–33

    Google Scholar 

  9. https://www.economyprofessor.com/pareto-optimality-1906

  10. Koziel S, Yang XS (2011) Computational optimization, methods and algorithms. Studies in computational intelligence. Springer, p 356

    Google Scholar 

  11. https://www.scholarpedia.org/article/Metaheuristic_Optimization

  12. Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison Wesley, USA

    MATH  Google Scholar 

  13. Storn R, Price KV (1997) Differential evolution-A simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359

    Article  MathSciNet  Google Scholar 

  14. Geem ZW, Kim JH (2001) A new heuristic optimization algorithm: harmony search. Simulation 76:60–68

    Article  Google Scholar 

  15. Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, Dec 1995, pp 1942–1948

    Google Scholar 

  16. Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12:702–713

    Article  Google Scholar 

  17. Erol OK, Eksin I (2006) A new optimization method: big bang-big crunch. Adv Eng Softw 37:106–111

    Article  Google Scholar 

  18. Yang XS (2009) Firefly algorithms for multimodal optimization. In: Stochastic algorithms: foundations and applications (SAGA-2009). Lecture notes in computer science, vol 5792. Springer, Berlin, pp 169–178

    Google Scholar 

  19. Yang XS (2010) A new metaheuristic bat-inspired algorithm. In: Gonzalez JR et al (eds) Nature inspired cooperative strategies for optimization (NISCO-2010). Studies in computational intelligence, Springer, Berlin, vol 284, pp 65–74

    Google Scholar 

  20. Yang XS, Deb S (2010) Engineering optimisation by cuckoo search. Int J Math Model Numer Optim 1:330–343

    MATH  Google Scholar 

  21. Bloom GS, Golomb SW (1977) Applications of numbered undirected graphs. Proc IEEE 65:562–570

    Article  Google Scholar 

  22. Thing VLL, Rao MK, Shum P (2003) Fractional optimal Golomb ruler based WDM channel allocation. In: The 8th opto-electronics and communication conference (OECC–2003), vol 23, pp 631–632

    Google Scholar 

  23. Shearer JB (1998) Some new disjoint Golomb rulers. IEEE Trans Inf Theory 44:3151–3153

    Article  MathSciNet  Google Scholar 

  24. https://theinf1.informatik.uni-jena.de/teaching/ss10/oberseminar-ss10

  25. Robinson JP (1979) Optimum Golomb rulers. IEEE Trans Comput 28:183–184

    Google Scholar 

  26. Shearer JB (1990) Some new optimum Golomb rulers. IEEE Trans Inf Theory 36:183–184

    Article  Google Scholar 

  27. Babcock WC (1953) Intermodulation interference in radio systems. Bell Syst Tech J 32:63–73

    Article  Google Scholar 

  28. Kwong WC, Yang GC (1997) An algebraic approach to the unequal-spaced channel-allocation problem in WDM lightwave systems. IEEE Trans Commun 45:352–359

    Article  Google Scholar 

  29. Aggarwal GP (2001) Nonlinear fiber optics, 2nd edn. Academic Press, San Diego, CA

    Google Scholar 

  30. Thing VLL, Shum P, Rao MK (2004) Bandwidth-efficient WDM channel allocation for four-wave mixing-effect minimization. IEEE Trans Commun 52:2184–2189

    Article  Google Scholar 

  31. Singh K, Bansal S (2013) Suppression of FWM crosstalk on WDM systems using unequally spaced channel algorithms—A survey. Int J Adv Res Comput Sci Softw Eng 3:25–31

    Google Scholar 

  32. Hwang B, Tonguz OK (1998) A generalized suboptimum unequally spaced channel allocation technique—Part I. IM/DDWDM Syst IEEE Trans Commun 46:1027–1037

    Article  Google Scholar 

  33. Tonguz OK, Hwang B (1998) A generalized suboptimum unequally spaced channel allocation technique—Part II: in coherent WDM systems. IEEE Trans Commun 46:1186–1193

    Article  Google Scholar 

  34. Atkinson MD, Santoro N, Urrutia J. Integer sets with distinct sums and differences and carrier frequency assignments for nonlinear repeaters. IEEE Trans. Commun. 34:614–617

    Google Scholar 

  35. Randhawa R, Sohal JS, Kaler RS (2009) Optimum algorithm for WDM channel allocation for reducing four-wave mixing effects. Optik 120:898–904

    Article  Google Scholar 

  36. Leitao T (2004) Evolving the maximum segment length of a Golomb ruler. In: Genetic and evolutionary computation conference, USA

    Google Scholar 

  37. Rankin WT (1993) Optimal Golomb rulers: an exhaustive parallel search implementation. M.S. thesis, Duke University

    Google Scholar 

  38. Cotta C, Dotú I, Fernández AJ, Hentenryck PV (2006) A memetic approach to Golomb rulers. Parallel problem solving from nature-PPSN IX. Lecture notes in computer science, vol 4193. Springer, Berlin, Heidelberg, pp 252–261

    Google Scholar 

  39. Robinson JP (2000) Genetic search for Golomb arrays. IEEE Trans Inf Theory 46:1170–1173

    Article  Google Scholar 

  40. Bansal S (2014) Optimal Golomb ruler sequence generation for FWM crosstalk elimination: soft computing versus conventional approaches. Appl Soft Comput 22:443–457

    Article  Google Scholar 

  41. Dotú I, Hentenryck PV (2005) A simple hybrid evolutionary algorithm for finding Golomb rulers. In: The 2005 IEEE congress on proceedings of evolutionary computation, vol 3, pp 2018–2023

    Google Scholar 

  42. Bansal S, Kumar S, Sharma H, Bhalla P (2011) Golomb ruler sequences optimization: a BBO approach. Int J Comput Sci Inf Secur 9:63–71

    Google Scholar 

  43. Bansal S, Kumar S, Sharma H, Bhalla P (2011) Generation of Golomb ruler sequences and optimization using biogeography based optimization. In: Proceedings of the 5th international multi conference on intelligent systems, sustainable, new and renewable energy technology and nanotechnology (IISN), 18–20 Feb 2011. Institute of Science and Technology Klawad, Haryana, India, pp 282–288

    Google Scholar 

  44. Bali S, Bansal S, Kamboj A (2015) A novel hybrid multi-objective BB-BC based channel allocation algorithm to reduce FWM crosstalk and its comparative study. Int J Comput Appl 124:38–45

    Google Scholar 

  45. Vyas J, Bansal S, Sharma K (2016) Generation of optimal Golomb rulers for FWM crosstalk reduction: BB-BC and FA approaches. In: Proceedings of the international conference on signal processing and communication (ICSC-2016), 26–28 Dec 2016. Jaypee Institute of Information Technology, Noida, India, pp 74–7.

    Google Scholar 

  46. Bansal S, Singh K (2014) A novel soft-computing algorithm for channel allocation in WDM systems. Int J Comput Appl 85:19–26

    Google Scholar 

  47. Bansal S, Jain P, Singh AK, Gupta N (2016) Improved multi-objective firefly algorithms to find optimal Golomb ruler sequences for optimal Golomb ruler channel allocation. World Acad Sci Eng Technol Int Sci Index Int J Math Comput Phys Electr Comput Eng 10:350–357

    Google Scholar 

  48. Bansal S, Gupta N, Singh AK (2021) Application of Bat inspired computing algorithm and its variants in search of near-optimal Golomb rulers for WDM systems: a comparative study. Dey N, Ra**ikanth V (eds) Applications of Bat algorithm and its variants. Springer book series Springer tracts in nature-inspired computing, pp 79–101

    Google Scholar 

  49. Bansal S (2019) A comparative study of nature–inspired metaheuristic algorithms in search of near-to-optimal Golomb rulers for the FWM crosstalk elimination in WDM systems. Appl Artif Intel 33:1199–1265

    Article  Google Scholar 

  50. Bansal S, Chauhan R, Kumar P (2014) A cuckoo search based WDM channel allocation algorithm. Int J Comput Appl 96:6–12

    Google Scholar 

  51. Kumari N, Singh T, Bansal S (2016) Optimal Golomb ruler sequences as WDM channel-allocation algorithm generation: Cuckoo search algorithm with mutation. Int J Comput Appl 142:21–27

    Google Scholar 

  52. Bansal S (2020) Performance comparison of five metaheuristic nature-inspired algorithms to find near-OGRs for WDM systems. Appl Artif Rev. https://doi.org/10.1007/s10462-020-09829-2

    Article  Google Scholar 

  53. Dollas A, Rankin WT, McCracken D (1998) A new algorithm for Golomb ruler derivation and proof of the 19 mark ruler. IEEE Trans Inf Theory 44:379–382

    Article  MathSciNet  Google Scholar 

  54. Lavoie P, Haccoun D, Savaria Y (1991) New VLSI architectures for fast soft-decision threshold decoders. IEEE Trans Commun 39:200–207

    Article  Google Scholar 

  55. Robinson JP, Bernstein AJ (1967) A class of binary recurrent codes with limited error propagation. IEEE Trans Inf Theory 13:106–113

    Article  Google Scholar 

  56. Cotta C, Fernández AJ (2005) Analyzing fitness landscapes for the optimal Golomb ruler problem. In: Gottlieb J, Raidl G (eds) Evolutionary computation in combinatorial optimization. Lecture notes in computer science, vol 3448. Springer, Berlin, pp 68–79

    Google Scholar 

  57. Fang RJF, Sandrin WA (1977) Carrier frequency assignment for non-linear repeaters. Comsat Tech Rev 7:227–245

    Google Scholar 

  58. Blum EJ, Biraud F, Ribes JC (1974) On optimal synthetic linear arrays with applications to radio astronomy. IEEE Trans Antennas Propag 22:108–109

    Article  Google Scholar 

  59. Memarsadegh N (2013) Golomb patterns: Introduction, applications, and citizen science game. In: Information science and technology (IS&T). Seminar Series NASA GSFC. https://istcolloq.gsfc.nasa.gov/fall2013/presentations/memarsadeghi.pdf

  60. Project educational NASA computational and scientific studies (enCOMPASS). https://encompass.gsfc.nasa.gov/cases.html

  61. Pant S, Kumar A, Ram M (2017) Flower pollination algorithm development: a state of art review. Int J Syst Assur Eng Manage 8:1858–1866

    Article  Google Scholar 

  62. Singh D, Singh U, Salgotra R (2018) An extended version of flower pollination algorithm. Arab J Sci Eng 43:7573–7603

    Article  Google Scholar 

  63. Dhal KG, Galvez J, Das S (2020) Toward the modification of flower pollination algorithm in clustering based image segmentation. Neural Comput Appl 32:3059–3077

    Article  Google Scholar 

  64. Jain P, Bansal S, Singh AK, Gupta N (2015) Golomb ruler sequences optimization for FWM crosstalk reduction: multi–population hybrid flower pollination algorithm. In: Proceedings of the progress in electromagnetics research symposium (PIERS), Prague, Czech Republic, 06–09 July 2015, pp 2463–2467

    Google Scholar 

  65. Colannino J (2003) Circular and modular Golomb rulers. https://cgm.cs.mcgill.ca/~athens/cs507/Projects/2003/JustinColannino/

  66. https://mathworld.wolfram.com/GolombRuler.html

  67. Distributed.net Project OGR. https://www.distributed.net/ogr

  68. Soliday SW, Homaifar A, Lebby GL (1995) Genetic algorithm approach to the search for Golomb rulers. In: Proceedings of the sixth international conference on genetic algorithms (ICGA–95), Morgan Kaufmann, pp 528–535

    Google Scholar 

  69. García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 special session on real parameter optimization. J Heuristics 15:617–644

    Article  Google Scholar 

Download references

Acknowledgements

Thank you for your cooperation and contribution.

Author information

Authors and Affiliations

  1. Department of Electronics and Communication Engineering, University Institute of Engineering, Chandigarh University, Gharuan, Mohali, India

    Shonak Bansal

  2. Department of Electronics and Communication Engineering, Punjab Engineering College (Deemed to be University), Sector-12, Chandigarh, India

    Neena Gupta & Arun K. Singh

Authors
  1. Shonak Bansal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Neena Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Arun K. Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shonak Bansal .

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, JIS University, Kolkata, India

    Nilanjan Dey

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Bansal, S., Gupta, N., Singh, A.K. (2021). Multi-objective Flower Pollination Algorithm and Its Variants to Find Optimal Golomb Rulers for WDM Systems. In: Dey, N. (eds) Applications of Flower Pollination Algorithm and its Variants. Springer Tracts in Nature-Inspired Computing. Springer, Singapore. https://doi.org/10.1007/978-981-33-6104-1_8

Download citation

Publish with us

Policies and ethics

Search

Navigation