Monarch butterfly optimization
In nature, the eastern North American monarch population is known for its southward migration during the late summer/autumn from the northern USA and southern Canada to Mexico, covering thousands of miles. By simplifying and idealizing the migration of monarch butterflies, a new kind of nature-inspired metaheuristic algorithm, called monarch butterfly optimization (MBO), a first of its kind, is proposed in this paper. In MBO, all the monarch butterfly individuals are located in two distinct lands, viz. southern Canada and the northern USA (Land 1) and Mexico (Land 2). Accordingly, the positions of the monarch butterflies are updated in two ways. Firstly, the offsprings are generated (position updating) by migration operator, which can be adjusted by the migration ratio. It is followed by tuning the positions for other butterflies by means of butterfly adjusting operator. In order to keep the population unchanged and minimize fitness evaluations, the sum of the newly generated butterflies in these two ways remains equal to the original population. In order to demonstrate the superior performance of the MBO algorithm, a comparative study with five other metaheuristic algorithms through thirty-eight benchmark problems is carried out. The results clearly exhibit the capability of the MBO method toward finding the enhanced function values on most of the benchmark problems with respect to the other five algorithms. Note that the source codes of the proposed MBO algorithm are publicly available at GitHub (https://github.com/ggw0122/Monarch-Butterfly-Optimization, C++/MATLAB) and MATLAB Central (http://www.mathworks.com/matlabcentral/fileexchange/50828-monarch-butterfly-optimization, MATLAB).
KeywordsEvolutionary computation Monarch butterfly optimization Migration Butterfly adjusting operator Benchmark problems
This work was supported by Research Fund for the Doctoral Program of Jiangsu Normal University (No. 13XLR041).
- 5.Fister Jr I, Yang X-S, Fister I, Brest J, Fister D (2013) A brief review of nature-inspired algorithms for optimization. arXiv:1307.4186
- 6.Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Paper presented at the proceeding of the IEEE international conference on neural networks, Perth, Australia, 27 November-1 DecemberGoogle Scholar
- 15.Yang XS, Deb S Cuckoo search via Lévy flights. In: Abraham A, Carvalho A, Herrera F, Pai V (eds) Proceeding of world congress on nature & biologically inspired computing (NaBIC 2009), Coimbatore, December 2009. IEEE Publications, USA, pp 210–214Google Scholar
- 20.Yang XS (2010) Nature-inspired metaheuristic algorithms, 2nd edn. Luniver Press, FromeGoogle Scholar
- 22.Fister Jr I, Fong S, Brest J, Fister I Towards the self-adaptation in the bat algorithm. In: Proceedings of the 13th IASTED international conference on artificial intelligence and applications, 2014. doi: 10.2316/P.2014.816-011
- 30.Meng X, Liu Y, Gao X, Zhang H (2014) A new bio-inspired algorithm: chicken swarm optimization. In: Tan Y, Shi Y, Coello CC (eds) Advances in swarm intelligence, vol 8794. Lecture notes in computer science. Springer, New York, pp 86-94. doi: 10.1007/978-3-319-11857-4_10
- 34.Goldberg DE (1998) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, New YorkGoogle Scholar
- 38.Hand D (1992) Genetic programming: on the programming of computers by means of natural selection. MIT Press, CambridgeGoogle Scholar
- 39.Beyer H, Schwefel H (2002) Natural computing. Kluwer Academic Publishers, DordrechtGoogle Scholar
- 42.Khatib W, Fleming P (1998) The stud GA: A mini revolution? In: Eiben A, Back T, Schoenauer M, Schwefel H (eds) Proceedings of the 5th international conference on parallel problem solving from nature, New York, 1998. Parallel problem solving from nature. Springer, London, pp 683–691Google Scholar
- 51.Garber SD (1998) The Urban Naturalist. Dover Publications, MineolaGoogle Scholar
- 52.Klots AB (1978) Field guide to the butterflies of North America, East of the great plains. Peterson Field Guides, Boston, USAGoogle Scholar