Skip to main content
SpringerLink
Log in

Modified group theory-based optimization algorithms for numerical optimization

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

Group Theory-based Optimization Algorithm (GTOA) is a novel population-based global optimization algorithm, which is used to solve combinatorial optimization problems. This paper studies the applicability of GTOA in numerical optimization and proposes two versions of GTOA based on binary coding (GTOA-b) and \(0\sim 9\) integer coding (GTOA-d). Firstly, the coding transformation methods for representing the feasible solutions are introduced, which make GTOA suitable for continuous optimization. On this basis, the original evolution operators are modified to reduce the deviation and speed up global convergence. The experiment using the CEC2017 test suit is carried out to validate the performance of the algorithms. The influence of parameter values and the differences between the calculated results are analyzed by nonparametric tests. Computation results showed that the convergence rate of GTOA-d is faster than that of GTOA-b, and it achieved better results on the benchmark functions with higher dimensions. The comparison against twelve state-of-the-art and recently introduced meta-heuristic algorithms showed that GTOA-d has the superiority on convergence stability, it obtained significantly better performance than seven of its competitors. Finally, all the algorithms are applied to an Amplitude Variation with Offset inversion case study. The simulation showed that the proposed GTOA-d achieved satisfactory inversion results, and it has better performance in terms of convergence rate and average accuracy. The results demonstrate that the proposed GTOA-d is an effective algorithm for numerical optimization.

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Horst R, Tuy H (2013) Global optimization: deterministic approaches. Springer, Verlag

  2. Dan S (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702

    Article  Google Scholar 

  3. Pillay N, Engelbrecht AP, Abraham A et al (2016) Advances in nature and biologically inspired computing. Springer International Publishing

  4. Ashlock D (2006) Evolutionary computation for modeling and optimization. Springer, New York. https://doi.org/10.1007/0-387-31909-3

  5. He Y, Wang X (2018) Group theory-based optimization algorithm for solving knapsack problems. Knowl Based Syst. https://doi.org/10.1016/j.knosys.2018.07.045

  6. Goldberg D E (1989) Genetic algorithms in search optimization and machine learning. Addison-Wesley, Boston

    MATH  Google Scholar 

  7. Zamani R (2013) A competitive magnet-based genetic algorithm for solving the resource-constrained project scheduling problem. Eur J Oper Res 229(2):552–559

    Article  MathSciNet  Google Scholar 

  8. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Procedings of IEEE int. Conf. Neural networks, Perth, pp 1942–1948

  9. Storn R, Price K (1997) Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341–359

    Article  MathSciNet  Google Scholar 

  10. Qin A K, Huang V L, Suganthan P N (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417

    Article  Google Scholar 

  11. Das S, Suganthan P N (2011) Differential Evolution: A Survey of the State-of-the-Art. IEEE Trans Evol Comput 15(1):4–31

    Article  Google Scholar 

  12. Dorigo M, Birattari M (2002) Ant colony optimization. Encyclopediaof Machine Learning. Springer, Boston, pp 36–39

  13. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39(3):459–471

    Article  MathSciNet  Google Scholar 

  14. Mirjalili S, Mirjalili S M, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69(3):46–61

    Article  Google Scholar 

  15. Al-Betar M A, Awadallah M A, Faris H, et al. (2018) Natural selection methods for Grey Wolf Optimizer. Expert Syst Appl 113:481–498

    Article  Google Scholar 

  16. Larranga P, Lozano J A (2002) Estimation of distribution algorithms: a new tool for evolutionary computation. Springer, New York

    Book  Google Scholar 

  17. Wang J, Tang K, Lozano J A, Yao X (2016) Estimation of the distribution algorithm with a stochastic local search for uncertain capacitated arc routing problems. IEEE Trans Evol Comput 20(1):96–109

    Article  Google Scholar 

  18. Mirjalili S (2016) SCA: A Sine Cosine Algorithm For solving optimization problems. Knowl Based Syst 96:120–133

    Article  Google Scholar 

  19. He Y, Wang X, Gao S (2019) Ring Theory-Based evolutionary algorithm and its application to d0-1KP. Appl Soft Comput 77:714–722

    Article  Google Scholar 

  20. Hossam F, Ala’m A-Z, oubi Asghar AH, et al. (2019) An Intelligent System for Spam Detection and Identification of the most Relevant Features based on Evolutionary Random Weight Networks. Inform Fusion 48:67–83. https://doi.org/10.1016/j.inffus.2018.08.002

  21. Abualigah L M, Khader A T, Hanandeh E S (2018) A new feature selection method to improve the document clustering using particle swarm optimization algorithm. J Comput Sci 25:456–466

    Article  Google Scholar 

  22. Marinakis Y, Marinaki M, Migdalas A (2019) A multi-adaptive particle swarm optimization for the vehicle routing problem with time windows. Inform Sci 481:311–329

    Article  Google Scholar 

  23. Decerle J, Grunder O, Hajjam A, et al. (2019) A hybrid memetic-ant colony optimization algorithm for the home health care problem with time window, synchronization and working time balancing. Swarm Evol Comput 46:171–183

    Article  Google Scholar 

  24. Sallam K M, Chakrabortty R K, Ryan M J (2020) A Two-stage multi-operator differential evolution algorithm for solving Resource Constrained Project Scheduling problems. Future Generation Computer Systems. https://doi.org/10.1016/j.future.2020.02.074

  25. Das K R, Das D, Das J (2015) Optimal tuning of PID controller using GWO algorithm for speed control in DC motor. In: International conference on soft computing techniques implementations. IEEE, Faridabad, pp 108–112

  26. Srikanth K, Panwar L K, Panigrahi B (2018) Meta-heuristic framework: Quantum inspired binary grey wolf optimizer for unit commitment problem. Comput Electr Eng 70:243– 260

    Article  Google Scholar 

  27. Kumar V, Chhabra J K, Kumar D (2016) Grey wolf Algorithm-Based clustering technique. J Intell Syst 26(1):153–168

    Article  Google Scholar 

  28. 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

  29. Askarzadeh A (2016) A novel metaheuristic method for solving constrained engineering optimization problems: Crow search algorithm. Compute Struct 169:1–12

    Article  Google Scholar 

  30. Hayyolalam V, Kazem A (2020) Black Widow Optimization Algorithm: A novel meta-heuristic approach for solving engineering optimization problems. Eng Appl Artif Intel 87:103249.1–103249.28

  31. Satnam K, Lalit K. A., Sangal A. L., Gaurav D (2020) Tunicate Swarm Algorithm: A new bio-inspired based metaheuristic paradigm for global optimization. Eng Appl Artif Intel 90:103541. https://doi.org/10.1016/j.engappai.2020.103541

  32. Zhai Q, He Y, Wang G, et al. (2021) A general approach to solving hardware and software partitioning problem based on evolutionary algorithms. Adv Eng Softw. https://doi.org/10.1016/j.advengsoft.2021.102998

  33. Awad N H, Ali M Z, Liang J J, et al. (2017) Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective bound constrained Real-Parameter numerical optimization, nanyang technological university, Technical. Report, Singapore

  34. Hashim F A, Hussain K, Houssein E H, et al. (2021) Archimedes optimization algorithm: a new metaheuristic algorithm for solving optimization problems. Appl Intell 51:1531–1551

    Article  Google Scholar 

  35. Sharma B, Prakash R, Tiwari S, et al. (2017) A variant of environmental adaptation method with real parameter encoding and its application in economic load dispatch problem. Appl Intell 47:409–429

    Article  Google Scholar 

  36. Xu G, Zhang T, Lai Q (2021) A new firefly algorithm with mean condition partial attraction. Appl Intell. https://doi.org/10.1007/s10489-021-02642-6

  37. Kruskal W H, Allen W (1952) Use of ranks in one-criterion variance analysis. Publ Am Stat Assoc 47(260):583–621

    Article  Google Scholar 

  38. Garcia S, Fernǎndez A, Luengo J (2009) A study of statistical techniques and performance measures for genetics-based machine learning: accuracy and interpretability. Soft Comput 13(10):959–977

    Article  Google Scholar 

  39. Demiar J, Schuurmans D (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7(1):1–30

    MathSciNet  Google Scholar 

  40. Hussain K, Salleh M N M, Cheng S, Shi Y (2018) On the exploration and exploitation in popular swarm-based metaheuristic algorithms. Neural Comput Appl 31(11):7665– 7683

    Article  Google Scholar 

  41. Yan X, Zhu Z, Wu Q, et al. (2019) Elastic parameter inversion problem based on brain storm optimization algorithm. Memet Comput 11(2):143–153

    Article  Google Scholar 

  42. Wang L (2015) Study on intelligent optimization algorithm with application to prestack AVO nonlinear inversion, Dissertation. China University of Geosciences

  43. Yan X, Li P, Tang K, et al. (2020) Clonal selection based intelligent parameter inversion algorithm for prestack seismic data. Inform Sci 517:86–99

    Article  Google Scholar 

Download references

Acknowledgements

This article has been supported by the Natural Science Foundation of China (grant nos. 42074155 and 41574131), the PetroChina Innovation Foundation under Grant(2019D-5007-0302), the Natural Science Foundation of Hebei Province (F2020403013), and the Fundamental Research Funds for the Central Universities of China.

Author information

Authors and Affiliations

  1. School of Geophysics and Information Technology, China University of Geosciences (Beijing), Beijing, 100083, China

    Zewen Li & Qisheng Zhang

  2. College of Information Engineering, Hebei GEO University, Shijiazhuang, 050031, China

    Yichao He

Authors
  1. Zewen Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qisheng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yichao He
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qisheng Zhang.

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, Z., Zhang, Q. & He, Y. Modified group theory-based optimization algorithms for numerical optimization. Appl Intell 52, 11300–11323 (2022). https://doi.org/10.1007/s10489-021-02982-3

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-021-02982-3

Keywords

Search

Navigation