Skip to main content

Advertisement

Springer Nature Link
Log in

RETRACTED ARTICLE: A hybrid slime mould algorithm for global optimization

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

This article was retracted on 09 August 2024

This article has been updated

Abstract

The local optima stagnation is a major issue with all meta-heuristic algorithms. In this paper, a hybrid slime mould algorithm (SMA) is proposed with the aid of quadratic approximation to address the aforesaid problem to expedite the explorative strength of slime mould in nature. As quadratic approximation performs better within the local confinement region, so the QA has been incorporated with SMA to propose the hybrid HSMA to improve the exploitation ability of the algorithm so that global optimum can be achieved. The effectiveness of the proposed algorithm has been compared with classical SMA, some state-of-the-art metaheuristics, some PSO variants using 20 benchmark problems and IEEE CEC 2017 suite. Convergence analysis and statistical tests are performed to validate the supremacy of the proposed algorithm. Moreover, three real-world engineering optimization problems are solved, and solutions are compared with various algorithms. Results and their analyses convey the fruitfulness of the proposed algorithm by showing encouraging performance on different search landscapes.

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

Similar content being viewed by others

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

Change history

References

  1. Civicioglu P (2013) Backtracking search optimization algorithm for numerical optimization problems. Appl Math Comput 219(15):8121–8144. https://doi.org/10.1016/j.amc.2013.02.017

    Article  MathSciNet  Google Scholar 

  2. Das S, Suganthan PN (2010) Problem definitions and evaluation criteria for CEC 2011 competition on testing evolutionary algorithms on real world optimization problems. Jadavpur University, Nanyang Technological University, Kolkata, pp 341–359

  3. 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

    Article  Google Scholar 

  4. Draz A, Elkholy MM, El-Fergany AA (2021) Slime mould algorithm constrained by the relay operating time for optimal coordination of directional overcurrent relays using multiple standardized tripping curves. Neural Comput & Applic 33(18):11875–11887

    Article  Google Scholar 

  5. Ewees AA, Abualigah L, Yousri D, Algamal ZY, Al-qaness MAA, Ibrahim RA, Abd Elaziz M (2021) Improved slime Mould algorithm based on firefly algorithm for feature selection: a case study on QSAR model. Eng Comput 38:2407–2421. https://doi.org/10.1007/s00366-021-01342-6

    Article  Google Scholar 

  6. Formato RA (2007) Central force optimization: a new metaheuristic with applications in applied electromagnetics. Prog Electromagn Res 77:425–491. https://doi.org/10.2528/PIER07082403

    Article  Google Scholar 

  7. Gao ZM, Zhao J, Li SR (2020) The improved slime Mould algorithm with cosine controlling parameters. J Phys Conf Ser 1631(1):12083. https://doi.org/10.1088/1742-6596/1631/1/012083

    Article  Google Scholar 

  8. Geem ZW, Kim JH, Loganathan G (2001) A new heuristic optimization algorithm: harmony search. Simulation 76:60–68

    Article  Google Scholar 

  9. Gupta J, Nijhawan P, Ganguli S (2021) Optimal parameter estimation of PEM fuel cell using slime mould algorithm. Int J Energy Res 45(10):14732–14744

    Article  Google Scholar 

  10. Gush T, Kim C-H, Admasie S, Kim J-S, Song J-S (2021) Optimal smart inverter control for PV and BESS to improve PV hosting capacity of distribution networks using slime mould algorithm. IEEE Access 9:52164–52176

    Article  Google Scholar 

  11. Hatamlou A (2013) Black hole: a new heuristic optimization approach for data clustering. Inf Sci 222:175–184. https://doi.org/10.1016/j.ins.2012.08.023

    Article  MathSciNet  Google Scholar 

  12. Holland JH (1975) Adaptation in natural and artificial systems | the MIT press. The University of Michigan Press. https://mitpress.mit.edu/books/adaptation-natural-and-artificial-systems

  13. Houssein EH, Mahdy MA, Blondin MJ, Shebl D, Mohamed WM (2021) Hybrid slime mould algorithm with adaptive guided differential evolution algorithm for combinatorial and global optimization problems. Expert Syst Appl 174:114689. https://doi.org/10.1016/j.eswa.2021.114689

    Article  Google Scholar 

  14. Karaboga DJ (2010) Artificial bee colony algorithm. Scholarpedia 5(3):6915

    Article  Google Scholar 

  15. Kaveh A, Khayatazad M (2012) A new meta-heuristic method: ray optimization. Comput Struct 112–113:283–294. https://doi.org/10.1016/j.compstruc.2012.09.003

    Article  Google Scholar 

  16. Kaveh A, Biabani Hamedani K, Kamalinejad M (2022) Improved slime mould algorithm with elitist strategy and its application to structural optimization with natural frequency constraints. Comput Struct 264:106760. https://doi.org/10.1016/j.compstruc.2022.106760

    Article  Google Scholar 

  17. Kennedy J, Eberhart R (1995) Particle swarm optimization. Proceedings of ICNN’95 - international conference on neural networks, 4, 1942–1948. https://doi.org/10.1109/ICNN.1995.488968

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

    Article  Google Scholar 

  19. Liang X, Wu D, Liu Y, He M, Sun L (2021) An enhanced slime Mould algorithm and its application for digital IIR filter design. Discret Dyn Nat Soc 2021:5333278–5333223. https://doi.org/10.1155/2021/5333278

    Article  Google Scholar 

  20. Lin WY (2010) A GA-DE hybrid evolutionary algorithm for path synthesis of four-bar linkage. Mech Mach Theory 45(8):1096–1107. https://doi.org/10.1016/j.mechmachtheory.2010.03.011

    Article  Google Scholar 

  21. Lin Q, Gao L, Li X, Zhang C (2015) A hybrid backtracking search algorithm for permutation flow-shop scheduling problem. Comput Ind Eng 85:437–446. https://doi.org/10.1016/j.cie.2015.04.009

    Article  Google Scholar 

  22. Lozano M, García-Martínez C (2010) Hybrid metaheuristics with evolutionary algorithms specializing in intensification and diversification: overview and progress report. Comput Oper Res 37(3):481–497. https://doi.org/10.1016/j.cor.2009.02.010

    Article  MathSciNet  Google Scholar 

  23. Lynden JM (2019) Diversification and Intensification in Hybrid Metaheuristics for Constraint Satisfaction Problems. PhD Thesis.https://nsuworks.nova.edu/gscis_etd/1076

  24. 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 

  25. Moosavian N, Roodsari BK (2013) Soccer league competition algorithm: a new method for solving systems of non-linear equations. Int J Intell Sci 4:7

    Google Scholar 

  26. Mortazavi A, Toğan V, Moloodpoor M (2019) Solution of structural and mathematical optimization problems using a new hybrid swarm intelligence optimization algorithm. Adv Eng Softw 127:106–123. https://doi.org/10.1016/j.advengsoft.2018.11.004

    Article  Google Scholar 

  27. Nama S (2021) A modification of I-SOS: performance analysis to large scale functions. Appl Intell 51:7881–7902. https://doi.org/10.1007/s10489-020-01974-z

    Article  Google Scholar 

  28. Nama S (2022) A novel improved SMA with quasi reflection operator: performance analysis, application to the image segmentation problem of Covid-19 chest X-ray images. Appl Soft Comput 118:108483. https://doi.org/10.1016/j.asoc.2022.108483

    Article  Google Scholar 

  29. Nama S, Saha AK (2018) An ensemble symbiosis organisms search algorithm and its application to real world problems. Decis Sci Lett 7(2):103–118. https://doi.org/10.5267/j.dsl.2017.6.006

    Article  Google Scholar 

  30. Nama S, Saha AK (2018) A new hybrid differential evolution algorithm with self-adaptation for function optimization. Appl Intell 48(7):1657–1671. https://doi.org/10.1007/s10489-017-1016-y

    Article  Google Scholar 

  31. Nama S, Saha AK (2019) A novel hybrid backtracking search optimization algorithm for continuous function optimization. Decis Sci Lett 8(2):163–174. https://doi.org/10.5267/j.dsl.2018.7.002

    Article  Google Scholar 

  32. Nama S, Saha AK (2020) A new parameter setting-based modified differential evolution for function optimization. Int J Model Simul Sci Comput 11(4):2050029. https://doi.org/10.1142/S1793962320500294

    Article  Google Scholar 

  33. Nama S, Saha AK, Ghosh S (2016) Improved symbiotic organisms search algorithm for solving unconstrained function optimization. Decis Sci Lett 5(3):361–380. https://doi.org/10.5267/j.dsl.2016.2.004

    Article  Google Scholar 

  34. Nama S, Kumar Saha A, Ghosh S (2017) A hybrid Symbiosis organisms search algorithm and its application to real world problems. Memetic Comput 9(3):261–280. https://doi.org/10.1007/s12293-016-0194-1

    Article  Google Scholar 

  35. Nama S, Saha AK, Sharma S (2019) A hybrid TLBO algorithm by quadratic approximation for function optimization and its application. In: Intelligent systems reference library, vol 172. Springer, pp 291–341. https://doi.org/10.1007/978-3-030-32644-9_30

    Chapter  Google Scholar 

  36. Nama S, Saha AK, Sharma S (2021) Performance up-gradation of symbiotic organisms search by backtracking search algorithm. J Ambient Intell Humaniz Comput 1:3–42. https://doi.org/10.1007/s12652-021-03183-z

    Article  Google Scholar 

  37. Örnek BN, Aydemir SB, Düzenli T, Özak B (2022) A novel version of slime mould algorithm for global optimization and real world engineering problems: enhanced slime mould algorithm. Math Comput Simul 198:253–288. https://doi.org/10.1016/j.matcom.2022.02.030

    Article  MathSciNet  Google Scholar 

  38. Pan J-S, Wang H-J, Nguyen T-T, Zou F-M, Chu S-C (2022) Dynamic reconfiguration of distribution network based on dynamic optimal period division and multi-group flight slime mould algorithm. Electr Power Syst Res 208:107925. https://doi.org/10.1016/j.epsr.2022.107925

    Article  Google Scholar 

  39. Precup R-E, David R-C, Roman R-C, Petriu EM, Szedlak-Stinean A-I (2021) Slime mould algorithm-based tuning of cost-effective fuzzy controllers for servo systems. Int J Comput Intell Syst 14(1):1042–1052

    Article  Google Scholar 

  40. Rao SS (2019) Engineering optimization: theory and practice. In: Engineering Optimization: Theory and Practice. Wiley. https://doi.org/10.1002/9781119454816

    Chapter  Google Scholar 

  41. Rao RV, Savsani VJ, Vakharia DP (2012) Teaching–learning-based optimization: an optimization method for continuous non-linear large scale problems.Information. Sciences 183(1):1–15. https://doi.org/10.1016/j.ins.2011.08.006

    Article  MathSciNet  Google Scholar 

  42. Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248. https://doi.org/10.1016/j.ins.2009.03.004

    Article  Google Scholar 

  43. Ren L, Heidari AA, Cai Z, Shao Q, Liang G, Chen H-L, Pan Z (2022) Gaussian kernel probability-driven slime mould algorithm with new movement mechanism for multi-level image segmentation. Measurement 192:110884. https://doi.org/10.1016/j.measurement.2022.110884

    Article  Google Scholar 

  44. Sadollah A, Bahreininejad A, Eskandar H, Hamdi M (2013) Mine blast algorithm: a new population based algorithm for solving constrained engineering optimization problems. Appl Soft Comput 13:2592–2612

    Article  Google Scholar 

  45. Saha A, Nama S, Ghosh S (2019) Application of HSOS algorithm on pseudo-dynamic bearing capacity of shallow strip footing along with numerical analysis. Int J Geotech Eng 15:1298–1311. https://doi.org/10.1080/19386362.2019.1598015

    Article  Google Scholar 

  46. Sharma S, Saha AK, Majumder A, Nama S (2021) MPBOA - a novel hybrid butterfly optimization algorithm with symbiosis organisms search for global optimization and image segmentation. Multimed Tools Appl 80(8):12035–12076. https://doi.org/10.1007/s11042-020-10053-x

    Article  Google Scholar 

  47. Storn R, Price K (1997) Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359. https://doi.org/10.1023/A:1008202821328

    Article  MathSciNet  Google Scholar 

  48. Sun K, Jia H, Li Y, Jiang Z (2021) Hybrid improved slime mould algorithm with adaptive β hill climbing for numerical optimization. J Intell Fuzzy Syst 40(1):1667–1679. https://doi.org/10.3233/JIFS-201755

    Article  Google Scholar 

  49. Tan Y, Zhu Y (2010) Fireworks Algorithm for Optimization. In: Tan, Y., Shi, Y., Tan, K.C. (eds) Advances in Swarm Intelligence. ICSI 2010. Lecture Notes in Computer Science, vol 6145. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13495-1_44

  50. Tiachacht S, Khatir S, Thanh CL, Rao RV, Mirjalili S,Wahab MA (2022) Inverse problem for dynamic structural health monitoring based on slime mould algorithm. Eng Comput 38(Suppl 3):2205–2228. https://doi.org/10.1007/s00366-021-01378-8

  51. Vashishtha G, Chauhan S, Singh M, Kumar RJM (2021) Bearing defect identification by swarm decomposition considering permutation entropy measure and opposition-based slime mould algorithm. Measurement 178:109389

    Article  Google Scholar 

  52. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82. https://doi.org/10.1109/4235.585893

    Article  Google Scholar 

  53. Yi W, Gao L, Li X, Zhou Y (2015) A new differential evolution algorithm with a hybrid mutation operator and self-adapting control parameters for global optimization problems. Appl Intell 42(4):642–660. https://doi.org/10.1007/s10489-014-0620-3

  54. Zhang C, Ning J, Lu S, Ouyang D, Ding T (2009) A novel hybrid differential evolution and particle swarm optimization algorithm for unconstrained optimization. Oper Res Lett 37(2):117–122. https://doi.org/10.1016/j.orl.2008.12.008

    Article  MathSciNet  Google Scholar 

  55. Zhao S, Wang P, Heidari AA, Chen H, Turabieh H, Mafarja M, Li C (2021) Multilevel threshold image segmentation with diffusion association slime mould algorithm and Renyi's entropy for chronic obstructive pulmonary disease. Comput Biol Med 134:104427

    Article  Google Scholar 

  56. Zobaa AM, Aleem SHA, Youssef HK (2021) Comparative analysis of double-tuned harmonic passive filter design methodologies using slime mould optimization algorithm. Paper presented at the 2021 IEEE Texas power and energy conference (TPEC)

  57. Zubaidi SL, Abdulkareem IH, Hashim KS, Al-Bugharbee H, Ridha HM, Gharghan SK, Al-Qaim FF, Muradov M, Kot P, Al-Khaddar R (2020) Hybridised artificial neural network model with slime mould algorithm: a novel methodology for prediction of urban stochastic water demand. Water (Switzerland) 12(10). https://doi.org/10.3390/w12102692

Download references

Availability of data and material

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

Author information

Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Agartala, Agartala, Tripura, 799046, India

    Prasanjit Chakraborty & Apu Kumar Saha

  2. Department of Science & Humanities, Gomati District Polytechnic, Udaipur, Tripura, 799013, India

    Sukanta Nama

Authors
  1. Prasanjit Chakraborty
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Sukanta Nama
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Apu Kumar Saha
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Apu Kumar Saha.

Ethics declarations

Conflicts of interests/competing interests

All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.

Additional information

Publisher’s note

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

This article has been retracted. Please see the retraction notice for more detail: https://doi.org/10.1007/s11042-024-20047-8"

Appendix-1

Appendix-1

Table 14 Twenty benchmark functions used for comparison with SS: Search Space, D: Dimension = 50, fmin = 0
Full size table

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.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chakraborty, P., Nama, S. & Saha, A.K. RETRACTED ARTICLE: A hybrid slime mould algorithm for global optimization. Multimed Tools Appl 82, 22441–22467 (2023). https://doi.org/10.1007/s11042-022-14077-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-022-14077-3

Keywords