Skip to main content
SpringerLink
Log in

Chaos embedded opposition based learning for gravitational search algorithm

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

Due to its robust search mechanism, Gravitational search algorithm (GSA) has achieved a lot of popularity in different research communities. However, stagnation reduces its searchability towards global optima for rigid and complex multi-modal problems. This paper proposes a GSA variant that incorporates chaos-embedded opposition-based learning into the basic GSA for the stagnation-free search. Additionally, a sine-cosine based chaotic gravitational constant is introduced to balance the trade-off between exploration and exploitation capabilities more effectively. The proposed variant is tested over 23 classical benchmark problems, 15 test problems of CEC 2015 test suite, and 15 test problems of CEC 2014 test suite. Different graphical, as well as empirical analyses, reveal the superiority of the proposed algorithm over conventional meta-heuristics and most recent GSA variants.

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

Similar content being viewed by others

Data Availability

The datasets generated during the current study are available from the corresponding author on reasonable request.

References

  1. Ahandani MA, Alavi-Rad H (2012) Opposition-based learning in the shuffled differential evolution algorithm. Soft Comput 16(8):1303–1337

    Article  Google Scholar 

  2. Bansal JC, Joshi SK, Nagar AK (2018) Fitness varying gravitational constant in gsa. Appl Intell 48(10):3446–3461

    Article  Google Scholar 

  3. Bansal JC, Singh S (2021) A better exploration strategy in grey wolf optimizer. J Ambient Intell Humaniz Comput 12(1):1099–1118

    Article  Google Scholar 

  4. Bhowmik AR, Chakraborty AK (2015) Solution of optimal power flow using non dominated sorting multi objective opposition based gravitational search algorithm. Int J Electr Power Energy Syst 64:1237–1250

    Article  Google Scholar 

  5. Braik M, Sheta A, Al-Hiary H (2021) A novel meta-heuristic search algorithm for solving optimization problems: capuchin search algorithm. Neural Comput Applic 33(7):2515– 2547

    Article  Google Scholar 

  6. Choi TJ, Togelius J, Cheong Y-G (2021) A fast and efficient stochastic opposition-based learning for differential evolution in numerical optimization. Swarm Evol Comput 60:100768

    Article  Google Scholar 

  7. Dinkar SK, Deep K, Mirjalili S, Thapliyal S (2021) Opposition-based laplacian equilibrium optimizer with application in image segmentation using multilevel thresholding. Expert Syst Appl 174:114766

    Article  Google Scholar 

  8. Ewees AA, Elaziz MA, Houssein EH (2018) Improved grasshopper optimization algorithm using opposition-based learning. Expert Syst Appl 112:156–172

    Article  Google Scholar 

  9. Ewees AA, Elaziz MA, Oliva D (2021) A new multi-objective optimization algorithm combined with opposition-based learning. Expert Syst Appl 165:113844

    Article  Google Scholar 

  10. Feng Y, Wang G-G, Dong J, Wang Ling (2018) Opposition-based learning monarch butterfly optimization with gaussian perturbation for large-scale 0-1 knapsack problem. Comput Electr Eng 67:454–468

    Article  Google Scholar 

  11. 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 

  12. Gupta S, Deep K (2019) A hybrid self-adaptive sine cosine algorithm with opposition based learning. Expert Syst Appl 119:210–230

    Article  Google Scholar 

  13. Gupta S, Deep K, Heidari AA, Moayedi H, Wang M (2020) Opposition-based learning harris hawks optimization with advanced transition rules: principles and analysis. Expert Syst Appl 158:113510

    Article  Google Scholar 

  14. Javad H et al (2021) Feature selection by using chaotic cuckoo optimization algorithm with levy flight, opposition-based learning and disruption operator. Soft Comput 25(4):2911–2933

    Article  Google Scholar 

  15. Hayyolalam V, Kazem AAP (2020) Black widow optimization algorithm: a novel meta-heuristic approach for solving engineering optimization problems. Eng Appl Artif Intell 87:103249

    Article  Google Scholar 

  16. Hooda H, Om PV (2022) Fuzzy clustering using gravitational search algorithm for brain image segmentation. Multimed Tools Appl:1–20

  17. Houssein EH, Neggaz N, Hosney ME, Mohamed WM, Hassaballah M (2021) Enhanced harris hawks optimization with genetic operators for selection chemical descriptors and compounds activities. Neural Comput Applic:1–18

  18. Joshi SK, Bansal JC (2020) Parameter tuning for meta-heuristics. Knowl-Based Syst 189:105094

    Article  Google Scholar 

  19. Joshi SK, Gopal A, Singh S, Nagar AK, Bansal JC (2021) A novel neighborhood archives embedded gravitational constant in gsa. Soft Comput 25(8):6539–6555

    Article  Google Scholar 

  20. 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  MATH  Google Scholar 

  21. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95-international conference on neural networks. IEEE, vol 4, pp 1942–1948

  22. Khan TA, Ling SH (2021) A novel hybrid gravitational search particle swarm optimization algorithm. Eng Appl Artif Intell 102:104263

    Article  Google Scholar 

  23. Li C, Li H, Kou P (2014) Piecewise function based gravitational search algorithm and its application on parameter identification of avr system. Neurocomputing 124:139–148

    Article  Google Scholar 

  24. Li C, Zhou J, Xiao J, Han X (2012) Parameters identification of chaotic system by chaotic gravitational search algorithm. Chaos Solitons & Fractals 45(4):539–547

    Article  Google Scholar 

  25. Liang JJ, Qu BY, Suganthan PN (2013) Problem definitions and evaluation criteria for the cec 2014 special session and competition on single objective real-parameter numerical optimization. Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, Singapore 635:490

    Google Scholar 

  26. JJ Liang, Qu BY, Suganthan PN, Chen Q (2014) Problem definitions and evaluation criteria for the cec 2015 competition on learning-based real-parameter single objective optimization. Technical Report201411A, computational intelligence laboratory, Zhengzhou University, Zhengzhou China and technical report, Nanyang Technological University, Singapore

  27. Long W, Jiao J, Liang X, Cai S, Ming X (2019) A random opposition-based learning grey wolf optimizer, vol 7

  28. Mirjalili S (2016) Sca: a sine cosine algorithm for solving optimization problems. Knowl-based Syst 96:120–133

    Article  Google Scholar 

  29. Mirjalili S, Gandomi AH (2017) Chaotic gravitational constants for the gravitational search algorithm. Appl Soft Comput

  30. Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191

    Article  Google Scholar 

  31. Mirjalili S, Siti ZMH (2010) A new hybrid psogsa algorithm for function optimization. In: 2010 international conference on computer and information application. IEEE, pp 374–377

  32. Mirjalili S, Lewis A (2014) Adaptive gbest-guided gravitational search algorithm. Neural Computing and Applications 25(7-8):1569–1584

    Article  Google Scholar 

  33. Mittal H, Pal R, Kulhari A, Mukesh S (2016) Chaotic kbest gravitational search algorithm (ckgsa)

  34. Muthusamy H, Ravindran S, Yaacob S, Polat K (2021) An improved elephant herding optimization using sine–cosine mechanism and opposition based learning for global optimization problems. Expert Syst Appl 172:114607

    Article  Google Scholar 

  35. Nasser AB, Zamli KZ, Hujainah F, Ghanem WAHM, Saad A-MHY, Alduais NAM (2021) An adaptive opposition-based learning selection: the case for jaya algorithm. IEEE Access 9:55581–55594

    Article  Google Scholar 

  36. Oliva D, Esquivel-Torres S, Hinojosa S, Pérez-Cisneros M, Osuna-Enciso V, Ortega-Sánchez N, Dhiman G, Heidari AA (2021) An opposition-based moth swarm algorithm for global optimization. Expert Syst Appl:115481

  37. Olivas F, Valdez F, Melin P, Sombra A, Castillo O (2019) Interval type-2 fuzzy logic for dynamic parameter adaptation in a modified gravitational search algorithm. Inf Sci 476:159–175

    Article  Google Scholar 

  38. Pelusi D, Mascella R, Tallini L, Nayak J, Naik B, Deng Y (2020) Improving exploration and exploitation via a hyperbolic gravitational search algorithm. Knowl-Based Syst 193:105404

    Article  Google Scholar 

  39. Poma Y, Melin P, González CI, Martínez GE (2020) Optimization of convolutional neural networks using the fuzzy gravitational search algorithm. J Autom Mob Robot Intell Syst:109–120

  40. Rahnamayan S, Tizhoosh HR, Salama MMA (2007) Quasi-oppositional differential evolution. In: 2007 IEEE Congress on evolutionary computation. IEEE, pp 2229–2236

  41. Rahnamayan S, Tizhoosh HR, Salama MMA (2008) Opposition-based differential evolution. IEEE Trans Evol Comput 12(1):64–79

    Article  Google Scholar 

  42. Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) Gsa: a gravitational search algorithm. Inf Sci 179(13):2232–2248

    Article  MATH  Google Scholar 

  43. Sadollah A, Sayyaadi H, Yadav A (2018) A dynamic metaheuristic optimization model inspired by biological nervous systems: neural network algorithm. Appl Soft Comput 71:747–782

    Article  Google Scholar 

  44. Saeidi-Khabisi F, Rashedi E (Oct 2012) Fuzzy gravitational search algorithm. In: 2012 2nd international econference on computer and knowledge engineering (ICCKE), pp 156–160

  45. Sapre S, Mini S (2019) Opposition-based moth flame optimization with cauchy mutation and evolutionary boundary constraint handling for global optimization. Soft Comput 23(15):6023–6041

    Article  Google Scholar 

  46. Sarkhel R, Chowdhury TM, Das M, Das N, Nasipuri M (2017) A novel harmony search algorithm embedded with metaheuristic opposition based learning. J Intell Fuzzy Syst 32(4):3189–3199

    Article  Google Scholar 

  47. Shan X, Liu K, Sun P-L (2016) Modified bat algorithm based on lévy flight and opposition based learning. Sci Program, 2016

  48. Binod S, Mukherjee V, Ghoshal SP (2012) A novel opposition-based gravitational search algorithm for combined economic and emission dispatch problems of power systems. Int J Electr Power Energy Syst 35(1):21–33

    Article  Google Scholar 

  49. Shaw B, Mukherjee V, Ghoshal SP (2014) Solution of reactive power dispatch of power systems by an opposition-based gravitational search algorithm. Int J Electr Power Energy Syst 55:29–40

    Article  Google Scholar 

  50. Shehadeh HA (2021) A hybrid sperm swarm optimization and gravitational search algorithm (hssogsa) for global optimization. Neural Comput Applic 33(18):11739–11752

    Article  Google Scholar 

  51. Sihwail R, Omar K, Ariffin KAZ, Tubishat M (2020) Improved harris hawks optimization using elite opposition-based learning and novel search mechanism for feature selection. IEEE Access 8:121127–121145

    Article  Google Scholar 

  52. Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713

    Article  Google Scholar 

  53. Singh T, Saxena N (2021) Chaotic sequence and opposition learning guided approach for data clustering. Pattern Anal Applic:1–15

  54. Sombra A, Valdez F, Melin P, Castillo O (2013) A new gravitational search algorithm using fuzzy logic to parameter adaptation. In: 2013 IEEE congress on evolutionary computation:1068–1074

  55. Song Z, Gao S, Yang Y, Sun J, Todo Y (2017) Multiple chaos embedded gravitational search algorithm. IEICE Trans Inf Syst 100(4):888–900

    Article  Google Scholar 

  56. 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

    Article  MathSciNet  MATH  Google Scholar 

  57. Sun G, Ma P, Ren J, Zhang A, Jia X (2018) A stability constrained adaptive alpha for gravitational search algorithm. Knowl-Based Syst 139:200–213

    Article  Google Scholar 

  58. Tizhoosh HR (2005) Opposition-based learning: a new scheme for machine intelligence. In: International conference on computational intelligence for modelling, control and automation and international conference on intelligent agents, web technologies and internet commerce (CIMCA-IAWTIC’06). IEEE, vol 1, pp 695–701

  59. Tubishat M, Idris N, Shuib L, Abushariah MAM, Mirjalili S (2020) Improved salp swarm algorithm based on opposition based learning and novel local search algorithm for feature selection. Expert Syst Appl 145:113122

    Article  Google Scholar 

  60. Verleysen M, François D (2005) The curse of dimensionality in data mining and time series prediction. In: International work-conference on artificial neural networks. Springer, pp 758–770

  61. Om PV, Aggarwal D, Patodi T (2016) Opposition and dimensional based modified firefly algorithm. Expert Syst Appl 44:168–176

    Article  Google Scholar 

  62. Wang H, Wu Z, Rahnamayan S, Liu Y, Ventresca M (2011) Enhancing particle swarm optimization using generalized opposition-based learning. Inf Sci 181(20):4699–4714

    Article  MathSciNet  Google Scholar 

  63. Wang W-C, Xu L, Chau K-W, Zhao Y, Xu D-M (2021) An orthogonal opposition-based-learning yin–yang-pair optimization algorithm for engineering optimization. Engineering with Computers:1–35

  64. Wang Y, Gao S, Yang Y, Wang Z, Cheng J, Yuki T (2020) A gravitational search algorithm with chaotic neural oscillators. IEEE Access 8:25938–25948

    Article  Google Scholar 

  65. Wang Y, Yang Y, Gao S, Pan H, Yang G (2019) A hierarchical gravitational search algorithm with an effective gravitational constant. Swarm Evol Comput 46:118–139

    Article  Google Scholar 

  66. Di W, Wang S, Liu Q, Abualigah L, Jia H (2022) An improved teaching-learning-based optimization algorithm with reinforcement learning strategy for solving optimization problems. Comput Intell Neurosci, 2022

  67. Yang X, Gong W (2021) Opposition-based jaya with population reduction for parameter estimation of photovoltaic solar cells and modules. Appl Soft Comput 104:107218

    Article  Google Scholar 

  68. Zamfirache IA, Precup R-E, Roman R-C, Petriu EM (2022) Reinforcement learning-based control using q-learning and gravitational search algorithm with experimental validation on a nonlinear servo system. Inf Sci 583:99–120

    Article  Google Scholar 

  69. Zhou Y, Hao J-K, Duval B (2017) Opposition-based memetic search for the maximum diversity problem. IEEE Trans Evol Comput 21(5):731–745

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computational Science and Humanities, Indian Institute of Information Technology, Kottayam, Kerala, 686635, India

    Susheel Kumar Joshi

Authors
  1. Susheel Kumar Joshi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Susheel Kumar Joshi.

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

Joshi, S.K. Chaos embedded opposition based learning for gravitational search algorithm. Appl Intell 53, 5567–5586 (2023). https://doi.org/10.1007/s10489-022-03786-9

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-022-03786-9

Keywords

Search

Navigation