Skip to main content

Advertisement

Springer Nature Link
Log in

ISSWOA: hybrid algorithm for function optimization and engineering problems

  • Published:
The Journal of Supercomputing Aims and scope Submit manuscript

Abstract

A hybrid algorithm based on the sparrow search algorithm (SSA) and whale optimization algorithm (WOA) is proposed to address numerical and engineering optimization problems. The hybrid algorithm has enhanced global search ability through the WOA's improved spiral update mechanism, so that it does not easily fall into the local optimum. Further, using the guard mechanism of SSA introduced by the Levy flight, it has a strong ability to escape from the local optimum. The performance of the improved sparrow search whale optimization algorithm (ISSWOA) was investigated using 23 benchmark functions (classified into standard unimodal, multimodal, and fixed-dimension multimodal benchmark functions) and compared with similar algorithms. The experimental results indicated that ISSWOA was significantly superior to other algorithms on most benchmark functions. To evaluate the performance of ISSWOA in complex engineering problems, seven engineering design problems and a large electrical engineering problem were solved using ISSWOA. Compared with other algorithms, the results showed that ISSWOA had high potential for practical engineering problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

Data availability

All data generated or analyzed during this study are included in this article.

References

  1. Zhang Y, Mo Y (2022) Chaotic adaptive sailfish optimizer with genetic characteristics for global optimization. J Supercomput 78:10950–10996. https://doi.org/10.1007/s11227-021-04255-9

    Article  Google Scholar 

  2. Tang KS, Man KF, Kwong S et al (2022) Genetic algorithms and their applications. IEEE Signal Proc Mag 13:22–37. https://doi.org/10.1109/79.543973

    Article  Google Scholar 

  3. Das S, Suganthan PN (2010) Differential evolution: a survey of the state-of-the-art. IEEE Trans Evol Comput 15:4–31. https://doi.org/10.1109/TEVC.2010.2059031

    Article  Google Scholar 

  4. Lee KY, Yang FF (1998) Optimal reactive power planning using evolutionary algorithms: a comparative study for evolutionary programming, evolutionary strategy, genetic algorithm, and linear programming. IEEE Trans Power Syst 13:101–108. https://doi.org/10.1109/59.651620

    Article  Google Scholar 

  5. Espejo PG, Ventura S, Herrera F (2009) A survey on the application of genetic programming to classification. IEEE Trans Syst Man Cybernet C 40:121–144. https://doi.org/10.1109/TSMCC.2009.2033566

    Article  Google Scholar 

  6. Zhong J, Feng L, Ong YS (2017) Gene expression programming: a survey. IEEE Comput Intell Mag 12:54–72

    Article  Google Scholar 

  7. Prajapati A (2022) A customized PSO model for large-scale many-objective software package restructuring problem. Arab J Sci Eng 47:10147–10162. https://doi.org/10.1007/s13369-021-06523-5

    Article  Google Scholar 

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

    Article  Google Scholar 

  9. Hashim FA, Hussien AG (2022) Snake optimizer: a novel meta-heuristic optimization algorithm. Knowl Based Syst 242:108320. https://doi.org/10.1016/j.knosys.2022.108320

    Article  Google Scholar 

  10. Salgotra R, Singh U, Saha S (2019) On some improved versions of whale optimization algorithm. Arab J Sci Eng 44:9653–9691. https://doi.org/10.1007/s13369-019-04016-0

    Article  Google Scholar 

  11. Peraza-Vázquez H, Peña-Delgado AF, Echavarría-Castillo G et al (2021) A bio-inspired method for engineering design optimization inspired by dingoes hunting strategies. Math Probl Eng. https://doi.org/10.1155/2021/9107547

    Article  Google Scholar 

  12. Zhang Z, He R, Yang K (2022) A bioinspired path planning approach for mobile robots based on improved sparrow search algorithm. Adv Manuf 10:114–130. https://doi.org/10.1007/s40436-021-00366-x

    Article  Google Scholar 

  13. Gürses D, Mehta P, Sait SM et al (2022) African vultures optimization algorithm for optimization of shell and tube heat exchangers. Mater Test 64:1234–1241. https://doi.org/10.1515/mt-2022-0050

    Article  Google Scholar 

  14. Barbarosoglu G, Ozgur D (1999) A tabu search algorithm for the vehicle routing problem. Comput Oper Res 26:255–270. https://doi.org/10.1016/S0305-0548(98)00047-1

    Article  MathSciNet  MATH  Google Scholar 

  15. Dai C, Chen W, Zhu Y et al (2009) Seeker optimization algorithm for optimal reactive power dispatch. IEEE Trans Power Syst 24:1218–1231. https://doi.org/10.1109/TPWRS.2009.2021226

    Article  Google Scholar 

  16. Ramezani F, Lotfi S (2013) Social-based algorithm (SBA). Appl Soft Comput 13:2837–2856. https://doi.org/10.1016/j.asoc.2012.05.018

    Article  Google Scholar 

  17. Ghorbani N, Babaei E (2014) Exchange market algorithm. Appl Soft Comput 19:177–187. https://doi.org/10.1016/j.asoc.2014.02.006

    Article  Google Scholar 

  18. Vincent FY, Jewpanya P, Redi AANP et al (2021) Adaptive neighborhood simulated annealing for the heterogeneous fleet vehicle routing problem with multiple cross-docks. Comput Oper Res 129:105205. https://doi.org/10.1016/j.cor.2020.105205

    Article  MathSciNet  MATH  Google Scholar 

  19. Pashaei E, Aydin N (2017) Binary black hole algorithm for feature selection and classification on biological data. Appl Soft Comput 56:94–106. https://doi.org/10.1016/j.asoc.2017.03.002

    Article  Google Scholar 

  20. Eskandar H, Sadollah A, Bahreininejad A et al (2012) Water cycle algorithm—a novel metaheuristic optimization method for solving constrained engineering optimization problems. Comput Struct 110:151–166. https://doi.org/10.1016/j.compstruc.2012.07.010

    Article  Google Scholar 

  21. Kaveh A, Khayatazad M (2012) A new meta-heuristic method: ray optimization. Comput Struct 112:283–294. https://doi.org/10.1016/j.compstruc.2012.09.003

    Article  Google Scholar 

  22. Kumar S, Tejani GG, Pholdee N et al (2021) Hybrid heat transfer search and passing vehicle search optimizer for multi-objective structural optimization. Knowl Based Syst 212:106556. https://doi.org/10.1016/j.knosys.2020.106556

    Article  Google Scholar 

  23. Yildiz AR, Mehta P (2022) Manta ray foraging optimization algorithm and hybrid Taguchi salp swarm-Nelder–Mead algorithm for the structural design of engineering components. Mater Test 64:706–713. https://doi.org/10.1515/mt-2022-0012

    Article  Google Scholar 

  24. Li Q, Wang W (2021) AVO inversion in orthotropic media based on SA-PSO. IEEE Trans Geosci Remote 99:1–10. https://doi.org/10.1109/TGRS.2021.3053044

    Article  Google Scholar 

  25. Mafarja MM, Mirjalili S (2017) Hybrid whale optimization algorithm with simulated annealing for feature selection. Neurocomputing 260:302–312. https://doi.org/10.1016/j.neucom.2017.04.053

    Article  Google Scholar 

  26. Laskar NM, Guha K, Chatterjee I et al (2019) HWPSO: a new hybrid whale-particle swarm optimization algorithm and its application in electronic design optimization problems. Appl Intell 49:265–291. https://doi.org/10.1007/s10489-018-1247-6

    Article  Google Scholar 

  27. Han X, Yue L, Dong Y et al (2020) Efficient hybrid algorithm based on moth search and fireworks algorithm for solving numerical and constrained engineering optimization problems. J Supercomput 76:9404–9429. https://doi.org/10.1007/s11227-020-03212-2

    Article  Google Scholar 

  28. Shehab M, Khader AT, Laouchedi M et al (2019) Hybridizing cuckoo search algorithm with bat algorithm for global numerical optimization. J Supercomput 75:2395–2422. https://doi.org/10.1007/s11227-018-2625-x

    Article  Google Scholar 

  29. Li X, Gu J, Sun X et al (2022) Parameter identification of robot manipulators with unknown payloads using an improved chaotic sparrow search algorithm. Appl Intell. https://doi.org/10.1007/s10489-021-02972-5

    Article  Google Scholar 

  30. Chakraborty S, Sharma S, Saha AK et al (2021) SHADE–WOA: a metaheuristic algorithm for global optimization. Appl Soft Comput 113:107866. https://doi.org/10.1016/j.asoc.2021.107866

    Article  Google Scholar 

  31. Xue J, Shen B (2020) A novel swarm intelligence optimization approach: sparrow search algorithm. Syst Sci Control Eng 8:22–34. https://doi.org/10.1080/21642583.2019.1708830

    Article  Google Scholar 

  32. 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 

  33. Iacca G, dos Santos JVC, de Melo VV (2021) An improved Jaya optimization algorithm with Lévy flight. Expert Syst Appl 165:113902. https://doi.org/10.1016/j.eswa.2020.113902

    Article  Google Scholar 

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

    Article  Google Scholar 

  35. Nadimi-Shahraki MH, Taghian S, Mirjalili S (2021) An improved grey wolf optimizer for solving engineering problems. Expert Syst Appl 166:113917. https://doi.org/10.1016/j.eswa.2020.113917

    Article  Google Scholar 

  36. Zhang M, Long D, Qin T et al (2020) A chaotic hybrid butterfly optimization algorithm with particle swarm optimization for high-dimensional optimization problems. Symmetry 12:1800. https://doi.org/10.3390/sym12111800

    Article  Google Scholar 

  37. Khalilpourazari S, Khalilpourazary S (2019) An efficient hybrid algorithm based on water cycle and moth-flame optimization algorithms for solving numerical and constrained engineering optimization problems. Soft Comput 23:1699–1722. https://doi.org/10.1007/s00500-017-2894-y

    Article  Google Scholar 

  38. Tang A, Zhou H, Han T et al (2021) A chaos sparrow search algorithm with logarithmic spiral and adaptive step for engineering problems. CMES Compt Model Eng 130:331–364. https://doi.org/10.32604/cmes.2021.017310

    Article  Google Scholar 

  39. Mirjalili S (2015) The ant lion optimizer. Adv V Eng Softw 83:80–98. https://doi.org/10.1016/j.advengsoft.2015.01.010

    Article  Google Scholar 

  40. Dhiman G, Kumar V (2017) Spotted hyena optimizer: a novel bio-inspired based metaheuristic technique for engineering applications. Adv Eng Softw 114:48–70. https://doi.org/10.1016/j.advengsoft.2017.05.014

    Article  Google Scholar 

  41. Krishna AB, Saxena S, Kamboj VK (2021) A novel statistical approach to numerical and multidisciplinary design optimization problems using pattern search inspired Harris hawks optimizer. Neural Comput Appl 33:7031–7072. https://doi.org/10.1007/s00521-020-05475-5

    Article  Google Scholar 

  42. Kamboj VK, Nandi A, Bhadoria A et al (2020) An intensify Harris Hawks optimizer for numerical and engineering optimization problems. Appl Soft Comput 89:106018. https://doi.org/10.1016/j.asoc.2019.106018

    Article  Google Scholar 

  43. Ferreira MP, Rocha ML, Neto AJS et al (2018) A constrained ITGO heuristic applied to engineering optimization. Expert Syst Appl 110:106–124. https://doi.org/10.1016/j.eswa.2018.05.027

    Article  Google Scholar 

  44. Zhang Z, Ding S, Jia W (2019) A hybrid optimization algorithm based on cuckoo search and differential evolution for solving constrained engineering problems. Eng Appl Artif Intel 85:254–268. https://doi.org/10.1016/j.engappai.2019.06.017

    Article  Google Scholar 

  45. Zahara E, Kao YT (2009) Hybrid Nelder–Mead simplex search and particle swarm optimization for constrained engineering design problems. Expert Syst Appl 36:3880–3886. https://doi.org/10.1016/j.eswa.2008.02.039

    Article  Google Scholar 

  46. Guo W, Chen M, Wang L et al (2016) Backtracking biogeography-based optimization for numerical optimization and mechanical design problems. Appl Intell 44:894–903. https://doi.org/10.1007/s10489-015-0732-4

    Article  Google Scholar 

  47. Baykasoğlu A, Ozsoydan FB (2015) Adaptive firefly algorithm with chaos for mechanical design optimization problems. Appl Soft Comput 36:152–164. https://doi.org/10.1016/j.asoc.2015.06.056

    Article  Google Scholar 

  48. Savsani P, Savsani V (2016) Passing vehicle search (PVS): a novel metaheuristic algorithm. Appl Math Model 40:3951–3978. https://doi.org/10.1016/j.apm.2015.10.040

    Article  Google Scholar 

  49. Hashim FA, Houssein EH, Mabrouk MS et al (2019) Henry gas solubility optimization: a novel physics-based algorithm. Future Gener Comput Syst 101:646–667. https://doi.org/10.1016/j.future.2019.07.015

    Article  Google Scholar 

  50. Abd EM, Oliva D, Xiong S (2017) An improved opposition-based sine cosine algorithm for global optimization. Expert Syst Appl 90:484–500. https://doi.org/10.1016/j.eswa.2017.07.043

    Article  Google Scholar 

  51. Singh N, Singh SB, Houssein EH (2020) Hybridizing salp swarm algorithm with particle swarm optimization algorithm for recent optimization functions. Evol Intell 1:1–34. https://doi.org/10.1007/s12065-020-00486-6

    Article  Google Scholar 

  52. Sadollah A, Bahreininejad A, Eskandar H et al (2013) Mine blast algorithm: a new population based algorithm for solving constrained engineering optimization problems. Appl Soft Comput 13:2592–2612. https://doi.org/10.1016/j.asoc.2012.11.026

    Article  Google Scholar 

  53. Braik MS (2021) Chameleon swarm algorithm: a bio-inspired optimizer for solving engineering design problems. Expert Syst Appl 174:114685. https://doi.org/10.1016/j.eswa.2021.114685

    Article  Google Scholar 

  54. Zhang C, Lin Q, Gao L et al (2015) Backtracking search algorithm with three constraint handling methods for constrained optimization problems. Expert Syst Appl 42:7831–7845. https://doi.org/10.1016/j.eswa.2015.05.050

    Article  Google Scholar 

  55. Yang XS, Gandomi AH (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput. https://doi.org/10.1108/02644401211235834

    Article  Google Scholar 

  56. Singh N, Singh SB (2017) A novel hybrid GWO-SCA approach for optimization problems. Eng Sci Technok 20:1586–1601. https://doi.org/10.1016/j.jestch.2017.11.001

    Article  Google Scholar 

  57. Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl Based Syst 89:228–249. https://doi.org/10.1016/j.knosys.2015.07.006

    Article  Google Scholar 

  58. Li Y, Lin X, Liu J (2021) An improved gray wolf optimization algorithm to solve engineering problems. Sustainability 13:3208. https://doi.org/10.3390/su13063208

    Article  Google Scholar 

  59. Chopra N, Ansari MM (2022) Golden jackal optimization: a novel nature-inspired optimizer for engineering applications. Expert Syst Appl 198:116924. https://doi.org/10.1016/j.eswa.2022.116924

    Article  Google Scholar 

  60. Ling SH, Iu HHC, Chan KY et al (2008) Hybrid particle swarm optimization with wavelet mutation and its industrial applications. IEEE Trans Syst Man Cybernet B 38:743–763. https://doi.org/10.1109/TSMCB.2008.921005

    Article  Google Scholar 

  61. Bayzidi H, Talatahari S, Saraee M et al (2021) Social network search for solving engineering optimization problems. Comput Intel Neurosci. https://doi.org/10.1155/2021/8548639

    Article  Google Scholar 

  62. Chen H, Wang M, Zhao X (2020) A multi-strategy enhanced sine cosine algorithm for global optimization and constrained practical engineering problems. Appl Math Comput 369:124872. https://doi.org/10.1016/j.amc.2019.124872

    Article  MathSciNet  MATH  Google Scholar 

  63. Chauhan S, Vashishtha G, Kumar A (2022) A symbiosis of arithmetic optimizer with slime mould algorithm for improving global optimization and conventional design problem. J Supercomput 78:6234–6274. https://doi.org/10.1007/s11227-021-04105-8

    Article  Google Scholar 

  64. Migallón H, Jimeno-Morenilla A, Rico H et al (2021) Multi-level parallel chaotic Jaya optimization algorithms for solving constrained engineering design problems. J Supercomput 77:12280–12319. https://doi.org/10.1007/s11227-021-03737-0

    Article  Google Scholar 

  65. Emami H (2022) Stock exchange trading optimization algorithm: a human-inspired method for global optimization. J Supercomput 78:2125–2174. https://doi.org/10.1007/s11227-021-03943-w

    Article  Google Scholar 

  66. Sinha N, Chakrabarti R, Chattopadhyay PK (2003) Evolutionary programming techniques for economic load dispatch. IEEE Trans Evolut Comput 7:83–94. https://doi.org/10.1109/TEVC.2002.806788

    Article  Google Scholar 

Download references

Funding

This work was supported by the National Natural Science Foundation of China Program under Grant 62073198.

Author information

Authors and Affiliations

  1. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, China

    Jianhui Zhang, Xuezhen Cheng, Meng Zhao & Jiming Li

Authors
  1. Jianhui Zhang
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Xuezhen Cheng
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Meng Zhao
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Jiming Li
    View author publications

    You can also search for this author inPubMed Google Scholar

Contributions

JZ and XC proposed the innovation and designed the experiment in this study, JZ, MZ, and JL performed the simulation experiments and analyzed the experiment results and wrote the manuscript, JL corrected the manuscript.

Corresponding author

Correspondence to Jiming Li.

Ethics declarations

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Ethical approval

This study will not cause harm to anyone or animals.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, J., Cheng, X., Zhao, M. et al. ISSWOA: hybrid algorithm for function optimization and engineering problems. J Supercomput 79, 8789–8842 (2023). https://doi.org/10.1007/s11227-022-04996-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11227-022-04996-1

Keywords