Abstract
Recently, inspired by the migration behavior of monarch butterflies in nature, a metaheuristic optimization algorithm, called monarch butterfly optimization (MBO), was proposed. In the present study, a novel chaotic MBO algorithm (CMBO) is proposed, in which chaos theory is introduced in order to enhance its global optimization ability. Here, 12 one-dimensional classical chaotic maps are used to tune two main migration processes of monarch butterflies. Meanwhile, applying Gaussian mutation operator to some worst individuals can effectively prevent premature convergence of the optimization process. The performance of CMBO is verified and analyzed by three groups of large-scale 0–1 knapsack problems instances. The results show that the introduction of appropriate chaotic map and Gaussian perturbation can significantly improve the solution quality together with the overall performance of the proposed CMBO algorithm. The proposed CMBO can outperform the standard MBO and other eight state-of-the-art canonical algorithms.
Similar content being viewed by others
References
Yang XS (2010) Nature-inspired metaheuristic algorithms. Luniver Press, Frome
Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: Proceeding of world congress on nature and biologically inspired computing (NaBIC 2009), IEEE Publications, pp 210–214
Karthikeyan S, Asokan P, Nickolas S, Page T (2015) A hybrid discrete firefly algorithm for solving multi-objective flexible job shop scheduling problems. Int J Bio-Inspir Comput 7(6):386–401
Wang GG, Deb S, Coelho LDS (2015) Earthworm optimization algorithm: a bio-inspired metaheuristic algorithm for global optimization problems. Int J Bio-Inspir Comput (accepted)
Wang GG, Deb S, Gao XZ, Coelho LDS (2016) A new metaheuristic optimization algorithm motivated by elephant herding behavior. Int J Bio-Inspir Comput (accepted)
Wang GG, Deb S, Coelho LDS (2015) Elephant herding optimization. In: 2015 3rd International symposium on computational and business intelligence (ISCBI 2015), Bali, Indonesia, pp 1–5
Wang GG, Guo LH, Wang HQ et al (2014) Incorporating mutation scheme into krill herd algorithm for global numerical optimization. Neural Comput Appl 24(3–4):853–871
Wang GG, Gandomi AH, Alavi AH (2014) Stud krill herd algorithm. Neurocomputing 128:363–370
Cui ZH, Fan S, Zeng J et al (2013) Artificial plant optimization algorithm with three-period photosynthesis. Int J Bio-Inspir Comput 5(2):133–139
Eusuff M, Lansey K, Pasha F (2006) Shuffled frog-leaping algorithm: a memetic metaheuristic for discrete optimization. Eng Optim 38(2):129–154
Tawhid MA, Ali AF (2016) A simplex social spider algorithm for solving integer programming and minimax problems. Mem Comput 1–20. doi:10.1007/s12293-016-0180-7
Wang GG, Deb S, Cui ZH (2015) Monarch butterfly optimization. Neural Comput Appl 1–20. doi:10.1007/s00521-015-1923-y
Feng YH, Wang GG, Deb S et al (2015) Solving 0–1 Knapsack problem by a novel binary monarch butterfly optimization. Neural Comput Appl 1–16. doi:10.1007/s00521-015-2135-1
Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39(3):459–471
Storn R, Price K (1997) Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359
Pecora L, Carroll T (1990) Synchronization in chaotic system. Phys Rev Lett 64:821
Yang DX, Li G, Cheng GD (2007) On the efficiency of chaos optimization algorithms for global optimization. Chaos Solit Fract 34(4):1366–1375
Alatas B (2010) Chaotic harmony search algorithms. Appl Math Comput 216:2687–2699
Alatas B, Akin E, Ozer AB (2009) Chaos embedded particle swarm optimization algorithms. Chaos Solit Fract 40(4):1715–1734
Gharooni-Fard G, Moein-Darbari F, Deldari H, Morvaridi A (2010) Scheduling of scientific workflows using a chaos-genetic algorithm. Proc Comput Sci 1(1):1445–1454
Wang GG, Deb S, Gandomi AH et al (2015) Chaotic cuckoo search. Soft Comput 5:1–14
Wang GG, Guo LH, Gandomi AH et al (2014) Chaotic krill herd algorithm. Inf Sci 274:17–34
Mathews GB (1988) On the partition of numbers. Introduction to analysis of the infinite. Springer, New York
Tavazoei MS, Haeri M (2007) Comparison of different one-dimensional maps as chaotic search pattern in chaos optimization algorithms. Appl Math Comput 187:1076–1085
Coelho LDS, Mariani VC (2008) Use of chaotic sequences in a biologically inspired algorithm for engineering design optimization. Expert Syst Appl 34(3):1905–1913
Rudolph G (1997) Local convergence rates of simple evolutionary algorithms with Cauchy mutations. IEEE Trans Evol Comput 1(4):249–258
Hinterding R (1995) Gaussian mutation and self-adaption for numeric genetic algorithms. In: Evolutionary computation, IEEE international conference on
He YC, Wang XZ, Kou YZ (2007) A binary differential evolution algorithm with hybrid encoding. J Comput Res Dev 44(9):1476–1484
He YC, Song JM, Zhang JM, Gou HY (2015) Research on genetic algorithms for solving static and dynamic knapsack problems. Appl Res Comput 32(4):1011–1015
Martello S, Toth P (1990) Knapsack problems: algorithms and computer implementations. Wiley, Amsterdam
He YC, Zhang XL, Li WB et al (2016) Algorithms for randomized time-varying knapsack problems. J Comb Optim 31(1):95–117
Patvardhan C, Bansal S, Srivastav A (2015) Quantum-inspired evolutionary algorithm for difficult knapsack problems. Memetic Comput 7(2):135–155
Acknowledgments
This work was supported by National Natural Science Foundation of China (Nos. 61272297, and 61402207) and Hebei GEO Universtiy Youth Foundation (No. QN201601).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Feng, Y., Yang, J., Wu, C. et al. Solving 0–1 knapsack problems by chaotic monarch butterfly optimization algorithm with Gaussian mutation. Memetic Comp. 10, 135–150 (2018). https://doi.org/10.1007/s12293-016-0211-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12293-016-0211-4