CINXE.COM

{"title":"Improved Multi\u2013Objective Firefly Algorithms to Find Optimal Golomb Ruler Sequences for Optimal Golomb Ruler Channel Allocation ","authors":"Shonak Bansal, Prince Jain, Arun Kumar Singh, Neena Gupta","volume":115,"journal":"International Journal of Physical and Mathematical Sciences","pagesStart":350,"pagesEnd":358,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10004930","abstract":"Recently nature\u2013inspired algorithms have widespread use throughout the tough and time consuming multi\u2013objective scientific and engineering design optimization problems. In this paper, we present extended forms of firefly algorithm to find optimal Golomb ruler (OGR) sequences. The OGRs have their one of the major application as unequally spaced channel\u2013allocation algorithm in optical wavelength division multiplexing (WDM) systems in order to minimize the adverse four\u2013wave mixing (FWM) crosstalk effect. The simulation results conclude that the proposed optimization algorithm has superior performance compared to the existing conventional computing and nature\u2013inspired optimization algorithms to find OGRs in terms of ruler length, total optical channel bandwidth and computation time.","references":"[1]\tW. C. Kwong, and G. C. Yang, \u201cAn Algebraic Approach to the Unequal\u2013Spaced Channel\u2013Allocation Problem in WDM Lightwave Systems\u201d, IEEE Transactions on Communications, Vol. 45, No. 3, pp. 352\u2013359, March\u20131997.\r\n[2]\tV. L. L. Thing, P. Shum, and M. K. Rao, \u201cBandwidth\u2013Efficient WDM Channel Allocation for Four\u2013Wave Mixing\u2013Effect Minimization\u201d, IEEE Transactions on Communications, Vol. 52, No. 12, pp. 2184\u20132189, December 2004.\r\n[3]\tO. K. Tonguz and B. Hwang, \u201cA Generalized Suboptimum Unequally Spaced Channel Allocation Technique\u2014Part II: In coherent WDM systems\u201d, IEEE Transactions on Communications, Vol. 46, pp. 1186\u20131193, September\u20131998.\r\n[4]\tR. Randhawa, J. S. Sohal, R. S. Kaler, \u201cOptimum Algorithm for WDM Channel Allocation for Reducing Four\u2013Wave Mixing Effects\u201d, Optik 120 (2009), pp. 898\u2013904, 2009.\r\n[5]\tG. S. Bloom and S. W. Golomb, \u201cApplications of Numbered Undirected Graphs\u201d, Proceedings of the IEEE, Vol. 65, No. 4, pp. 562\u2013570, April\u20131977.\r\n[6]\tJ. B. Shearer, \u201cSome New Disjoint Golomb Rulers\u201d, IEEE Transactions on Information Theory, Vol. 44, No. 7, pp. 3151\u20133153, November\u20131998.\r\n[7]\tDistributed.net, \u201cProject OGR\u201d. Available at http:\/\/www.distributed.net\/ogr.\r\n[8]\tK. Drakakis and S. Rickard, \u201cOn the Construction of Nearly Optimal Golomb Rulers by Unwrapping Costas Arrays\u201d, Contemporary Engineering Sciences, Vol. 3, No. 7, pp. 295\u2013309, July\u20132010. \r\n[9]\tS. Bansal, \u201cOptimal Golomb Ruler Sequence Generation for FWM Crosstalk Elimination: Soft Computing Versus Conventional Approaches\u201d, Applied Soft Computing, Vol. 22, pp. 443\u2013457, September\u20132014.\r\n[10]\thttp:\/\/mathworld.wolfram.com\/PerfectRuler.html.\r\n[11]\thttp:\/\/mathworld.wolfram.com\/GolombRuler.html.\r\n[12]\tC. Meyer and P. A. Papakonstantinou, \u201cOn the complexity of constructing Golomb Rulers\u201d, Discrete Applied Mathematics, Vol. 157, pp. 738\u2013748, 2009.\r\n[13]\tN. Memarsadegh, \u201cGolomb Patterns: Introduction, Applications, and Citizen Science Game\u201d, Information Science and Technology (IS&T), Seminar Series NASA GSFC, September 11, 2013. Available at http:\/\/istcolloq.gsfc.nasa.gov\/fall2013\/presentations\/memarsadeghi.pdf.\r\n[14]\tJ. P. Robinson, \u201cOptimum Golomb Rulers\u201d, IEEE Transactions on Computers, Vol. 28, No. 12, pp. 183\u2013184, December\u20131979.\r\n[15]\tJ. B. Shearer, \u201cSome New Optimum Golomb Rulers\u201d, IEEE Transactions on Information Theory, Vol. 36, pp. 183\u2013184, January\u20131990.\r\n[16]\tC. Cotta, I. Dot\u00fa, A. J. Fern\u00e1ndez, and P. V. Hentenryck, \u201cA Memetic Approach to Golomb Rulers\u201d, Parallel Problem Solving from Nature\u2013PPSN IX, Lecture Notes in Computer Science, Vol. 4193, pp. 252\u2013261, Springer\u2013Verlag Berlin Heidelberg, September 9\u201313, 2006.\r\n[17]\tS. W. Soliday, A. Homaifar and Gary L. Lebby, \u201cGenetic Algorithm Approach to the Search for Golomb Rulers\u201d, Proceedings of the Sixth International Conference on Genetic Algorithms (ICGA\u201395), Morgan Kaufmann, pp. 528\u2013535, 1995.\r\n[18]\tJ. P. Robinson, \u201cGenetic Search for Golomb Arrays\u201d, IEEE Transactions on Information Theory, Vol. 46, No. 3, pp. 1170\u20131173, May\u20132000.\r\n[19]\tI. Dot\u00fa, P. V. Hentenryck, \u201cA Simple Hybrid Evolutionary Algorithm for Finding Golomb Rulers\u201d, Evolutionary Computation, 2005, The 2005 IEEE Congress on, Vol. 3, pp. 2018\u20132023, September 2\u20135, 2005.\r\n[20]\tN. Ayari; The\u0301 Van Luong and A. Jemai, \u201cA Hybrid Genetic Algorithm for Golomb Ruler Problem\u201d, ACS\/IEEE International Conference on Computer Systems and Applications (AICCSA\u20132010), pp.1\u20134, May 16\u201319, 2010.\r\n[21]\tS. Bansal, S. Kumar and P. Bhalla, \u201cA Novel Approach to WDM Channel Allocation: Big Bang\u2013Big Crunch Optimization\u201d, In the Proceeding of Zonal Seminar on Emerging Trends in Embedded System Technologies (ETECH\u20132013) organized by The Institution of Electronics and Telecommunication Engineers (IETE)\u201d, Chandigarh Centre, Chandigarh, pp. 80\u201381, 2013.\r\n[22]\tS. Bansal and K. Singh, \u201cA Novel Soft\u2013Computing Algorithm for Channel Allocation in WDM Systems\u201d, International Journal of Computer Applications (IJCA), Vol. 85, No. 9, pp. 19\u201326, January\u20132014.\r\n[23]\tK. Singh, \u201cSoft Computing Algorithms fot WDM Channel Allocation for Reducing FWM Crosstalk\u201d, M.Tech. Thesis, Department of Electronics and Communication Engineering, Institute of Science and Technology, Klawad, India, December\u20132013.\r\n[24]\tS. Bansal, R. Chauhan and P. Kumar, \u201cA Cuckoo Search based WDM Channel Allocation Algorithm\u201d, International Journal of Computer Applications (IJCA), Vol. 96, No. 20, pp. 6\u201312, June\u20132014.\r\n[25]\tS. Bali, S. Bansal and A. Kamboj, \u201cA Novel Hybrid Multi\u2013objective BB\u2013BC Based Channel Allocation Algorithm to Reduce FWM Crosstalk and its Comparative Study\u201d, International Journal of Computer Applications (IJCA), Vol. 124, No. 12, pp. 38\u201345, August\u20132015.\r\n[26]\tP. Jain, S. Bansal, A. K. Singh, and N. Gupta, \u201cGolomb Ruler Sequences Optimization for FWM Crosstalk Reduction: Multi\u2013population Hybrid Flower Pollination Algorithm\u201d, Progress in Electromagnetics Research Symposium (PIERS), Prague, Czech Republic, pp. 2463\u20132467, July 06\u201309, 2015.\r\n[27]\tS. Bali, S. Bansal, and A. Kamboj, \u201cA Novel Hybrid Multi\u2013objective BB\u2013BC Based Channel Allocation Algorithm to Reduce FWM Crosstalk and its Comparative Study\u201d, International Journal of Computer Applications (IJCA), Vol. 124, No. 12, pp. 38\u201345, August\u20132015.\r\n[28]\tX.\u2013S. Yang, \u201cFlower Pollination Algorithm for Global Optimization\u201d, in: Unconventional Computation and Natural Computation, Lecture Notes in Computer Science, Vol. 7445, Springer, Berlin, pp. 240\u2013249, 2012.\r\n[29]\tR. Storn and K. V. Price, \u201cDifferential Evolution\u2014A Simple and Efficient Heuristic for Global Optimization Over Continuous Spaces,\u201d Journal of Global Optimization, Vol. 11, No. 4, pp. 341\u2013359, December\u20131997.\r\n[30]\tS. Koziel and X.\u2013S. Yang, \u201cComputational Optimization, Methods and Algorithms\u201d, Studies in Computational Intelligence, Vol. 356, Springer, 2011.\r\n[31]\tX.\u2013S. Yang, \u201cMultiobjective Firefly Algorithm for Continuous Optimization\u201d, Engineering with Computers, Vol. 29, No. 2, pp. 175\u2013184, 2013.\r\n[32]\tX.\u2013S. Yang, \u201cFirefly Algorithms for Multimodal Optimization\u201d, in: Stochastic Algorithms: Foundations and Applications (SAGA\u20132009), Lecture Notes in Computer Science, Vol. 5792, Springer\u2013Verlag, Berlin, pp. 169\u2013178, 2009. \r\n[33]\tX.\u2013S. Yang, \u201cReview of Metaheuristics and Generalized Evolutionary Walk Algorithm\u201d, International Journal of Bio\u2013Inspired Computation (IJBIC), Vol. 3, No. 2, pp. 77\u201384, 2011.\r\n[34]\tA. Dollas, W. T. Rankin, and D. McCracken, \u201cA New Algorithm for Golomb Ruler Derivation and Proof of the 19 Mark Ruler\u201d, IEEE Transactions on Information Theory, Vol. 44, No. 1, pp. 379\u2013382, January\u20131998.\r\n[35]\tJ. B. Shearer, \u201cGolomb Ruler Table\u201d, Mathematics Department, IBM Research. Available at http:\/\/www.research.ibm.com\/people\/s\/shearer\/grtab.html, 2001.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 115, 2016"}