Skip to main content
SpringerLink
Log in

An improved Henry gas solubility optimization algorithm based on Lévy flight and Brown motion

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

Henry gas solubility optimization (HGSO) algorithm is a physical heuristic algorithm based on Henry’s law. It is a heuristic algorithm proposed to simulate the process of gas solubility in liquid changing with temperature. In this paper, Lévy’s flight operator and Brown motion operator are introduced respectively, which are inspired by the flight trajectory of animals and the thermal motion of particles. This increases the diversity of search strategies and enhances the ability of local search. It greatly improves the shortcoming of the original HGSO algorithm, which has a single position updating method and sometimes slow convergence speed. Lévy motion based Henry gas solubility optimization algorithm (Lévy-HGSO), Brown motion based Henry gas solubility optimization algorithm (Brown-HGSO) are proposed in this paper. It is worth mentioning that in this paper, an improved Henry gas solubility optimization algorithm (BL-HGSO) based on the Lévy and Brown motion is proposed by combining the Lévy flight operator and Brown motion operator. Different from the former two, the effective combination of different motion modes can more accurately find the optimal solution, which not only guarantees the original global search ability, but also strengthens the local search strategy, and is not easy to fall into the local optimal value. In order to verify the performance of the proposed algorithms, 40 benchmark functions were optimized by this algorithm, and two practical engineering design problems were solved. The sine and cosine algorithm (SCA), whale optimization algorithm (WOA), lightning search algorithm (LSA), water cycle algorithm(WCA)and HGSO algorithms were used in comparison experiments. The simulation results show that three improved HGSO algorithms proposed in this paper have strong ability of balancing exploration and exploitation, fast convergence speed and high precision.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Boussaid I, Lepagnot J, Siarry P (2013) A survey on optimization metaheuristics[J]. Inf Sci 237(237):82–117

    Article  MathSciNet  Google Scholar 

  2. J. Kennedy, R. Eberhart, Particle swarm optimisation, vol. 4, in: Proceedings of the IEEE international conference on neural networks, Piscataway, NJ, (1999), pp.1942–1948

  3. Tan, Y. and Y. Zhu. Fireworks Algorithm for Optimization. in Advances in Swarm Intelligence. 2010. Berlin, Heidelberg: Springer Berlin Heidelberg

  4. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer[J]. Adv Eng Softw 69:46–61

    Article  Google Scholar 

  5. Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor

    Google Scholar 

  6. Kennedy, J. and Eberhart, R. (1995) Particle swarm optimization, in neural networks. Proceedings of IEEE interna-tional conference on neural networks, Piscataway, 15-18 may 1995, 1942-1948

  7. Shi Y, Eberhart RC (2002) Empirical study of particle swarm optimization[C]// congress on evolutionary computation. IEEE

  8. Lei K (2006) Particle swarm optimization and its application research [D]. Southwest University

  9. Yang XS (2010) A new metaheuristic bat-inspired algorithm[J]. Computer Knowledge & Technology 284:65–74

    MATH  Google Scholar 

  10. Chu SC, Tsai P, Pan JS (2006) Cat swarm optimization[J]. Lect Notes Comput Sci 6:854–858

    Article  Google Scholar 

  11. Ma Z, Shi Q (2014) Review of cat swarm algorithm [J]. Journal of Gansu Radio and TV University 2:41–45

    Google Scholar 

  12. Jaza Mahmood Abdullah, Tarik Ahmed. Fitness Dependent Optimizer: Inspired by the Bee Swarming Reproductive Process. IEEE Acess (Volume:7):43473–43486

  13. Moosavi SHS (November 2019) Vahid Khatibi Bardsiri. Poor and rich optimization algorithm: A new human-based and multi populations algorithm Engineering Applicetions of Artificial Intelligence Voleme 86:165–181

    Google Scholar 

  14. Human Shayanfar, Farhad Soleimanian Gharehchopogh. Farmland fertility: A new metaheuristic algorithm for solving continuous optimization problems.Applied Soft Computing.Volume 71,October 2018,Pages 728–746

  15. Kirkpatrick, Scott, C. Daniel Gelatt, and Mario P. Vecchi. "Optimization by simulated annealing." science 220.4598 (1983): 671–680

  16. Bayraktar Z,Komurcu M,Wemer D H.Wind Driven Optimization(WDO);A novel nature-inspired optimization algorithm and its application to electromagnetics[C].Antennas and Propagation Society International Symposium (APSURSI),2010 IEEE.IEEE,2010:1–4

  17. Dhiman G, Kumar V (2017) Spotted hyena optimizer: a novel bio-inspired based metaheuristic technique for engineering applications. Adv Eng Softw 114:48–70

    Article  Google Scholar 

  18. Eskandar H et al (2012) Water cycle algorithm–a novel metaheuristic optimization method for solving constrained engineering optimization problems. Comput Struct 110:151–166

    Article  Google Scholar 

  19. Hussain Shareef,Ahmad Asrual lbrahim, Ammar Hussein Mutlag.Lightning search algorit-hm.Applied Soft Computing 36(2015) 315–333

  20. Ebadinezhad S (2020) DEACO: adopting dynamic evaporation strategy to enhance ACO algorithm for the traveling salesman problem. Eng Appl Artif Intell 92:103649

    Article  Google Scholar 

  21. Gao W (2020) New ant Colony optimization algorithm for the traveling salesman problem. International Journal of Computational Intelligence Systems 13(1):44–55

    Article  Google Scholar 

  22. Seyedali Mirjalili SCA (2016) A sine cosine algorithm for solving optimization problems[J]. Knowl-Based Syst 96:120–133

    Article  Google Scholar 

  23. Sun X (2009) Research on routing protocol of wireless sensor network based on SCA algorithm [D]. Harbin Engineering University:3313–3316

  24. Alatas, Bilal, Erhan Akin, and A. Bedri Ozer. "Chaos embedded particle swarm optimization algorithms." Chaos, Solitons & Fractals 40.4 (2009): 1715-1734

  25. Sun WZ, Wang JS (2017) Elman neural network soft-sensor model of conversion velocity in polymerization process optimized by chaos whale optimization algorithm. IEEE Access 5:13062–13076

    Article  Google Scholar 

  26. Gao S, Vairappan C, Wang Y, Cao Q, Tang Z (2014) Gravitational search algorithm combined with chaos for unconstrained numerical optimization. Appl Math Comput 231:48–62

    MathSciNet  MATH  Google Scholar 

  27. Meng XB, Gao XZ, Liu Y, Zhang H (2015) A novel bat algorithm with habitat selection and Doppler effect in echoes for optimization[J]. Expert Syst Appl 42(17–18):6350–6364

    Article  Google Scholar 

  28. Yaseen ZM, Allawi MF, Karami H, Ehteram M, Farzin S, Ahmed AN, Koting SB, Mohd NS, Jaafar WZB, Afan HA, el-Shafie A (2019) A hybrid bat–swarm algorithm for optimizing dam and reservoir operation. Neural Comput & Applic 31:8807–8821

    Article  Google Scholar 

  29. W.-Z. Sun, J.-S. Wang, and X. Wei, “An improved whale optimization algorithm based on different searching paths and perceptual disturbance,“Symmetry, vol. 10, no. 6, p. 210, 2018, doi: https://doi.org/10.3390/sym10060210

  30. Long W, Liang X, Cai S, Jiao J, Zhang W (2016) A modified augmented Lagrangian with improved grey wolf optimization to constrained optimization problems[J]. Neural Comput & Applic 28:421–438

    Article  Google Scholar 

  31. Kohli M, Arora S (2017) Chaotic grey wolf optimization algorithm for constrained optimization problems[J]. Journal of Computational Design and Engineering S2288430016301142:458–472

    Google Scholar 

  32. Juliano Pierezan, Leandro Dos Santos Coelho.Coyote Optimization Algorithm:A New Metaheuristic for Global Optimization Problems.2018 IEEE Congress on Evolutionary Computation(CEC)

  33. Staudinger J, Roberts PV (1996) A critical review of Henry's law constants for environmental applications. Crit Rev Environ Sci Technol 26(3):205–297

    Article  Google Scholar 

  34. Hashim FA, Houssein EH, Mabrouk MS, Al-Atabany W, Mirjalili S (2019) Henry gas solubility optimization: a novel physics-based algorithm. Futur Gener Comput Syst 101:646–667

    Article  Google Scholar 

  35. Mohamed Abd Elaziz,lbrahim Attiya.An improved Henry gas solubility optimization for task scheduling in cloud computing. Artifical Intelligence Review 54,3599–3637(2021)

  36. Fatma A.Hashim,Essam H.Houssein,Kashif Hussain,Mai S.Mabrouk&Waild Al-Atabany.A modified Henry gas solubility optimization for solving motif discovery problem.Netural Computing and Application 32,10759–10771(2020)

  37. Nabil Neggaz,Essam H.Houssein,Kashif Hussain.An efficient henry gas solubility optimization for feature selection.Expert Systems With Application 152 (2020) 113364

  38. Zhou B, Liao X (2020) Particle filter and levy flight-based decomposed multi-objective evolution hybridized particle swarm for flexible job shop greening scheduling with crane transportation. Appl Soft Comput 106217

  39. Liu Y, Cao B, Li H (2020) Improving ant colony optimization algorithm with epsilon greedy and levy flight. JSP 24(25):54

    Google Scholar 

  40. Sarangi, Shubhendu Kumar, Rutuparna Panda, and Ajith Abraham. "Design of optimal low-pass filter by a new Levy swallow swarm algorithm

  41. Wang Qingxi,Guo Xiaobo.Particle swarm optimization algorithm based on Levy flight[J].Application Research of Computers,2011,28(9):3295–3297

  42. Wei Xie, Cheng, Xing, Jiesheng, Wang, Shasha,Guo, Mengwei, Guo. Hybrid Henry Gas Solubility Optimization Algorithm Based on the Harris Hawk Optimization. IEEE Access,144665–144692

  43. Faramarzi A, Heidarinejad M, Mirjalili S, Gandomi AH (2020) Marine predators algorithm: a nature-inspired metaheuristic[J]. Expert SystemsWith Applications 152:1–50

    Google Scholar 

  44. Guo MW, Wang JS, Zhu LF, Guo SS, Xie W (2020) An improved Grey wolf optimizer based on tracking and seeking modes to solve function optimization problems. IEEE Access 8:69861–69893

    Article  Google Scholar 

  45. Gandomi AH, Yang XS, Alavi AH (2013) Cuckoo search algorithm:a metaheuristic approach to solve structural optimization problems[J]. Eng Comput 29(2):245–245

    Article  Google Scholar 

  46. Mahdavi M,Feasanghary M,Damangir E.An improved harmony search algorithm for solving optimization problems[J].Applied Mathematics and Computation,2007,188(2):1567–1579

  47. Zahara E, Kao YT (2009) Hybrid Nelder–Mead simplex search and particle swarm optimization for constrained engineering design problems. Expert Syst Appl 36(2):3880–3886

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Basic Scientific Research Project of Institution of Higher Learning of Liaoning Province (Grant No. 2017FWDF10), and the Project by Liaoning Provincial Natural Science Foundation of China (Grant No. 20180550700 and 20190550263).

Author information

Authors and Affiliations

  1. School of Electronic and Information Engineering, University of Science & Technology Liaoning, Anshan, 114044, People’s Republic of China

    Song Li, Jie-Sheng Wang, Wei Xie & Xue-Long Li

Authors
  1. Song Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jie-Sheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xue-Long Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

A substantial amount of Song Li’s contributions participated in the algorithm simulation and the draft writing. Jie-Sheng Wang ‘s contributions participated in the concept, design and critical revision of this paper. Wei Xie’s contributions participated in the data collection and analysis. Xue-Long Li participated in the interpretation and commented on the manuscript.

Corresponding author

Correspondence to Jie-Sheng Wang.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this article.

Additional information

Publisher’s note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, S., Wang, JS., Xie, W. et al. An improved Henry gas solubility optimization algorithm based on Lévy flight and Brown motion. Appl Intell 52, 12584–12608 (2022). https://doi.org/10.1007/s10489-021-02811-7

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-021-02811-7

Keywords

Search

Navigation