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Solving large-scale global optimization problems and engineering design problems using a novel biogeography-based optimization with Lévy and Brownian movements

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Abstract

To make biogeography-based optimization (BBO) suitable for large-scale optimization problems, this paper proposes a novel BBO variant based on marine predators algorithm (MPA) and steepest descent (SD) method, named BBOMPSD. Firstly, the example learning strategy is used to eliminate the damage of inferior solutions to superior solutions. Secondly, the hybrid migration operator is designed to make the population move rapidly to the global optimal solution, which improves the convergence speed and accuracy. Then, the Lévy and Brownian movements in MPA is combined with BBO to make the algorithm effectively balance the exploitation and exploration. BBOMPSD realizes free switching between local search and global search through the two movements. Finally, the SD method is merged with BBO, which further improves the convergence accuracy. Meanwhile, the sequence convergence model is established to prove the convergence of BBOMPSD. Comparing BBOMPSD with standard BBO, seven advanced BBO variants and seven state-of-the-art evolutionary algorithms on 24 benchmark functions and CEC2017 test set, the experimental results show that BBOMPSD outperforms all compared algorithms, and the dimension of solving global optimization problems can reach 5000. Applying it to engineering design problems, the results demonstrate that the proposed algorithm is also effective on real-world constrained optimization problems.

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Data Availability

All the data in Sect. 5 is obtained under the same experimental environment. Then, all the source programs of the compared BBO variants in Sect. 5.2 are coded according to their original references. The simulation of 24 benchmark functions in Table 2 can be downloaded from http://www.sfu.ca/~ssurjano/emulat.html. The simulation of CEC2017 test set can be downloaded from http://www5.zzu.edu.cn/cilab/Benchmark/wysyhwtcsj.htm. The simulation of WOA, MSA, HHO, SSA, AOA, ChOA and RSO in Sect. 5.4 can be downloaded from https://mianbaoduo.com/o/bread/mbd-YZaTlppv. We solemnly declare that all data in this paper are true and valid.

References

  1. Arqub OA, Abo-Hammour Z (2014) Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm. Inf Sci 279:396–415. https://doi.org/10.1016/j.ins.2014.03.128

    Article  MATH  Google Scholar 

  2. Zhang Z, Gao Y, Zuo W (2022) A dual biogeography-based optimization algorithm for solving high-dimensional global optimization problems. IEEE Access 10:55988–56016. https://doi.org/10.1109/ACCESS.2022.3177218

    Article  Google Scholar 

  3. Arqub OA, Abo-Hammour Z, Momani S et al (2012) Solving singular two-point boundary value problems using continuous genetic algorithm//abstract and applied analysis. Hindawi 2012:1–25. https://doi.org/10.1155/2012/205391

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  5. Li X, Chen J, Zhou D et al (2022) A modified biogeography-based optimization algorithm based on cloud theory for optimizing a fuzzy PID controller. Optim Control Appl Methods. https://doi.org/10.1002/oca.2848

    Article  Google Scholar 

  6. Kumar MM, Alli Rani A, Sundaravazhuthi V (2020) A computational algorithm based on biogeography-based optimization method for computing power system security constrains with multi FACTS devices. Comput Intell 36(4):1493–1511. https://doi.org/10.1111/coin.12282

    Article  Google Scholar 

  7. Li Wei, Xiaohui Hu, Wang Hongchuang (2018) Two-dimensional cross entropy multi-threshold image segmentation based on improved BBO algorithm. J Meas Sci Instrum 9(1):42–49. https://doi.org/10.3969/j.jssn.1674-8402.2018.01.006

    Article  Google Scholar 

  8. Zhang Y, Phillips P, Wang S et al (2016) Fruit classification by biogeography-based optimization and feedforward neural network. Expert Syst 33(3):239–253. https://doi.org/10.1111/exsy.12146

    Article  Google Scholar 

  9. Shufen L, Pengfei W, Zhilin Y (2018) An effective biogeography-based optimization algorithm for flow shop scheduling with intermediate buffers. Chin J Electron 27(6):1141–1150. https://doi.org/10.1049/cje.2018.06.003

    Article  Google Scholar 

  10. Ma HP (2010) An analysis of the equilibrium of migration models for biogeography-based optimization. Inf Sci 180(18):3444–3464. https://doi.org/10.1016/j.ins.2010.05.035

    Article  MATH  Google Scholar 

  11. Saremi S, Mirjalili S (2013) Integrating chaos to biogeography-based optimization algorithm. Int J Comput Commun Eng 2(6):655. https://doi.org/10.7763/IJCCE.2013.V2.268

    Article  Google Scholar 

  12. Xiong G, Li Y, Chen J et al (2014) Polyphyletic migration operator and orthogonal learning aided biogeography-based optimization for dynamic economic dispatch with valve-point effects. Energy Conv Manag 80:457–468. https://doi.org/10.1016/j.enconman.2013.12.052

    Article  Google Scholar 

  13. Zheng YJ, Ling HF, Shi HH et al (2014) Emergency railway wagon scheduling by hybrid biogeography-based optimization. Comput Oper Res 43:1–8. https://doi.org/10.1016/j.cor.2013.09.002

    Article  MATH  Google Scholar 

  14. Zhu W, Duan H (2014) Chaotic predator-prey biogeography-based optimization approach for UCAV path planning. Aerospace Sci Technol 32(1):153–161. https://doi.org/10.1016/j.ast.2013.11.003

    Article  Google Scholar 

  15. Garg V, Deep K (2016) Performance of Laplacian biogeography-based optimization algorithm on CEC 2014 continuous optimization benchmarks and camera calibration problem. Swarm Evol Comput 27:132–144. https://doi.org/10.1016/j.swevo.2015.10.006

    Article  Google Scholar 

  16. Chen X, Tianfield H, Du W et al (2016) Biogeography-based optimization with covariance matrix based migration. Appl Soft Comput 45:71–85. https://doi.org/10.1016/j.asoc.2016.04.022

    Article  Google Scholar 

  17. Feng Q, Liu S, Zhang J et al (2017) Improved biogeography-based optimization with random ring topology and Powell’s method. Appl Math Model 41:630–649. https://doi.org/10.1016/j.apm.2016.09.020

    Article  MATH  Google Scholar 

  18. Li LL, Yang YF, Wang CH et al (2018) Biogeography-based optimization based on population competition strategy for solving the substation location problem. Expert Syst Appl 97:290–302. https://doi.org/10.1016/j.eswa.2017.12.039

    Article  Google Scholar 

  19. Zhao F, Qin S, Zhang Y et al (2019) A two-stage differential biogeography-based optimization algorithm and its performance analysis. Expert Syst Appl 115:329–345. https://doi.org/10.1016/j.eswa.2018.08.012

    Article  Google Scholar 

  20. Zhang X, Wang D, Fu Z et al (2020) Novel biogeography-based optimization algorithm with hybrid migration and global-best Gaussian mutation. Appl Math Model 86:74–91. https://doi.org/10.1016/j.apm.2020.05.016

    Article  MATH  Google Scholar 

  21. Liang S, Fang Z, Sun G et al (2022) Biogeography-based optimization with adaptive migration and adaptive mutation with its application in sidelobe reduction of antenna arrays. Appl Soft Comput. https://doi.org/10.1016/j.asoc.2022.108772

  22. Savsani P, Jhala RL, Savsani V (2014) Effect of hybridizing biogeography-based optimization (BBO) technique with artificial immune algorithm (AIA) and ant colony optimization (ACO). Appl Soft Comput 21:542–553. https://doi.org/10.1016/j.asoc.2014.03.011

    Article  Google Scholar 

  23. Khademi G, Mohammadi H, Simon D (2017) Hybrid invasive weed/biogeography-based optimization. Eng Appl Artif Intell 64:213–231. https://doi.org/10.1016/j.engappai.2017.05.017

    Article  Google Scholar 

  24. Karimkashi S, Kishk AA (2010) Invasive weed optimization and its features in electromagnetics. IEEE Trans Antenn Propag 58(4):1269–1278. https://doi.org/10.1109/TAP.2010.2041163

    Article  Google Scholar 

  25. Nath R, Rauniyar A, Muhuri PK (2019) Brain storm optimization algorithm in objective space for reliability-redundancy allocation problem. In: 2019 IEEE congress on evolutionary computation (CEC), pp 248–253. https://doi.org/10.1109/CEC.2019.8790080

  26. Xiong G, Shi D (2018) Hybrid biogeography-based optimization with brain storm optimization for non-convex dynamic economic dispatch with valve-point effects. Energy 157:424–435. https://doi.org/10.1016/j.energy.2018.05.180

    Article  Google Scholar 

  27. Cui Z, Gao XZ (2019) Special issue on evolutionary multi-objective optimization (EMO): theory and applications. Int J Mach Learn Cybern 10(8):1927–1929. https://doi.org/10.1007/s13042-019-00971-0

    Article  Google Scholar 

  28. Alsattar HA, Zaidan AA, Zaidan BB (2020) Novel meta-heuristic bald eagle search optimisation algorithm. Artif Intell Rev 53(3):2237–2264. https://doi.org/10.1007/s10462-019-09732-5

    Article  Google Scholar 

  29. Dhiman G, Singh KK, Slowik A et al (2021) EMoSOA: a new evolutionary multi-objective seagull optimization algorithm for global optimization. Int J Mach Learn Cybern 12(2):571–596. https://doi.org/10.1007/s13042-020-01189-1

    Article  Google Scholar 

  30. Yang Z, Deng LB, Wang Y et al (2021) Aptenodytes Forsteri optimization: algorithm and applications. Knowl Based Syst 232:107483. https://doi.org/10.1016/j.knosys.2021.107483

    Article  Google Scholar 

  31. Mohamed AW, Hadi AA, Mohamed AK (2020) Gaining-sharing knowledge based algorithm for solving optimization problems: a novel nature-inspired algorithm. Int J Mach Learn Cybern 11(7):1501–1529. https://doi.org/10.1007/s13042-019-01053-x

    Article  Google Scholar 

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

    Article  Google Scholar 

  33. Zhang X, Kang Q, Cheng J et al (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

    Article  Google Scholar 

  34. Wang GG, Deb S, Gao XZ et al (2016) A new metaheuristic optimisation algorithm motivated by elephant herding behaviour. Int J Bio-Inspir Comput 8(6):394–409. https://doi.org/10.1504/IJBIC.2016.081335

    Article  Google Scholar 

  35. Li W, Wang GG (2021) Elephant herding optimization using dynamic topology and biogeography-based optimization based on learning for numerical optimization. Eng Comput. https://doi.org/10.1007/s00366-021-01293-y

  36. Ma H, Simon D, Siarry P et al (2017) Biogeography-based optimization: a 10-year review. IEEE Trans Emerg Top Comput Intell 1(5):391–407. https://doi.org/10.1109/TETCI.2017.2739124

    Article  Google Scholar 

  37. Guo W, Chen M, Wang L et al (2017) A survey of biogeography-based optimization. Neural Comput Appl 28:1909–1926. https://doi.org/10.1007/s00521-016-2179-x

    Article  Google Scholar 

  38. Yang Z, Tang K, Yao X (2007) Differential evolution for high-dimensional function optimization. In: 2007 IEEE congress on evolutionary computation. IEEE, pp 3523–3530. https://doi.org/10.1109/CEC.2007.4424929

  39. Mahdavi S, Shiri ME, Rahnamayan S (2015) Metaheuristics in large-scale global continues optimization: a survey. Inf Sci 295:407–428. https://doi.org/10.1016/j.ins.2014.10.042

    Article  Google Scholar 

  40. Cai X, Zhang J, Liang H et al (2019) An ensemble bat algorithm for large-scale optimization. Int J Mach Learn Cybern 10(11):3099–3113. https://doi.org/10.1007/s13042-019-01002-8

    Article  Google Scholar 

  41. Chakraborty S, Saha AK, Chakraborty R et al (2021) An enhanced whale optimization algorithm for large scale optimization problems. Knowl Based Syst 233:107543. https://doi.org/10.1016/j.knosys.2021.107543

    Article  Google Scholar 

  42. Arqub OA, Singh J, Maayah B et al (2021) Reproducing kernel approach for numerical solutions of fuzzy fractional initial value problems under the Mittag–Leffler kernel differential operator. Math Methods Appl Sci. https://doi.org/10.1002/mma.7305

  43. Faramarzi A, Heidarinejad M, Mirjalili S et al (2020) Marine predators algorithm: a nature-inspired metaheuristic. Expert Syst Appl 152:113377. https://doi.org/10.1016/j.eswa.2020.113377

    Article  Google Scholar 

  44. Bouza G, Quintana E, Tammer C (2021) A steepest descent method for set optimization problems with set-valued mappings of finite cardinality. J Optim Theory Appl 190(3):711–743. https://doi.org/10.1007/s10957-021-01887-y

    Article  MATH  Google Scholar 

  45. Li J, Gao Y, Wang K et al (2021) A dual opposition-based learning for differential evolution with protective mechanism for engineering optimization problems. Appl Soft Comput 113:107942. https://doi.org/10.1016/j.asoc.2021.107942

    Article  Google Scholar 

  46. Roy PK, Mandal D (2014) Oppositional biogeography-based optimisation for optimal power flow. Int J Power Energy Convers 5(1):47–69. https://doi.org/10.1504/IJPEC.2014.059983

    Article  Google Scholar 

  47. Wang WL, Li WK, Wang Z et al (2019) Opposition-based multi-objective whale optimization algorithm with global grid ranking. Neurocomputing 341:41–59. https://doi.org/10.1016/j.neucom.2019.02.054

    Article  Google Scholar 

  48. Niknamfar AH, Niaki STA, Niaki SAA (2017) Opposition-based learning for competitive hub location: a bi-objective biogeography-based optimization algorithm. Knowl Based Syst 128:1–19. https://doi.org/10.1016/j.knosys.2017.04.017

    Article  Google Scholar 

  49. Hussien AG, Amin M (2022) A self-adaptive Harris Hawks optimization algorithm with opposition-based learning and chaotic local search strategy for global optimization and feature selection. Int J Mach Learn Cybern 13(2):309–336. https://doi.org/10.1007/s13042-021-01326-4

    Article  Google Scholar 

  50. Zhang X, Kang Q, Tu Q et al (2019) 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

    Article  Google Scholar 

  51. Zhang X, Wen S, Wang D (2022) Multi-population biogeography-based optimization algorithm and its application to image segmentation. Appl Soft Comput. https://doi.org/10.1016/j.asoc.2022.109005

  52. Du Z, Li S, Sun Y et al (2017) Adaptive particle swarm optimization algorithm based on levy flights mechanism. In: 2017 Chinese automation congress (CAC). IEEE, pp 479–484. https://doi.org/10.1109/CAC.2017.8242815

  53. Abdel-Basset M, El-Shahat D, Sangaiah AK (2019) A modified nature inspired meta-heuristic whale optimization algorithm for solving 0–1 knapsack problem. Int J Mach Learn Cybern 10(3):495–514. https://doi.org/10.1007/s13042-017-0731-3

    Article  Google Scholar 

  54. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008

    Article  Google Scholar 

  55. Abualigah L, Diabat A, Elaziz MA (2021) Improved slime mould algorithm by opposition-based learning and Levy flight distribution for global optimization and advances in real-world engineering problems. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-021-03372-w

  56. Li S, Chen H, Wang M et al (2020) Slime mould algorithm: a new method for stochastic optimization. Future Gener Comput Syst 111:300–323. https://doi.org/10.1016/j.future.2020.03.055

    Article  Google Scholar 

  57. Awad N, Ali M, Liang J et al (2017) Problem definitions and evaluation criteria for the CEC 2017 special session and competition on singe objective bound constrained real-parameter numerical optimization. Nanyang Technological University, Technical report, Singapore

  58. Derrac J, García S, Molina D et al (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

    Article  Google Scholar 

  59. Farswan P, Bansal JC (2019) Fireworks-inspired biogeography-based optimization. Soft Comput 23(16):7091–7115. https://doi.org/10.1007/s00500-018-3351-2

    Article  Google Scholar 

  60. Mohamed AAA, Mohamed YS, El-Gaafary AAM et al (2017) Optimal power flow using moth swarm algorithm. Electric Power Syst Res 142:190–206. https://doi.org/10.1016/j.epsr.2016.09.025

    Article  Google Scholar 

  61. Heidari AA, Mirjalili S, Faris H et al (2019) Harris hawks optimization: algorithm and applications. Future Gener Comput Syst 97:849–872. https://doi.org/10.1016/j.future.2019.02.028

    Article  Google Scholar 

  62. Jain M, Singh V, Rani A (2019) A novel nature-inspired algorithm for optimization: squirrel search algorithm. Swarm Evol Comput 44:148–175. https://doi.org/10.1016/j.swevo.2018.02.013

    Article  Google Scholar 

  63. Hashim FA, Hussain K, Houssein EH et al (2021) Archimedes optimization algorithm: a new metaheuristic algorithm for solving optimization problems. Appl Intell 51(3):1531–1551. https://doi.org/10.1007/s10489-020-01893-z

    Article  Google Scholar 

  64. Khishe M, Mosavi MR (2020) Chimp optimization algorithm. Expert Syst Appl 149:113338. https://doi.org/10.1016/j.eswa.2020.113338

    Article  Google Scholar 

  65. Dhiman G, Garg M, Nagar A et al (2021) A novel algorithm for global optimization: rat swarm optimizer. J Ambient Intell Humaniz Comput 12(8):8457–8482. https://doi.org/10.1007/s12652-020-02580-0

    Article  Google Scholar 

  66. Arqub OA, Singh J, Alhodaly M (2021) Adaptation of kernel functions-based approach with Atangana-Baleanu-Caputo distributed order derivative for solutions of fuzzy fractional Volterra and Fredholm integrodifferential equations. Math Methods Appl Sci. https://doi.org/10.1002/mma.7228

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Acknowledgements

The authors wish to thank the editors and anonymous reviewers whose kind assistance and constructive comments helped to signifcantly improve this paper. This work was supported by the Key Project of Ningxia Natural Science Foundation “Several Swarm Intelligence Algorithms and Their Application” (2022AAC02043), the 2022 Graduate Innovation Project of North Minzu University (YCX22095), the National Natural Science Foundation of China under Grant (11961001), the Construction Project of First-class Subjects in Ningxia Higher Education (NXYLXK2017B09), and the Major Proprietary Funded Project of North Minzu University (ZDZX201901).

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  1. School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, China

    Ziyu Zhang & Yuelin Gao

  2. Ningxia Province Key Laboratory of Intelligent Information and Data Processing, Yinchuan, 750021, China

    Ziyu Zhang & Yuelin Gao

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Zhang, Z., Gao, Y. Solving large-scale global optimization problems and engineering design problems using a novel biogeography-based optimization with Lévy and Brownian movements. Int. J. Mach. Learn. & Cyber. 14, 313–346 (2023). https://doi.org/10.1007/s13042-022-01642-3

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