Abstract
Bat algorithm (BA) is one of the recently proposed heuristic algorithms imitating the echolocation behavior of bats to perform global optimization. The superior performance of this algorithm has been proven among the other most well-known algorithms such as genetic algorithm (GA) and particle swarm optimization (PSO). However, the original version of this algorithm is suitable for continuous problems, so it cannot be applied to binary problems directly. In this paper, a binary version of this algorithm is proposed. A comparative study with binary PSO and GA over twenty-two benchmark functions is conducted to draw a conclusion. Furthermore, Wilcoxon’s rank-sum nonparametric statistical test was carried out at 5 % significance level to judge whether the results of the proposed algorithm differ from those of the other algorithms in a statistically significant way. The results prove that the proposed binary bat algorithm (BBA) is able to significantly outperform others on majority of the benchmark functions. In addition, there is a real application of the proposed method in optical engineering called optical buffer design at the end of the paper. The results of the real application also evidence the superior performance of BBA in practice.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, pp 1942–1948
Holland J (1975) Adaptation in natural and artificial systems. The University of Michigan Press, Ann Arbor, Michigan
Kirkpatrick S, Gelati CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680
Dorigo M, Maniezzo V, Colorni A (1996) The ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern B 26:29–41
Rashedi E, Nezamabadi S, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179:2232–2248
Kaveh A, Talatahari S (2010) A novel heuristic optimization method: charged system search. Acta Mech 213:267–289
Kaveh A, Share MAM, Moslehi M (2013) Magnetic charged system search: a new meta-heuristic algorithm for optimization. Acta Mech 224:85–107
Kaveh A, Khayatazad M (2012) A new meta-heuristic method: ray optimization. Comput Struct 112:283–294
Kaveh A, Farhoudi N (2013) A new optimization method: dolphin echolocation. Adv Eng Softw 59:53–70
Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evolut Comput 1:67–82
Yang XS (2010) A new metaheuristic bat-inspired algorithm. In: Gonzalez JR et al (eds) Nature inspired cooperative strategies for optimization (NICSO 2010), vol 284. Springer, Berlin, pp 65–74
Pal A, Maiti J (2010) Development of a hybrid methodology for dimensionality reduction in Mahalanobis–Taguchi system using Mahalanobis distance and binary particle swarm optimization. Expert Syst Appl 37:1286–1293
Babaoglu İ, Findik O, Ülker E (2010) A comparison of feature selection models utilizing binary particle swarm optimization and genetic algorithm in determining coronary artery disease using support vector machine. Expert Syst Appl 37:3177–3183
Qiao L-Y, Peng X-Y, Peng Y (2006) BPSO-SVM wrapper for feature subset selection. Dianzi Xuebao (Acta Electronica Sinica) 34:496–498
Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. J Simul 76:60–68
Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359
Tayarani-N MH, Akbarzadeh-T MR (2008) Magnetic optimization algorithms a new synthesis. In: IEEE congress on evolutionary computation, pp 2659–2664
Wang L, Xu Y, Mao Y, Fei M (2010) A discrete harmony search algorithm. In: Li K, Li X, Ma S, Irwin GW (eds) Life system modeling and intelligent computing. Communications in computer and information science, vol 98. Springer, Berlin, pp 37–43. http://dx.doi.org/10.1007/978-3-642-15859-9_6
Wang L, Fu X, Menhas MI, Fei M (2010) A modified binary differential evolution algorithm. In: Li K, Fei M, Jia L, Irwin GW (eds) Life system modeling and intelligent computing, Lecture notes in computer science, vol 6329. Springer, Berlin, pp 49–57. http://dx.doi.org/10.1007/978-3-642-15597-0_6
Mirjalili S, Mohd Hashim SZ (2011) BMOA: binary magnetic optimization algorithm. In: 2011 3rd international conference on machine learning and computing (ICMLC 2011), Singapore, 2011, pp 201–206
Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) BGSA: binary gravitational search algorithm. Nat Comput 9:727–745
Kennedy J, Eberhart RC (1997) A discrete binary version of the particle swarm algorithm. In: IEEE international conference on computational cybernetics and simulation, pp 4104–4108
Tasgetiren MF, Suganthan PN, Pan QK (2007) A discrete particle swarm optimization algorithm for the generalized traveling salesman problem. In: 9th annual conference on genetic and evolutionary computation (GECCO ‘07), New York, NY, USA, 2007, pp 158–167
Mirjalili S, Lewis A (2013) S-shaped versus V-shaped transfer functions for binary particle swarm optimization. Swarm Evol Comput 9:1–14. http://dx.doi.org/10.1016/j.swevo.2012.09.002
Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evolut Comput 3:82–102
Yang X-S (ed) (2010) Test problems in optimization. An introduction with metaheuristic applications. Wiley, London
Molga M, Smutnicki C (2005) Test functions for optimization needs. Available at http://www.zsd.ict.pwr.wroc.pl/files/docs/functions.pdf
Digalakis JG, Margaritis KG (2001) On benchmarking functions for genetic algorithms. Int J Comput Math 77:481–506
Liang JJ, Suganthan PN, Deb K (2005) Novel composition test functions for numerical global optimization. In: IEEE In swarm intelligence symposium pp 68–75
Derrac J, Molina GSD, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evolut Comput 1:3–18
Garcia S, Molina D, Lozano M, Herrera F (2009) A study on the use of non. J Heuristics 15:617–644
Wilcoxon F (1945) Individual comparisons by ranking methods. Biometrics 1:80–83
Okawachi Y, Foster MA, Sharping JE, Gaeta AL, Xu Q, Lipson M (2006) All-optical slow-light on a photonic chip. Opt Express 14:2317–2322
Freude W, Brosi J-M, Koos C, Vorreau P, Andreani L, Dumon P, Baets R, Esembeson B, Biaggio I, Michinobu T (2008) Silicon-organic hybrid (SOH) devices for nonlinear optical signal processing. In: Transparent optical networks 2008. ICTON 2008. 10th anniversary international conference on, 2008, pp 84–87
Tucker RS, Ku P-C, Chang-Hasnain CJ (2005) Slow-light optical buffers: capabilities and fundamental limitations. J Lightwave Technol 23:4046
Long F, Tian H, Ji Y (2010) A study of dynamic modulation and buffer capability in low dispersion photonic crystal waveguides. J Lightwave Technol 28:1139–1143
Mirjalili SM, Mirjalili S (2012) Light property and optical buffer performance enhancement using particle swarm optimization in oblique ring-shape-hole photonic crystal waveguide. Photon Glob Conf (PGC) 2012:1–4. doi:10.1109/PGC.2012.6457997
Dai L, Jiang C (2009) Photonic crystal slow light waveguides with large delay-bandwidth product. Appl Phys B 95:105–111
Hou J, Gao D, Wu H, Hao R, Zhou Z (2009) Flat band slow light in symmetric line defect photonic crystal waveguides. Photon Technol Lett IEEE 21:1571–1573
Kurt H, Üstün K, Ayas L (2010) Study of different spectral regions and delay bandwidth relation in slow light photonic crystal waveguides. Opt Express 18:26965–26977
Zhai Y, Tian H, Ji Y (2011) Slow light property improvement and optical buffer capability in ring-shape-hole photonic crystal waveguide. Lightwave Technol J 29:3083–3090
Guo S, Albin S (2003) Simple plane wave implementation for photonic crystal calculations. Opt Express 11:167–175
Säynätjoki A, Mulot M, Ahopelto J, Lipsanen H (2007) Dispersion engineering of photonic crystal waveguides with ring-shaped holes. Opt Express 15:8323–8328
Wang D, Zhang J, Yuan L, Lei J, Chen S, Han J, Hou S (2011) Slow light engineering in polyatomic photonic crystal waveguides based on square lattice. Opt Commun 284:5829–5832
Engelen R, Sugimoto Y, Watanabe Y, Korterik JP, Ikeda N, van Hulst NF, Asakawa K, Kuipers L (2006) The effect of higher order dispersion on slow light propagation in photonic crystal waveguides. In: Lasers and electro-optics, 2006 and 2006 quantum electronics and laser science conference. CLEO/QELS 2006. conference on, 2006, pp 1–2
Frandsen LH, Lavrinenko A, Fage-Pedersen J, Borel PI (2006) Photonic crystal waveguides with semi-slow light and tailored dispersion properties. Opt Express 14:9444–9450
Kuramochi E, Notomi M, Hughes S, Shinya A, Watanabe T, Ramunno L (2005) Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs. Phys Rev B 72:161318
Mirjalili SM, Abedi K, Mirjalili S (2013) Optical buffer performance enhancement using particle swarm optimization in ring-shape-hole photonic crystal waveguide. Opt - Int J Light Electron Opt 124:5989–5993. doi:10.1016/j.ijleo.2013.04.114
Mirjalili SM, Mirjalili S, Lewis A, Abedi K (2013) A tri-objective particle swarm optimizer for designing line defect photonic crystal waveguides. Photonics Nanostructures-Fundam Appl. doi:10.1016/j.photonics.2013.11.001
Mirjalili SM, Mirjalili S, Lewis A (2013) A novel multi-objective optimization framework for designing photonic crystal waveguides. IEEE Photonics Technol Lett 99:1041–1135. doi:10.1109/LPT.2013.2290318
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mirjalili, S., Mirjalili, S.M. & Yang, XS. Binary bat algorithm. Neural Comput & Applic 25, 663–681 (2014). https://doi.org/10.1007/s00521-013-1525-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-013-1525-5