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An Improved Monarch Butterfly Optimization with Equal Partition and F/T Mutation

  • Gai-Ge WangEmail author
  • Guo-Sheng Hao
  • Shi Cheng
  • Zhihua Cui
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10385)

Abstract

In general, the population of most metaheuristic algorithms is randomly initialized at the start of search. Monarch Butterfly Optimization (MBO) with a randomly initialized population, as a kind of metaheuristic algorithm, is recently proposed by Wang et al. In this paper, a new population initialization strategy is proposed with the aim of improving the performance of MBO. Firstly, the whole search space is equally divided into NP (population size) parts at each dimension. And then, in order to add the diversity of the initialized population, two random distributions (T and F distribution) are used to mutate the equally divided population. Accordingly, five variants of MBOs are proposed with new initialization strategy. By comparing five variants of MBOs with the basic MBO algorithm, the experimental results presented clearly demonstrate five variants of MBOs have much better performance than the basic MBO algorithm.

Keywords

Benchmark Monarch butterfly optimization Equal partition F mutation T mutation 

Notes

Acknowledgements

This work was supported by the Natural Science Foundation of Jiangsu Province (No. BK20150239) and National Natural Science Foundation of China (No. 61503165 and No. 61673196).

References

  1. 1.
    Storn, R., Price, K.: Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11, 341–359 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Wang, G.-G., Gandomi, A.H., Alavi, A.H., Hao, G.-S.: Hybrid krill herd algorithm with differential evolution for global numerical optimization. Neural Comput. Appl. 25, 297–308 (2014)CrossRefGoogle Scholar
  3. 3.
    Yang, X.-S., Deb, S.: Cuckoo search via Lévy flights. In: Proceeding of World Congress on Nature & Biologically Inspired Computing (NaBIC 2009), pp. 210–214. IEEE Publications (2009)Google Scholar
  4. 4.
    Li, X., Yin, M.: Modified cuckoo search algorithm with self adaptive parameter method. Inf. Sci. 298, 80–97 (2015)CrossRefGoogle Scholar
  5. 5.
    Wang, G.-G., Deb, S., Gandomi, A.H., Zhang, Z., Alavi, A.H.: Chaotic cuckoo search. Soft. Comput. 20, 3349–3362 (2016)CrossRefGoogle Scholar
  6. 6.
    Wang, G.-G., Gandomi, A.H., Yang, X.-S., Alavi, A.H.: A new hybrid method based on krill herd and cuckoo search for global optimization tasks. Int. J. Bio-Inspired Comput. 8, 286–299 (2016)CrossRefGoogle Scholar
  7. 7.
    Wang, G.-G., Gandomi, A.H., Zhao, X., Chu, H.E.: Hybridizing harmony search algorithm with cuckoo search for global numerical optimization. Soft. Comput. 20, 273–285 (2016)CrossRefGoogle Scholar
  8. 8.
    Wang, G., Guo, L., Duan, H., Liu, L., Wang, H., Wang, J.: A hybrid meta-heuristic DE/CS algorithm for UCAV path planning. J. Inform. Comput. Sci. 9, 4811–4818 (2012)Google Scholar
  9. 9.
    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceeding of the IEEE International Conference on Neural Networks, vol. 4, pp. 1942–1948. IEEE, Perth (1995)Google Scholar
  10. 10.
    Shieh, H.-L., Kuo, C.-C., Chiang, C.-M.: Modified particle swarm optimization algorithm with simulated annealing behavior and its numerical verification. Appl. Math. Comput. 218, 4365–4383 (2011)zbMATHGoogle Scholar
  11. 11.
    Mirjalili, S., Lewis, A.: S-shaped versus V-shaped transfer functions for binary particle swarm optimization. Swarm Evol. Comput. 9, 1–14 (2013)CrossRefGoogle Scholar
  12. 12.
    Wang, G.-G., Gandomi, A.H., Yang, X.-S., Alavi, A.H.: A novel improved accelerated particle swarm optimization algorithm for global numerical optimization. Eng. Comput. 31, 1198–1220 (2014)CrossRefGoogle Scholar
  13. 13.
    Simon, D.: Biogeography-based optimization. IEEE Trans. Evolut. Comput. 12, 702–713 (2008)CrossRefGoogle Scholar
  14. 14.
    Zheng, Y.-J., Ling, H.-F., Xue, J.-Y.: Ecogeography-based optimization: enhancing biogeography-based optimization with ecogeographic barriers and differentiations. Comput. Oper. Res. 50, 115–127 (2014)CrossRefzbMATHGoogle Scholar
  15. 15.
    Duan, H., Zhao, W., Wang, G., Feng, X.: Test-sheet composition using analytic hierarchy process and hybrid metaheuristic algorithm TS/BBO. Math. Probl. Eng. 2012, 1–22 (2012)Google Scholar
  16. 16.
    Geem, Z.W., Kim, J.H., Loganathan, G.V.: A new heuristic optimization algorithm: harmony search. Simulation 76, 60–68 (2001)CrossRefGoogle Scholar
  17. 17.
    Wang, G., Guo, L., Duan, H., Wang, H., Liu, L., Shao, M.: Hybridizing harmony search with biogeography based optimization for global numerical optimization. J. Comput. Theor. Nanos. 10, 2318–2328 (2013)Google Scholar
  18. 18.
    Rashedi, E., Nezamabadi-pour, H., Saryazdi, S.: GSA: a gravitational search algorithm. Inf. Sci. 179, 2232–2248 (2009)CrossRefzbMATHGoogle Scholar
  19. 19.
    Yin, M., Hu, Y., Yang, F., Li, X., Gu, W.: A novel hybrid K-harmonic means and gravitational search algorithm approach for clustering. Expert Syst. Appl. 38, 9319–9324 (2011)CrossRefGoogle Scholar
  20. 20.
    Tan, Y., Zhu, Y.: Fireworks algorithm for optimization. In: Tan, Y., Shi, Y., Tan, K. (eds.) Advances in Swarm Intelligence, vol. 6145, pp. 355–364. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  21. 21.
    Shi, Y.: An optimization algorithm based on brainstorming process. Int. J. Swarm Intell. Res. 2, 35–62 (2011)CrossRefGoogle Scholar
  22. 22.
    Shi, Y., Xue, J., Wu, Y.: Multi-objective optimization based on brain storm optimization algorithm. Int. J. Swarm Intell. Res. 4, 1–21 (2013)CrossRefGoogle Scholar
  23. 23.
    Wang, G.-G., Deb, S., Coelho, L.D.S.: Earthworm optimization algorithm: a bio-inspired metaheuristic algorithm for global optimization problems. Int. J. Bio-Inspired Comput. (2015)Google Scholar
  24. 24.
    Wang, G.-G., Deb, S., Coelho, L.D.S.: Elephant herding optimization. In: 2015 3rd International Symposium on Computational and Business Intelligence (ISCBI 2015), pp. 1–5. IEEE (2015)Google Scholar
  25. 25.
    Wang, G.-G., Deb, S., Gao, X.-Z., Coelho, L.D.S.: A new metaheuristic optimization algorithm motivated by elephant herding behavior. Int. J. Bio-Inspired Comput. 8, 394–409 (2016)Google Scholar
  26. 26.
    Zheng, Y.-J.: Water wave optimization: a new nature-inspired metaheuristic. Comput. Oper. Res. 55, 1–11 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Mirjalili, S.: The ant lion optimizer. Adv. Eng. Softw. 83, 80–98 (2015)CrossRefGoogle Scholar
  28. 28.
    Mirjalili, S., Mirjalili, S.M., Hatamlou, A.: Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput. Appl. 27, 495–513 (2016)CrossRefGoogle Scholar
  29. 29.
    Yang, X.S.: Firefly algorithm, stochastic test functions and design optimisation. Int. J. Bio-Inspired Comput. 2, 78–84 (2010)CrossRefGoogle Scholar
  30. 30.
    Guo, L., Wang, G.-G., Wang, H., Wang, D.: An effective hybrid firefly algorithm with harmony search for global numerical optimization. Sci. World J. 2013, 1–10 (2013)Google Scholar
  31. 31.
    Dorigo, M., Maniezzo, V., Colorni, A.: Ant system: optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. B Cybern. 26, 29–41 (1996)CrossRefGoogle Scholar
  32. 32.
    Yang, X.-S.: Nature-Inspired Metaheuristic Algorithms. Luniver Press, Frome (2010)Google Scholar
  33. 33.
    Wang, G., Guo, L.: A novel hybrid bat algorithm with harmony search for global numerical optimization. J. Appl. Math. 2013, 1–21 (2013)MathSciNetzbMATHGoogle Scholar
  34. 34.
    Wang, G.-G., Chu, H.E., Mirjalili, S.: Three-dimensional path planning for UCAV using an improved bat algorithm. Aerosp. Sci. Technol. 49, 231–238 (2016)CrossRefGoogle Scholar
  35. 35.
    Xue, F., Cai, Y., Cao, Y., Cui, Z., Li, F.: Optimal parameter settings for bat algorithm. Int. J. Bio-Inspired Comput. 7, 125–128 (2015)CrossRefGoogle Scholar
  36. 36.
    Mirjalili, S., Mirjalili, S.M., Lewis, A.: Grey wolf optimizer. Adv. Eng. Softw. 69, 46–61 (2014)CrossRefGoogle Scholar
  37. 37.
    Gandomi, A.H., Alavi, A.H.: Krill herd: a new bio-inspired optimization algorithm. Commun. Nonlinear Sci. Numer. Simul. 17, 4831–4845 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Wang, G.-G., Gandomi, A.H., Alavi, A.H.: Stud krill herd algorithm. Neurocomputing 128, 363–370 (2014)CrossRefGoogle Scholar
  39. 39.
    Wang, G.-G., Gandomi, A.H., Alavi, A.H.: An effective krill herd algorithm with migration operator in biogeography-based optimization. Appl. Math. Model. 38, 2454–2462 (2014)MathSciNetCrossRefGoogle Scholar
  40. 40.
    Wang, G.-G., Gandomi, A.H., Alavi, A.H., Deb, S.: A hybrid method based on krill herd and quantum-behaved particle swarm optimization. Neural Comput. Appl. 27, 989–1006 (2016)CrossRefGoogle Scholar
  41. 41.
    Wang, G.-G., Deb, S., Gandomi, A.H., Alavi, A.H.: Opposition-based krill herd algorithm with Cauchy mutation and position clamping. Neurocomputing 177, 147–157 (2016)CrossRefGoogle Scholar
  42. 42.
    Wang, G.-G., Gandomi, A.H., Alavi, A.H., Deb, S.: A multi-stage krill herd algorithm for global numerical optimization. Int. J. Artif. Intell. Tools 25, 1550030 (2016)CrossRefGoogle Scholar
  43. 43.
    Wang, G.-G., Gandomi, A.H., Alavi, A.H., Gong, D.: A comprehensive review of krill herd algorithm: variants, hybrids and applications. Artif. Intell. Rev. (2017)Google Scholar
  44. 44.
    Wang, G.-G., Deb, S., Cui, Z.: Monarch butterfly optimization. Neural Comput. Appl. (2015)Google Scholar
  45. 45.
    Wang, G.-G., Zhao, X., Deb, S.: A novel monarch butterfly optimization with greedy strategy and self-adaptive crossover operator. In: 2015 2nd International Conference on Soft Computing & Machine Intelligence (ISCMI 2015), pp. 45–50. IEEE (2015)Google Scholar
  46. 46.
    Feng, Y., Wang, G.-G., Deb, S., Lu, M., Zhao, X.: Solving 0–1 knapsack problem by a novel binary monarch butterfly optimization. Neural Comput. Appl. (2015)Google Scholar
  47. 47.
    Ghetas, M., Yong, C.H., Sumari, P.: Harmony-based monarch butterfly optimization algorithm. In: 2015 IEEE International Conference on Control System, Computing and Engineering (ICCSCE), pp. 156–161. IEEE (2015)Google Scholar
  48. 48.
    Wang, G.-G., Deb, S., Zhao, X., Cui, Z.: A new monarch butterfly optimization with an improved crossover operator. Oper. Res.: Int. J. (2016)Google Scholar
  49. 49.
    Feng, Y., Yang, J., Wu, C., Lu, M., Zhao, X.-J.: Solving 0–1 knapsack problems by chaotic monarch butterfly optimization algorithm. Memetic Comput. (2016)Google Scholar
  50. 50.
    Ghanem, W.A.H.M., Jantan, A.: Hybridizing artificial bee colony with monarch butterfly optimization for numerical optimization problems. Neural Comput. Appl. (2016)Google Scholar
  51. 51.
    Wang, G.-G., Hao, G.-S., Cheng, S., Qin, Q.: A discrete monarch butterfly optimization for Chinese TSP problem. In: Tan, Y., Shi, Y., Niu, B. (eds.) Advances in Swarm Intelligence: 7th International Conference, ICSI 2016, Bali, Indonesia, June 25-30, 2016, Proceedings, Part I, vol. 9712, pp. 165–173. Springer International Publishing, Cham (2016)Google Scholar
  52. 52.
    Feng, Y., Wang, G.-G., Li, W., Li, N.: Multi-strategy monarch butterfly optimization algorithm for discounted {0–1} knapsack problem. Neural Comput. Appl. (2017)Google Scholar
  53. 53.
    Wang, G., Guo, L., Wang, H., Duan, H., Liu, L., Li, J.: Incorporating mutation scheme into krill herd algorithm for global numerical optimization. Neural Comput. Appl. 24, 853–871 (2014)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Gai-Ge Wang
    • 1
    Email author
  • Guo-Sheng Hao
    • 1
  • Shi Cheng
    • 2
  • Zhihua Cui
    • 3
  1. 1.School of Computer Science and TechnologyJiangsu Normal UniversityXuzhouChina
  2. 2.School of Computer ScienceShaanxi Normal UniversityXi’anChina
  3. 3.Complex System and Computational Intelligence LaboratoryTaiyuan University of Science and TechnologyTaiyuanChina

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