Skip to main content

Advertisement

Springer Nature Link
Log in

A grey wolf optimizer-based chaotic gravitational search algorithm for global optimization

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

Abstract

Gravitational search algorithm (GSA) is widely accepted as one of the effective optimization algorithms providing promising results. However, it suffers with local optima and premature convergence. To deal with those problems, chaotic gravitational constants for the gravitational search algorithm (CGSA) are proposed to enhance the efficiency of exploration via embedding chaotic maps, but the enhancement of exploration throughout iterations could somehow degrade the exploitation ability of GSA. Accordingly, this paper introduces a location update strategy inspired by the hunting mechanism of grey wolf optimizer (GWO) for improving the exploitation process of CGSA. In addition, a negative entropy function is designed to effectively control the implementation of the proposed strategy. In order to show the superior performance of the grey wolf chaotic gravitational search algorithm (GWCGSA), we carry out a comparative study of 30 benchmark functions (CEC 2014) with multiple GSAs and state-of-the-art algorithms. The experimental results show that the proposed strategy achieves better performance in most functions (greater than 20/30). Also, the experiments on seven engineering optimization problems indicate that the practicality of the proposed algorithm can be ensured.

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

Similar content being viewed by others

References

  1. Wei YY, Chen ZZ, Zhao C, Tu YH, Chen X, Yang R (2021) A BiLSTM hybrid model for ship roll multi-step forecasting based on decomposition and hyperparameter optimization. Ocean Eng 242:110138

    Google Scholar 

  2. Akay B, Karaboga D (2012) Artificial bee colony algorithm for large-scale problems and engineering design optimization. J Intell Manuf 23(4):1001–1014

    Google Scholar 

  3. Sefati S, Mousavinasab M, Zareh Farkhady R (2022) Load balancing in cloud computing environment using the Grey wolf optimization algorithm based on the reliability: performance evaluation. J Supercomput 78(1):18–42

    Google Scholar 

  4. Younes Z, Alhamrouni I, Mekhilef S, Reyasudin M (2021) A memory-based gravitational search algorithm for solving economic dispatch problem in micro-grid. Ain Shams Eng J 12(2):1985–1994

    Google Scholar 

  5. Angeli D, Amrit R, Rawlings JB (2012) On average performance and stability of economic model predictive control. IEEE Trans Autom Control 57(7):1615–1626

    MathSciNet  MATH  Google Scholar 

  6. Makhadmeh SN, Abasi AK, Al-Betar MA (2022) Hybrid multi-verse optimizer with grey wolf optimizer for power scheduling problem in smart home using IoT. J Supercomput 78(9):11794–11829

    Google Scholar 

  7. Xiao YY, Zhao QH, Kaku I, Xu YC (2012) Development of a fuel consumption optimization model for the capacitated vehicle routing problem. Comput Oper Res 39(7):1419–1431

    MathSciNet  MATH  Google Scholar 

  8. Xu YF, Wandelt S, Sun XQ (2021) Airline integrate d robust sche duling with a variable neighborhood search based heuristic. Transport Res Part B-Methodol 149:181–203

    Google Scholar 

  9. Jokar E, Mosleh M, Kheyrandish M (2022) GWBM: an algorithm based on grey wolf optimization and balanced modularity for community discovery in social networks. J Supercomput 78(5):7354–7377

    Google Scholar 

  10. Dodu JC, Martin P, Merlin A, Pouget J (1972) An optimal formulation and solution of short-range operating problems for a power system with flow constraints. Proc IEEE 60(1):54–63

    Google Scholar 

  11. El-Keib A, Ding H (1994) Environmentally constrained economic dispatch using linear programming. Electr Power Syst Res 29(3):155–159

    Google Scholar 

  12. Chen CL, Wang SC (1993) Branch-and-bound scheduling for thermal generating units. IEEE Trans Energy Convers 8(2):184–189

    Google Scholar 

  13. Garcia-Rodenas R, Linares LJ, Lopez-Gomez JA (2019) A memetic chaotic gravitational search algorithm for unconstrained global optimization problems. Appl Soft Comput 79:14–29

    Google Scholar 

  14. Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133

    Google Scholar 

  15. Kirkpatrick S, Gelatt C D, Jr., Vecchi M P (1983) Optimization by simulated annealing. Science (New York, N.Y.) 220(4598):671–680

  16. Glover F (1990) Tabu search: a tutorial. INFORMS J Appl Anal 20(4):74–94

    Google Scholar 

  17. Holland JH (1992) Genetic algorithms. Sci Am 267(1):66–73

    Google Scholar 

  18. Kennedy J, Eberhart R, (1995) Particle swarm optimization. In: Icnn95-international conference on neural networks

  19. 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

    MathSciNet  MATH  Google Scholar 

  20. Pelusi D, Mascella R, Tallini L, Nayak J, Naik B, Deng Y (2020) An improved moth-flame optimization algorithm with hybrid search phase. Knowl-Based Syst 191:105277

    Google Scholar 

  21. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey Wolf Optimizer. Adv Eng Softw 69:46–61

    Google Scholar 

  22. Mahafzah BA, Jabri R, Murad O (2021) Multithreaded scheduling for program segments based on chemical reaction optimizer. Soft Comput 25(4):2741–2766

    Google Scholar 

  23. Khattab H, Mahafzah B A, Sharieh A (2022) A hybrid algorithm based on modified chemical reaction optimization and best-first search algorithm for solving minimum vertex cover problem. Neural Computing and Applications

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

    MATH  Google Scholar 

  25. Jiang JH, Jiang R, Meng XQ, Li KQ (2020) SCGSA: a sine chaotic gravitational search algorithm for continuous optimization problems. Expert Syst Appl 144:113118

    Google Scholar 

  26. Jin X, Liu Q, Long HZ (2021) Impact of cost-benefit analysis on financial benefit evaluation of investment projects under back propagation neural network. J Comput Appl Math 384:113172

    MathSciNet  MATH  Google Scholar 

  27. Mittal H, Saraswat M (2019) An automatic nuclei segmentation method using intelligent gravitational search algorithm based superpixel clustering. Swarm Evol Comput 45:15–32

    Google Scholar 

  28. Niu WJ, Feng ZK, Zeng M, Feng BF, Min YW, Cheng CT, Zhou JZ (2019) Forecasting reservoir monthly runoff via ensemble empirical mode decomposition and extreme learning machine optimized by an improved gravitational search algorithm. Appl Soft Comput 82:105589

    Google Scholar 

  29. Wang Y, Tan ZP, Chen YC (2021) An adaptive gravitational search algorithm for multilevel image thresholding. J Supercomput 77(9):10590–10607

    Google Scholar 

  30. Niu WJ, Feng ZK, Liu S (2021) Multi-strategy gravitational search algorithm for constrained global optimization in coordinative operation of multiple hydropower reservoirs and solar photovoltaic power plants. Appl Soft Comput 107:107315

    Google Scholar 

  31. Acharya D, Das DK (2021) Optimal coordination of over current relay using opposition learning-based gravitational search algorithm. J Supercomput 77(9):10721–10741

    Google Scholar 

  32. Guvenc U, Katircioglu F (2019) Escape velocity: a new operator for gravitational search algorithm. Neural Comput Appl 31(1):27–42

    Google Scholar 

  33. Wang YR, Yu Y, Gao SC, Pan HY, Yang G (2019) A hierarchical gravitational search algorithm with an effective gravitational constant. Swarm Evol Comput 46:118–139

    Google Scholar 

  34. Wang YR, Gao SC, Zhou MC, Yu Y (2021) A multi-layered gravitational search algorithm for function optimization and real-world problems. IEEE-Caa J Automatica Sinica 8(1):94–109

    Google Scholar 

  35. Yuan Y L, Mu X K, Shao X Y, Ren J J, Zhao Y, Wang Z X (2022) Optimization of an auto drum fashioned brake using the elite opposition-based learning and chaotic k-best gravitational search strategy based grey wolf optimizer algorithm. Appl Soft Comput 123

  36. Mirjalili S, Lewis A (2014) Adaptive gbest-guided gravitational search algorithm. Neural Comput Appl 25(7–8):1569–1584

    Google Scholar 

  37. 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

    Google Scholar 

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

    Google Scholar 

  39. Acharya D, Das DK (2021) Optimal coordination of over current relay using opposition learning-based gravitational search algorithm. J Supercomput 77(9):10721–10741

    Google Scholar 

  40. Wang Y, Tan Z, Chen Y-C (2021) An adaptive gravitational search algorithm for multilevel image thresholding. J Supercomput 77(9):10590–10607

    Google Scholar 

  41. Mittal H, Pal R, Kulhari A, Saraswat M, (2016) Chaotic kbest gravitational search algorithm (CKGSA). In: 2016 ninth international conference on contemporary computing, pp. 355-360

  42. Lei Z, Gao S, Gupta S, Cheng J, Yang G (2020) An aggregative learning gravitational search algorithm with self-adaptive gravitational constants. Expert Syst Appl 152:113396

    Google Scholar 

  43. Yu Xianrui YX, Xiaobing Y, Chenliang L, Hong C (2020) An improved parameter control based on a fuzzy system for gravitational search algorithm. Int J Comput Intell Syst 13:893–903

    Google Scholar 

  44. 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

    Google Scholar 

  45. Mirjalili S, Gandomi AH (2017) Chaotic gravitational constants for the gravitational search algorithm. Appl Soft Comput 53:407–419

    Google Scholar 

  46. Zhang AZ, Sun GY, Ren JC, Li XD, Wang ZJ, Jia XP (2018) A dynamic neighborhood learning-based gravitational search algorithm. IEEE Trans Cybern 48(1):436–447

    Google Scholar 

  47. D.~Halliday, R.~Resnick, J.~Walker, Fundamentals of Physics, 2003.

  48. Patriksson M, Stromberg C (2015) Algorithms for the continuous nonlinear resource allocation problem—new implementations and numerical studies. Eur J Oper Res 243(3):703–722

    MathSciNet  MATH  Google Scholar 

  49. Nielsen SS, Zenios SA (1992) Massively parallel algorithms for singly constrained convex programs. ORSA J Comput 4(2):166–181

    MathSciNet  MATH  Google Scholar 

  50. Liang J J, Qu B Y, Suganthan P N (2013) Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization

  51. Mirjalili S, Hashim S Z M, (2010) A new hybrid PSOGSA algorithm for function optimization. In: 2010 international conference on computer and information application, pp. 374-377

  52. Dhargupta S, Ghosh M, Mirjalili S, Sarkar R (2020) Selective opposition based Grey Wolf Optimization. Expert Syst Appl 151:113389

    Google Scholar 

  53. Rodriguez L, Castillo O, Soria J, Melin P, Valdez F, Gonzalez CI, Martinez GE, Soto J (2017) A fuzzy hierarchical operator in the grey wolf optimizer algorithm. Appl Soft Comput 57:315–328

    Google Scholar 

  54. Gupta S, Deep K (2020) A memory-based Grey Wolf Optimizer for global optimization tasks. Appl Soft Comput 93:106367

    Google Scholar 

  55. Coello Coello CA (2000) Use of a self-adaptive penalty approach for engineering optimization problems. Comput Ind 41(2):113–127

    MATH  Google Scholar 

  56. Belegundu AD (1985) A study of mathematical programming methods for structural optimization. Int J Numer Meth Eng 21(9):1601–1623

    MathSciNet  MATH  Google Scholar 

  57. Onwubolu G C, Babu B V, (2004) New optimization techniques in engineering, new optimization techniques in engineering

  58. Camp CV, Farshchin M (2014) Design of space trusses using modified teaching-learning based optimization. Eng Struct 62–63:87–97

    Google Scholar 

  59. Sakthivel VP, Bhuvaneswari R, Subramanian S (2010) Artificial immune system for parameter estimation of induction motor. Expert Syst Appl 37(8):6109–6115

    Google Scholar 

  60. Nolan R, Pillay P, Haque T, (1994) Application of genetic algorithms to motor parameter determination, In: proceedings of 1994 IEEE industry applications society annual meeting, pp. 47–54 vol.41

Download references

Acknowledgements

The authors thank sincerely the reviewers and the editor for their valuable comments and suggestions. The work of this study is supported by National Natural Science Foundation of China (NSFC) under projects Nos. 71731001 and 72174019.

Author information

Authors and Affiliations

  1. School of Economics and Management, Beihang University, Beijing, 100191, China

    Xianrui Yu & Qiuhong Zhao

  2. Beijing Key Laboratory of Emergency Support Simulation Technologies for City Operations, Beijing, 100191, China

    Qiuhong Zhao

  3. Beijing International Science and Technology Cooperation Base for City Safety Operation and Emergency Support, Beijing, 100191, China

    Qiuhong Zhao

  4. School of Information Technology and Management, University of International Business and Economics, Beijing, 100029, China

    Qi Lin

  5. School of Economics, Ocean University of China, Qingdao, 266100, China

    Tongyu Wang

Authors
  1. Xianrui Yu
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Qiuhong Zhao
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Qi Lin
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Tongyu Wang
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Qiuhong Zhao.

Ethics declarations

Conflict of interest

The authors declare no conflicts of interest.

Data availability

Data are available from the authors upon reasonable request.

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 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

Yu, X., Zhao, Q., Lin, Q. et al. A grey wolf optimizer-based chaotic gravitational search algorithm for global optimization. J Supercomput 79, 2691–2739 (2023). https://doi.org/10.1007/s11227-022-04754-3

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11227-022-04754-3

Keywords