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Improved GWO for large-scale function optimization and MLP optimization in cancer identification

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Abstract

Grey wolf optimizer (GWO) is a novel nature-inspired algorithm, and it has the characteristics of strong local search ability but weak global search ability when dealing with some large-scale problems. So a GWO based on random opposition learning, strengthening hierarchy of grey wolves and modified evolutionary population dynamics (EPD), named as RSMGWO, is proposed. Firstly, a search way based on strengthening hierarchy of grey wolves is added; each grey wolf uses two kinds of updating modes, including a global-best search way based on random dimensions and the original search way of GWO, to improve the optimization performance. Secondly, a modified EPD is embedded to improve the optimization performance further. Finally, a random opposition learning strategy is merged to avoid falling into local optima. Experimental results on 19 different (especially large scale) dimensional benchmark functions and multi-layer perceptron (MLP) optimization for cancer identification show that compared with GWO and quite a few state-of-the-art algorithms, RSMGWO is able to provide more competitive results, in terms of both accuracy and convergence.

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References

  1. 1.

    Gupta S, Deep K (2018) A novel random walk grey wolf optimizer. Swarm Evol Comput 44:1–12. https://doi.org/10.1016/j.swevo.2018.01.001

  2. 2.

    Zhang HJ, Llorca J, Davis CC, Milner SD (2012) Nature-Inspired self-organization, control, and optimization in heterogeneous wireless networks. IEEE Trans Mob Comput 11(7):1207–1222. https://doi.org/10.1109/TMC.2011.141

  3. 3.

    Blum C (2005) Ant colony optimization: introduction and recent trends. Phys Life Rev 2(4):353–373. https://doi.org/10.1016/j.plrev.2005.10.001

  4. 4.

    Ning JX, Zhang Q, Zhang CS, Zhang B (2018) A best-path-updating information-guided ant colony optimization algorithm. Inf Sci 433:142–162. https://doi.org/10.1016/j.ins.2017.12.047

  5. 5.

    Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings of the IEEE international conference on neural networks, pp 1942–1948. https://doi.org/10.1109/ICNN.1995.488968.

  6. 6.

    Chen YG, Li LX, Xiao JH, Yang YX, Liang J, Li T (2018) Particle swarm optimizer with crossover operation. Eng Appl Artif Intel 70:159–169. https://doi.org/10.1016/j.engappai.2018.01.009

  7. 7.

    Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713. https://doi.org/10.1109/TEVC.2008.919004

  8. 8.

    Zhang XM, Kang Q, Cheng JF, Wang X (2018) A novel hybrid algorithm based on biogeography-based optimization and grey wolf optimizer. Appl Soft Comput 67:197–214. https://doi.org/10.1016/j.asoc.2018.02.049

  9. 9.

    Karaboga D, Basturk B (2008) On the performance of artificial bee colony (ABC) algorithm. Appl Soft Comput 8(1):687–697. https://doi.org/10.1016/j.asoc.2007.05.007

  10. 10.

    Gong DW, Han YY, Sun JY (2018) A novel hybrid multi-objective artificial bee colony algorithm for blocking lot-streaming flow shop scheduling problems. Knowl Based Syst 48:115–130. https://doi.org/10.1016/j.knosys.2018.02.029

  11. 11.

    Abualigah LM, Khader AT, Hanandeh ES (2018) A combination of objective functions and hybrid krill herd algorithm for text document clustering analysis. Eng Appl Artif Intel 73:111–125. https://doi.org/10.1016/j.engappai.2018.05.003

  12. 12.

    Wang GG, Tan Y (2017) Improving metaheuristic algorithms with information feedback models. IEEE Trans Cybern 48:1–14. https://doi.org/10.1109/TCYB.2017.2780274

  13. 13.

    Zhang HJ, Cao X, Ho JKL, Chow TWS (2017) Object-level video advertising: an optimization framework. IEEE Trans Ind Inform 13(2):520–531. https://doi.org/10.1109/TII.2016.2605629

  14. 14.

    Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69(3):46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007

  15. 15.

    Heidari AA, Pahlavani P (2017) An efficient modified grey wolf optimizer with lévy flight for optimization tasks. Appl Soft Comput 60:115–134. https://doi.org/10.1016/j.asoc.2017.06.044

  16. 16.

    Kumar V, Kumar D (2017) An astrophysics-inspired grey wolf algorithm for numerical optimization and its application to engineering design problems. Adv Eng Softw 112:231–254. https://doi.org/10.1016/j.advengsoft.2017.05.008

  17. 17.

    Emary E, Zawbaa HM, Grosan C (2018) Experienced gray wolf optimization through reinforcement learning and neural networks. IEEE Trans Neural Netw Learn Syst 29(3):681–694. https://doi.org/10.1109/TNNLS.2016.2634548

  18. 18.

    Saremi S, Mirjalili SZ, Mirjalili SM (2015) Evolutionary population dynamics and grey wolf optimizer. Neural Comput Appl 26(5):1257–1263. https://doi.org/10.1007/s00521-014-1806-7

  19. 19.

    Long W, Jiao JJ, Liang XM, Tang MZ (2018) An exploration-enhanced grey wolf optimizer to solve high-dimensional numerical optimization. Eng Appl Artif Intel 68:63–80. https://doi.org/10.1016/j.engappai.2017.10.024

  20. 20.

    Abbass HA (2002) An evolutionary artificial neural network approach for breast cancer diagnosis. Artif Intell Med 25(3):265–281. https://doi.org/10.1016/S0933-3657(02)00028-3

  21. 21.

    Deo RC, Ghorbani MA, Samadianfrad S, Maraseni T, Bilgili M, Biazar M (2018) Multi-layer perceptron hybrid model integrated with the firefly optimizer algorithm for windspeed prediction of target site using a limited set of neighboring reference station data. Renew Energy 116:309–323. https://doi.org/10.1016/j.renene.2017.09.078

  22. 22.

    Hadavandi E, Mostafayi S, Soltani P (2018) A grey wolf optimizer-based neural network coupled with response surface method for modeling the strength of siro-spun yarn in spinning mills. Appl Soft Comput 72:1–13. https://doi.org/10.1016/j.asoc.2018.07.055

  23. 23.

    Chen KH, Wang KJ, Wang KM, Angelia MA (2014) Applying particle swarm optimization-based decision tree classifier for cancer identification on gene expression data. Appl Soft Comput 24:773–780. https://doi.org/10.1016/j.asoc.2014.08.032

  24. 24.

    Rodríguez L, Castillo O, Soria J, Melin P, Valdez F, Gonzalez CI, Martinez GE, Soto J (2017) A fuzzy hierarchical operator in the grey wolf optimizer algorithm. Appl Soft Comput 57:315–328. https://doi.org/10.1016/j.asoc.2017.03.048

  25. 25.

    Omran MGH, Mahdavi M (2008) Global-best harmony search. Appl Math Comput 198(2):643–656. https://doi.org/10.1016/j.amc.2007.09.004

  26. 26.

    Bak P, Tang C, Wiesenfeld K (1987) Self-organized criticality: an explanation of the \({{\rm 1/f}}\) noise. Phys Rev Lett 59(4):381–384. https://doi.org/10.1103/PhysRevLett.59.381

  27. 27.

    Bak P (1997) How nature works. Oxford University Press, Oxford

  28. 28.

    Lewis A, Mostaghim S, Randall M (2008) Evolutionary population dynamics and multi-objective optimization problems. Multiobjective optimization in computational intelligence: theory and practice, pp 185–206

  29. 29.

    Tizhoosh H (2005) Opposition-based learning: a new scheme for machine intelligence. In: Proceedings of IEEE international conference of intelligent for modeling, control and automation. Inst of Elec. and Elec. Eng. Computer Society, PiscatAWay, pp 695–701

  30. 30.

    Ouyang HB, Gao LQ, Li S, Kong XY (2017) Improved global-best-guided particle swarm optimization with learning operation for global optimization problems. Appl Soft Comput 52:987–1008. https://doi.org/10.1016/j.asoc.2016.09.030

  31. 31.

    Dong WY, Kang LL, Zhang WS (2017) Opposition-based particle swarm optimization with adaptive mutation strategy. Soft Comput 21(17):5081–5090. https://doi.org/10.1007/s00500-016-2102-5

  32. 32.

    Cui LZ, Li GH, Zhu ZX, Lin QZ, Wen ZK, Lu N, Wong KC, Chen JY (2017) A novel artificial bee colony algorithm with an adaptive population size for numerical function optimization. Inf Sci 414:53–67. https://doi.org/10.1016/j.ins.2017.05.044

  33. 33.

    Wang GG, Gandomi AH, Yang XS, Alavi AH (2016) A new hybrid method based on krill herd and cuckoo search for global optimization tasks. Int J Bio Inspir Comput 8(5):286–299. https://doi.org/10.1504/IJBIC.2016.10000414

  34. 34.

    Zhang XM, Kang Q, Tu Q, Cheng JF, Wang X (2018) Efficient and merged biogeography-based optimization algorithm for global optimization problems. Soft Comput 23(12):4483–4502. https://doi.org/10.1007/s00500-018-3113-1

  35. 35.

    Wu GH (2016) Across neighborhood search for numerical optimization. Inf Sci 329:597–618. https://doi.org/10.1016/j.ins.2015.09.051

  36. 36.

    Wang H, Cui ZH, Sun H, Rahnamayan S, Yang XS (2017) Randomly attracted firefly algorithm with neighborhood search and dynamic parameter adjustment mechanism. Soft Comput 21(18):5325–5339. https://doi.org/10.1007/s00500-016-2116-z

  37. 37.

    Suganthan PN, Hansen N, Liang JJ, Deb K, Chen YP, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. KanGAL. Rep, Kanpur Genetic Algorithms Laboratory, Singapore and Zhengzhou University, Zhengzhou China and Nanyang Technological University, Singapore

  38. 38.

    Zhang XM, Wang DD, Chen HY (2019) Improved biogeography-based optimization algorithm and its application to clustering optimization and medical image segmentation. IEEE ACCESS 7:28810–28825. https://doi.org/10.1109/ACCESS.2019.2901849

  39. 39.

    Dolan ED, Moré JJ (2002) Benchmarking optimization software with performance profiles. Math Program 91(2):201–213. https://doi.org/10.1007/s101070100263

  40. 40.

    Wang H, Wu ZJ, Rahnamayan S, Sun H, Liu Y, Pan JS (2014) Multi-strategy ensemble artificial bee colony algorithm. Inf Sci 279:587–603. https://doi.org/10.1016/j.ins.2014.04.013

  41. 41.

    Zhang XM, Wang X, Kang Q, Cheng JF (2019) Differential mutation and novel social learning particle swarm optimization algorithm. Inf Sci 480:109–129. https://doi.org/10.1016/j.ins.2018.12.030

  42. 42.

    Draa A, Bouzoubia S, Boukhalfa I (2015) A sinusoidal differential evolution algorithm for numerical optimisation. Appl Soft Comput 27:99–126. https://doi.org/10.1016/j.asoc.2014.11.003

  43. 43.

    Wang GG, Deb S, Gandomi AH, Zhang Z, Alavi AH (2016) Chaotic cuckoo search. Soft Comput 20(9):3349–3362. https://doi.org/10.1007/s00500-015-1726-1

  44. 44.

    Tang DY, Yang J, Dong SB, Liu Z (2016) A lévy flight-based shuffled frog-leaping algorithm and its applications for continuous optimization problems. Appl Soft Comput 49:641–662. https://doi.org/10.1016/j.asoc.2016.09.002

  45. 45.

    Long W, Wu TB, Liang XM, Xu SJ (2019) Solving high-dimensional global optimization problems using an improved sine cosine algorithm. Expert Syst Appl 123:108–126. https://doi.org/10.1016/j.eswa.2018.11.032

  46. 46.

    Jensi R, Jiji GW (2016) An enhanced particle swarm optimization with levy flight for global optimization. Appl Soft Comput 43:248–261. https://doi.org/10.1016/j.asoc.2016.02.018

  47. 47.

    Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18. https://doi.org/10.1016/j.swevo.2011.02.002

  48. 48.

    Mirjalili S, Mirjalili SM, Lewis A (2014) Let a biogeography-based optimizer train your multi-layer perceptron. Inf Sci 269:188–209. https://doi.org/10.1016/j.ins.2014.01.038

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Acknowledgements

This work was supported by Key Research Projects of Higher Education Institutions of Henan Province, China under Grant (No. 19A520026).

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Correspondence to Haiyan Chen.

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Cite this article

Zhang, X., Wang, X., Chen, H. et al. Improved GWO for large-scale function optimization and MLP optimization in cancer identification. Neural Comput & Applic 32, 1305–1325 (2020). https://doi.org/10.1007/s00521-019-04483-4

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Keywords

  • Intelligent optimization algorithm
  • Grey wolf optimizer (GWO)
  • Opposition learning
  • Large scale
  • Cancer identification