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Performance comparison of five metaheuristic nature-inspired algorithms to find near-OGRs for WDM systems

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Abstract

The metaheuristic approaches inspired by the nature are becoming powerful optimizing algorithms for solving NP-complete problems. This paper presents five nature-inspired metaheuristic optimization algorithms to find near-optimal Golomb ruler (OGR) sequences in a reasonable time. In order to improve the search space and further improve the convergence speed and optimization precision of the metaheuristic algorithms, the improved algorithms based on mutation strategy and Lévy-flight search distribution are proposed. These two strategies help the metaheuristic algorithms to jump out of the local optimum, improve the global search ability so as to maintain the good population diversity. The OGRs found their potential application in channel-allocation method to suppress the four-wave mixing crosstalk in optical wavelength division multiplexing systems. The results conclude that the proposed algorithms are superior to the existing conventional computing algorithms i.e. extended quadratic congruence and search algorithm and nature-inspired optimization algorithms i.e. genetic algorithms, biogeography based optimization and simple big bang–big crunch to find near-OGRs in terms of ruler length, total optical channel bandwidth and computation time. The idea of computational complexity for the proposed algorithms is represented through the Big O notation. In order to validate the proposed algorithms, the non-parametric statistical Wilcoxon analysis is being considered.

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References

  • Afshar MH, Motaei I (2011) Constrained big bang-big crunch algorithm for optimal solution of large scale reservoir operation problem. Int J Optim Civil Eng 2:357–375

    Google Scholar 

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

    Google Scholar 

  • Atkinson MD, Santoro N, Urrutia J (1986) Integer sets with distinct sums and differences and carrier frequency assignments for nonlinear repeaters. IEEE Trans Commun 34(6):614–617

    Google Scholar 

  • Ayari N, Thé Van Luong, Jemai A (2010) A hybrid genetic algorithm for Golomb ruler problem. In: ACS/IEEE international conference on computer systems and applications (AICCSA-2010), pp 1–4

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

    Google Scholar 

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

    MathSciNet  Google Scholar 

  • 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 Publisher, ‎Philadelphia, pp 175–211

  • 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 Intell 33(14):1199–1265

    Google Scholar 

  • 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 Publisher, ‎Philadelphia, pp 1–25

  • Bloom GS, Golomb SW (1977) Applications of numbered undirected graphs. Proc IEEE 65(4):562–570

    Google Scholar 

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

    Google Scholar 

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

  • 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 

  • Cotta C, Hemert JV (eds) (2008) Recent advances in evolutionary computation for combinatorial optimization. In: Studies in computational intelligence, vol 153. Springer

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

  • Dimitromanolakis A (2002) Analysis of the Golomb ruler and the sidon set problems, and determination of large, near-optimal Golomb rulers. Master’s Thesis, Department of Electronic and Computer Engineering, Technical University of Crete

  • Distributed.net. Project OGR. http://www.distributed.net/ogr

  • 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(1):379–382

    MathSciNet  MATH  Google Scholar 

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

  • Drakakis K (2009) A review of the available construction methods for Golomb rulers. Adv Math Commun 3(3):235–250

    MathSciNet  MATH  Google Scholar 

  • Drakakis K, Rickard S (2010) On the construction of nearly optimal Golomb rulers by unwrapping costas arrays. Contemp Eng Sci 3(7):295–309

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • Forghieri F, Tkach RW, Chraplyvy AR (1995) WDM systems with unequally spaced channels. J Lightw Technol 13:889–897

    Google Scholar 

  • Galinier P, Jaumard B, Morales R, Pesant G (2001) A constraint-based approach to the Golomb ruler problem. In: 3rd international workshop on integration of AI and OR techniques (CP-AI-OR 2001)

  • Gandomi AH, Yang X-S, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput Int J Simul Based Eng 29(1):17–35

    Google Scholar 

  • 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(6):617–644

    MATH  Google Scholar 

  • Guo S-S, Wang J-S, Ma X-X (2019) Improved bat algorithm based on multipopulation strategy of Island model for solving global function optimization problem. Comput Intell Neurosci 2019(1):1–12

    Google Scholar 

  • http://theinf1.informatik.uni-jena.de/teaching/ss10/oberseminar-ss10

  • http://mathworld.wolfram.com/PerfectRuler.html

  • http://mathworld.wolfram.com/GolombRuler.html

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

    Google Scholar 

  • Iglesias A, Gálvez A, Suárez P, Shinya M, Yoshida N, Otero C, Manchado C, Gomez-Jauregui V (2018) Cuckoo search algorithm with Lévy flights for global-support parametric surface approximation in reverse engineering. Symmetry 10(58):1–25

    Google Scholar 

  • Koziel S, Yang X-S (eds) (2011) Computational optimization, methods and algorithms. In: Studies in computational intelligence, vol 356. Springer

  • Kwong WC, Yang GC (1997) An algebraic approach to the unequal-spaced channel–allocation problem in WDM lightwave systems. IEEE Trans Commun 45(3):352–359

    Google Scholar 

  • Lam AW, Sarwate DV (1988) On optimal time-hopping patterns. IEEE Trans Commun 36:380–382

    Google Scholar 

  • Lavoie P, Haccoun D, Savaria Y (1991) New VLSI architectures for fast soft-decision threshold decoders. IEEE Trans Commun 39(2):200–207

    Google Scholar 

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

  • Li Y, Li X, Liu J, Ruan X (2019) An improved bat algorithm based on Lévy flights and adjustment factors. Symmetry 11(7):1–19

    Google Scholar 

  • Mareli M, Twala B (2018) An adaptive Cuckoo search algorithm for optimisation. Appl Comput Inform 14(2):107–115

    Google Scholar 

  • Memarsadegh N (2013) Golomb patterns: introduction, applications, and citizen science game. In: Information Science and Technology (IS&T), Seminar Series NASA GSFC. http://istcolloq.gsfc.nasa.gov/fall2013/presentations/memarsadeghi.pdf

  • Mitchell M (2004) An introduction to genetic algorithms. Prentice Hall of India Pvt. Ltd., New Delhi

    MATH  Google Scholar 

  • Price K, Storn R, Lampinen J (2005) Differential evolution—a practical approach to global optimization. Springer, Berlin

    MATH  Google Scholar 

  • Project Educational NASA Computational and Scientific Studies (enCOMPASS). http://encompass.gsfc.nasa.gov/cases.html

  • Rajasekaran S, Vijayalakshmi Pai GA (2004) Neural networks, fuzzy logic, and genetic algorithms-synthesis and applications. Prentice Hall of India Pvt. Ltd., New Delhi

    Google Scholar 

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

    Google Scholar 

  • Rankin WT (1993) Optimal Golomb rulers: an exhaustive parallel search implementation. M.S. Thesis, Duke University. http://people.ee.duke.edu/~wrankin/golomb/golomb.html. Accessed Dec 2003

  • Robinson JP (1979) Optimum Golomb rulers. IEEE Trans Comput 28(12):183–184

    Google Scholar 

  • Robinson JP (2000) Genetic search for Golomb arrays. IEEE Trans Inf Theory 46(3):1170–1173

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Sardesai HP (1999) A simple channel plan to reduce effects of nonlinearities in dense WDM systems. Lasers Electro-Opt 5:183–184

    Google Scholar 

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

    Google Scholar 

  • Shearer JB (1998) Some new disjoint Golomb rulers. IEEE Trans Inf Theory 44(7):3151–3153

    MathSciNet  MATH  Google Scholar 

  • Singh K, Bansal S (2013) Suppression of FWM crosstalk on WDM systems using unequally spaced channel algorithms—a survey. Int J Adv Comput Sci Softw Eng (IJARCSSE) 3(12):25–31

    Google Scholar 

  • 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

  • Storn R, Price KV (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359

    MathSciNet  MATH  Google Scholar 

  • Tabakov PY (2011) Big bang-big crunch optimization method in optimum design of complex composite laminates. World Acad Sci Eng Technol 77:835–839

    Google Scholar 

  • Thing VLL, Shum P, Rao MK (2004) Bandwidth-efficient WDM channel allocation for four-wave mixing-effect minimization. IEEE Trans Commun 52(12):2184–2189

    Google Scholar 

  • 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

    Google Scholar 

  • Yang X-S (2010a) Nature-inspired metaheuristic algorithms, 2nd edn. Luniver Press, Bristol

    Google Scholar 

  • Yang X-S (2010b) Firefly algorithm, stochastic test functions and design optimisation. Int J Bio-Inspired Comput 2(2):78–84

    Google Scholar 

  • Yang X-S (2010c) Firefly algorithm, Levy flights and global optimization. In: Bramer M, Ellis R, Petridis (eds) Research and development in intelligent systems XXVI. Springer, London, pp 209–218

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

  • Yang X-S (2011a) Chaos-enhanced firefly algorithm with automatic parameter tuning. Int J Swarm Intell Res (IJSIR) 2(4):1–11

    Google Scholar 

  • Yang X-S (2011b) Review of metaheuristics and generalized evolutionary walk algorithm. Int J Bio-Inspired Comput 3(2):77–84

    Google Scholar 

  • Yang X-S (2012a) Nature-inspired mateheuristic algorithms: success and new challenges. J Comput Eng Inf Technol (JCEIT) 1(1):1–3

    Google Scholar 

  • Yang X-S (2012b) Flower pollination algorithm for global optimization. In: Unconventional computation and natural computation 2012, Lecture notes in computer science, vol 7445, Springer, Berlin, pp 240–249

  • Yang X-S (2013a) Optimization and metaheuristic algorithms in engineering. In: Yang XS, Gandomi AH, Talatahari S, Alavi AH (eds) Metaheursitics in water, geotechnical and transport engineering. Elsevier, New York. https://doi.org/10.1016/B978-0-12-398296-4.00001-5

    Chapter  Google Scholar 

  • Yang X-S (2013b) Bat algorithm: literature review and applications. Int J Bio-Inspired Computat 5(3):141–149

    Google Scholar 

  • Yang X-S, Deb S (2010a) Eagle strategy using levy walk and firefly algorithms for stochastic optimization. In: Gonzalez JR et al (eds) Nature inspired cooperative strategies for optimization (NISCO-2010), Studies in computational intelligence, vol 284. Springer, Berlin, pp 101–111

  • Yang X-S, Deb S (2010b) Engineering optimisation by Cuckoo search. Int J Math Model Numer Optim 1(4):330–343

    MATH  Google Scholar 

  • Yang X-S, Deb S (2014) Cuckoo search: recent advances and applications. Neural Comput Appl 24(1):169–174

    Google Scholar 

  • Yang X-S, He XS (2013) Firefly algorithm: recent advances and applications. Int J Swarm Intell 1(1):36–50

    Google Scholar 

  • Yang X-S, Karamanoglu M, He XS (2014) Flower pollination algorithm: a novel approach for multiobjective optimization. Eng Optim 46(9):1222–1237

    MathSciNet  Google Scholar 

  • Yesil E, Urbas L (2010) Big bang-big crunch learning method for fuzzy cognitive maps. World Acad Sci Eng Technol 71:815–824

    Google Scholar 

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

    Shonak Bansal

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  1. Shonak Bansal
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Appendix

Appendix

Tables 8 and 9 lists the near-OGRs found by proposed algorithms for various marks.

Table 8 Near-OGRs found by MBB–BC, FA and MFA
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Table 9 Near-OGRs found by BA, MBA, CSA, CSAM, FPA and FPAM
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Bansal, S. Performance comparison of five metaheuristic nature-inspired algorithms to find near-OGRs for WDM systems. Artif Intell Rev 53, 5589–5635 (2020). https://doi.org/10.1007/s10462-020-09829-2

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