Comparative Study of Krill Herd, Firefly and Cuckoo Search Algorithms for Unimodal and Multimodal Optimization

Gobind Preet Singh, Abhay Singh
  • Gobind Preet Singh
    Guru Gobind Singh Indraprastha University, India |
  • Abhay Singh
    Guru Gobind Singh Indraprastha University, India


Today, in computer science, a computational challenge exists in finding a globally optimized solution from an enormously large search space. Various metaheuristic methods can be used for finding the solution in a large search space.These methods can be explained as iterative search processes that efficiently perform the exploration and exploitation in the solution space. In this context, three such nature inspired metaheuristic algorithms namely Krill Herd Algorithm (KH), Firefly Algorithm (FA) and Cuckoo search Algorithm (CS) can be used to find optimal solutions of various mathematical optimization problems. In this paper, the proposed algorithms were used to find the optimal solution of fifteen unimodal and multimodal benchmark test functions commonly used in the field of optimization and then compare their performances on the basis of efficiency, convergence, time and conclude that for both unimodal and multimodal optimization Cuckoo Search Algorithm via Lévy flight has outperformed others and for multimodal optimization Krill Herd algorithm is superior than Firefly algorithm but for unimodal optimization Firefly is superior than Krill Herd algorithm.


Metaheuristic Algorithm;Krill Herd Algorithm;Firefly Algorithm;Cuckoo Search Algorithm;Unimodal Optimization;Multimodal Optimization

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Submitted: 2013-10-14 20:20:15
Published: 2014-07-01 00:00:00
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X. S. Yang, “Nature-Inspired Metaheuristic Algorithms”, Luniver Press, 2008.

Christian Blum, Maria Jos´e Blesa Aguilera, Andrea Roli, Michael Sampels, Hybrid Metaheuristics, An Emerging Approach to Optimization, Springer, 2008 .

Christian Blum, and Maria Jos´e Blesa Aguilera. Metaheuristics in Combinatorial Optimization: Overview and Conceptual Comparison, Springer, 2008.

Amir Hossein Gandomi, Amir Hossein Alavi. Krill herd: A new bio-inspired optimization algorithm, Elsvier, 2012.

X.-S. Yang, S. Deb, “Cuckoo search via L´evy flights”, in: Proc. Of World Congress on Nature & Biologically Inspired Computing (NaBIC 2009), December 2009, India. IEEE Publications, USA, pp. 210-214 (2009).

Hofmann EE, Haskell AGE, Klinck JM, Lascara CM. Lagrangian modelling studies of Antarctic krill (Euphasia superba) swarm formation. ICES J Mar Sci 2004;61:617–31.

Price HJ. Swimming behavior of krill in response to algal patches: a mesocosm study. Limnol Oceanogr 1989;34:649–59.

Morin A, Okubo A, Kawasaki K. Acoustic data analysis and models of krill spatial distribution. Scientific Committee for the Conservation of Antarctic Marine Living Resources, Selected Scientific Papers, Part I; 1988. p.311–29.

Sh. M. Farahani, A. A. Abshouri, B. Nasiri, and M. R. Meybodi, “A Gaussian Firefly Algorithm”, International Journal of Machine Learning and Computing, Vol. 1, No. December 2011.

Xin-She Yang, Chaos-Enhanced Firefly Algorithm with Automatic Parameter Tuning, International Journal of Swarm Intelligence Research, December 2011.

Flierl G, Grunbaum D, Levin S, Olson D. From individuals to aggregations: the interplay between behavior and physics. J Theor Biol 1999;196:397–454.

Okubo A. Dynamical aspects of animal grouping: swarms, schools, flocks, and herds. Adv Biophys 1986;22:1–94.

Hardy AC, Gunther ER. The plankton of the South Georgia whaling grounds and adjacent waters, 1926–1927. Disc Rep 1935;11:1–456.

Marr JWS. The natural history and geography of the Antarctic krill (Euphausia superba Dana). Disc Rep 1962;32:33–464.

Nicol S. Living krill, zooplankton and experimental investigations. Proceedings of the international workshop on understanding living krill for improved management and stock assessment marine and freshwater behaviour and physiology 2003;36(4):191–205.

Murphy EJ, Morris DJ, Watkins JL, Priddle J. Scales of interaction between Antarctic krill and the environment. In: Sahrhage D, editor. Antarctic Ocean and resources variability. Berlin: Springer-Verlag; 1988. p. 120–30.

Brown C., Liebovitch L. S., Glendon R., Lévy flights in Dobe Ju/’hoansi foraging patterns, Human Ecol., 35, 129-138 (2007).

Pavlyukevich I., Lévy flights, non-local search and simulated annealing, J. Computational Physics, 226, 1830-1844 (2007).

Pavlyukevich I., Cooling down Lévy flights, J. Phys. A:Math. Theor., 40, 12299-12313 (2007).

Reynolds A. M. and Frye M. A., Free-flight odor tracking in Drosophila is consistent with an optimal intermittent scale-free search, PLoS One, 2, e354 (2007).

Shlesinger M. F., Zaslavsky G. M. and Frisch U. (Eds), Lévy Flights and Related Topics in Phyics, Springer, (1995).

Shlesinger M. F., Search research, Nature, 443, 281- 282 (2006).

Barthelemy P., Bertolotti J., Wiersma D. S., A Lévy flight for light, Nature, 453, 495-498 (2008).

Viswanathan, G. M. et al. Optimizing the success of random searches. Nature 401, 911–914(1999)

Bartumeus, F. et al. Optimizing the encounter rate in biological interactions: Lévy versus Brownian strategies. Phys. Rev. Lett. 88, 097901 (2002)

Yao X, Liu Y, Lin G. Evolutionary programming made faster. IEEE Trans Evolut Comput 1999;3:82–102.

MominJamil,Xin-SheYang, Hans-Ju¨rgenZepernick. ” Test Functions for Global Optimization: A Comprehensive Survey” in Swarm Intelligence and BioInspired Optimization, Elsevier, Part I; 2013.p. 193-222

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