Skip to main content
SpringerLink
Log in

Niching comprehensive learning gravitational search algorithm for multimodal optimization problems

  • Research Paper
  • Published:
Evolutionary Intelligence Aims and scope Submit manuscript

Abstract

Many niching algorithms have been proposed in recent times to cater complex real-world problems having several global/local optima. These algorithms help in locating as many global/local optima as possible. However, to explore the search space along with locating and maintaining a large number of global solutions is always a challenging problem. Hence, we propose a new niching strategy named, ‘niching Comprehensive Learning Gravitational Search algorithm’, in which the CLGSA algorithm is used to solve complex problems having multiple solutions. The proposed algorithm first efficiently tries to explore the search space without trapping in local optima’s and secondly it locates all possible global optima’s. This algorithm has an external memory that enhances its capability to find the maximum number of optima’s. The proposed approach is tested on the IEEE CEC-2013 Multimodal Optimization benchmark problems (Li et al. in Evolutionary computation and machine learning group, RMIT University, Melbourne, Australia, Technical Report, 2013). The results of the proposed scheme are compared with five other state-of-the-art methods. In order to show the efficiency of CLGSA algorithm over real-life multimodal optimization problems, it applied to non-linear, and a mixed variable problem this is, the Reactive Power Dispatch problem (RPD). A standard benchmark IEEE-57 bus system is considered to evaluate the efficiency of the CLGSA. The evaluated simulation results show that CLGSA algorithm successfully solve multimodal problems and the RPD problem with significant accuracy.

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

References

  1. Mahfoud SW (1995) Niching methods for genetic algorithms. Ph.D. dissertation, University of Illinois at Urbana-Champaign, Champaign, IL, USA

  2. De Jong KA (1975) An analysis of the behavior of a class of genetic adaptive systems. Ph.D. Dissertation, University of Michigan, USA

  3. Goldberg DE, Richardson J (1987) Genetic algorithms with sharing for multimodal function optimization. In: Proceedings of the second international conference on genetic algorithms on genetic algorithms and their application, Hillsdale, NJ, USA, 1987, pp 41–49

  4. Tasoulis DK, Plagianakos VP, Vrahatis MN (2005) Clustering in evolutionary algorithms to efficiently compute simultaneously local and global minima. In: IEEE congress on evolutionary computation, vol 2, pp 1847–1854

  5. Petrowski A (1996) A clearing procedure as a niching method for genetic algorithms. In: IEEE international conference on evolutionary computation, pp 798–803

  6. Parsopoulos KE, Plagianakos VP, Magoulas GD, Vrahatis MN (2001) Objective function”stretching” to alleviate convergence to local minima. Nonlinear Anal 47(5):3419–3424

    Article  MathSciNet  Google Scholar 

  7. Li JP, Balazs ME, Parks GT, Clarkson PJ (2002) A species conserving genetic algorithm for multimodal function optimization. Evol Comput 10(3):207–234

    Article  Google Scholar 

  8. Beasley D, Bull DR, Martin RR (1993) A sequential niche technique for multimodal function optimization. Evol Comput 1(2):101–125

    Article  Google Scholar 

  9. Harik GR (1995) Finding multimodal solutions using restricted tournament selection. In: Proceedings of the 6th international conference on genetic algorithms, San Francisco, CA, USA, pp 24–31

  10. Bessaou M, Petrowski A, Siarry P (2000) Island model cooperating with speciation for multimodal optimization. In: Parallel Problem Solving from Nature-PPSN VI 6th international conference, H.-P. S. et al., Ed. Paris, France: Springer Verlag, pp 16–20

  11. Epitropakis MG, Plagianakos VP, Vrahatis MN (2011) Finding multiple global optima exploiting differential evolution’s niching capability. In: 2011 IEEE symposium on differential evolution (SDE), pp 1–8

  12. Epitropakis MG, Plagianakos VP, Vrahatis MN (2012) Multimodal optimization using niching differential evolution with index-based neighborhoods. In: IEEE congress on evolutionary computation, 2012. CEC 2012. (IEee world congress on computational intelligence), Brisbane, Australia, June 2012, pp 1–8

  13. Maree SC, Alderliesten T, Thierens D, Bosman PA (2018, July) Real-valued evolutionary multi-modal optimization driven by hill-valley clustering. In: Proceedings of the genetic and evolutionary computation conference, pp 857–864

  14. Li X (2004) Adaptively choosing neighborhood bests using species in a particle swarm optimizer for multimodal function optimization. In: Proceedings of genetic and evolutionary computation conference 2004 (GECCO’04) (LNCS 3102), pp 105–116

  15. Li X (2005) Efficient differential evolution using speciation for multimodal function optimization. In: GECCO’05: Proceedings of the 2005 conference on Genetic and evolutionary computation, pp 873–88

  16. Brits R, Engelbrecht A, van den Bergh F (2002) A Niching Particle Swarm Optimizer. In: Proceedings of the 4th Asia-Pacific conference on simulated evolution and learning 2002, pp 692–696

  17. Li X (2010) Niching without niching parameters: particle swarm optimization using a ring topology. IEEE Trans Evol Comput 14(1)

  18. Yadav A, Kim JH (2014) A Niching co-swarm gravitational search algorithm for multi-modal optimization. In: Proceedings of fourth international conference on soft computing for problem solving, pp 599–607

  19. Anita, Yadav A (2019) AEFA: artificial electric field algorithm for global optimization. Swarm Evol Comput 48:93–108

    Article  Google Scholar 

  20. 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 

  21. Yadav A, Kim JH (2019) Convergence of gravitational search algorithm on linear and quadratic functions, decision science in action, pp 31–39

  22. Sayyaadi H, Sadollah A, Yadav A, Yadav N (2018) Stability and iterative convergence of water cycle algorithm for computationally expensive and combinatorial Internet shopping optimisation problems. J Exp Theor Artif Intell. https://doi.org/10.1080/0952813x.2018.1549109

    Article  Google Scholar 

  23. Yadav A, Sadollah A, Yadav N, Kim JH (2018) Self-adaptive global mine blast algorithm for numerical optimization. Neural Comput Appl 1–22

  24. Li J, Li X, Wood A (2010) Species based evolutionary algorithms for multimodal optimization: a brief review. In: 2010 IEEE congress on evolutionary computation (CEC), July 2010. IEEE, pp 1–8

  25. Stoean C, Preuss M, Stoean R, Dumitrescu D (2010) Multimodal optimization by means of a topological species conservation algorithm. IEEE Trans Evol Comput 9:1–23

    Google Scholar 

  26. Thomsen R (2004) Multimodal optimization using crowding-based differential evolution. In: IEEE congress on evolutionary computation, vol 2, pp 1382–1389

  27. Cioppa AD, De Stefano C, Marcelli A (2004) On the role of population size and niche radius in fitness sharing. IEEE Trans Evol Comput 8(5):580–592

    Google Scholar 

  28. Das S, Maity S, Qu B-Y, Suganthan PN (2011) Real parameter evolutionary multimodal optimization: a survey of the state of-the-art. Swarm Evol Computn 1(2):71–88

    Article  Google Scholar 

  29. Dick G (2010) Automatic identification of the niche radius using spatially structured clearing methods. In: 2010 IEEE world congress on computational intelligence, WCCI 2010-2010 IEEE congress on evolutionary computation, CEC 2010

  30. Fayek MB, Darwish NM, Ali MM (2010) Context based clearing procedure: a niching method for genetic algorithms. J Adv Res 1(4):301–307

    Article  Google Scholar 

  31. Carpentier J (1979) Optimal power flows”. Int J Electr Power Energy Syst 1(1):3–15

    Article  Google Scholar 

  32. Rashedi E, Nezamabadi HP, Saryadi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248

    Article  Google Scholar 

  33. Li X, Engelbrecht A, Epitropakis MG (2013) Benchmark functions for cec’2013 special session and competition on niching methods for multimodal function optimization. Evolutionary Computation and Machine Learning Group, RMIT University, Melbourne, Australia, Tech. Rep. https://titan.csit.rmit.edu.au/~e46507/cec13-niching/competition/cec2013-niching-benchmark-tech-report.pdf

  34. Yazdani S, Nezamabadi-pour H, Kamyab S (2014) A gravitational search algorithm for multimodal optimization. Swarm Evol Comput 14:1–14

    Article  Google Scholar 

  35. Newton I (1714) Philosophiae naturalis principia mathematica, sumptibus Soc

  36. Bala I, Yadav A (2019) Gravitational search algorithm: a state-of-the-art review. In: Yadav N, Yadav A, Bansal J, Deep K, Kim J (eds) Harmony search and nature inspired optimization algorithms. Advances in intelligent systems and computing, vol 741. Springer, Singapore, pp 27–37

    Google Scholar 

  37. Formato RA (2007) Central Force Optimization: a new metaheuristic with application in applied electromagnetic. Prog Electromagn Res 77:425–449

    Article  Google Scholar 

  38. Bala I, Yadav A (2019) Comprehensive learning gravitational search algorithm for global optimization of multimodal functions. Neural Comput Appl 32:7347–7382

    Article  Google Scholar 

  39. Brits R, Engelbrecht A, den Bergh FV (2007) Locating multiple optima using particle swarm optimization. Appl Math Comput 189(2):1859–1883

    MathSciNet  MATH  Google Scholar 

  40. Zhai Z, Li X (2011) A dynamic archive based niching particle swarm optimizer using a small population size. In: ACSC ‘11: proceedings of the thirty-fourth australasian computer science conference, vol 113, pp 83–90

  41. Epitropakis MG, Li X, Burke EK (2013) A dynamic archive niching differential evolution algorithm for multimodal optimization. In: 2013 IEEE congress on evolutionary computation June 20-23, Cancún, México

  42. Molina D, Bello APR, Herrera F (2013) Variable mesh optimization for the 2013 CEC special session niching methods for multimodal optimization. In: 2013 IEEE congress on evolutionary computation June 20-23, Cancún, México, pp 88–94

  43. Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of non parametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18

    Article  Google Scholar 

  44. Bosman PAN, Grahl J, Thierens D (2013) Benchmarking parameter-free AMaLGaM on functions with and without noise. Evol Comput 21(3):445–469

    Article  Google Scholar 

  45. Mallipeddi R, Jeyadevi S, Suganthan PN, Baskar S (2012) Efficient constraint handling for optimal reactive power dispatch problems. Swarm Evol Comput 5:28–36

    Article  Google Scholar 

  46. Bouchekara HR, Abido MA, Boucherma M (2014) Optimal power flow using teaching-learning-based optimization technique. Electr Power Syst 114(49–59):2014

    Google Scholar 

  47. Zhao B, Guo CX, Cao YJ (2005) A multi-agent based particle swarm optimization approach for reactive power dispatch. IEEE Trans Power Syst 20(2):1070–1078

    Article  Google Scholar 

  48. Wu QH, Cao YJ, Wen JY (1998) Optimal reactive power dispatch using an adaptive genetic algorithm. Int J Electr Power Energy Syst 20:563–569

    Article  Google Scholar 

  49. Zimmerman RD, Murillo-Sánchez CE, Gan D (2006) Matlab Power System Simulation Package (Version 3.1b2). http://www.pserc.cornell.edu/matpower/

  50. Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: Proceedings of the IEEE world congress computational intelligence, pp 69–73, May 1998

  51. Clerc M, Kennedy J (2002) The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6(1):58–73

    Article  Google Scholar 

  52. Liang JJ et al (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10(3):67–82

    Article  Google Scholar 

  53. Standard PSO 2007 (SPSO-07) on the Particle Swarm Central, Programs section, 2007. http://www.particleswarm.info

  54. Brest J (2006) Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans Evol Comput 10(6):646–657

    Article  Google Scholar 

  55. Qin AK, Suganthan PN (2005) Self-adaptive differential evolution algorithm for numerical optimization. In: Proceedings of the IEEE congress evolutionary computation, Edinburgh, UK, pp 1785–1791

  56. Oppacher F, Wineberg M (1998) A canonical genetic algorithm based approach to genetic programming. Artif Neural Netw Genet Algorithms 2:401–404

    Article  Google Scholar 

  57. Dai C, Chen W, Zhu Y, Zhang X (2009) Seeker optimization algorithm for optimal reactive power dispatch. IEEE Trans Power 24(3):1218–1231

    Google Scholar 

Download references

Acknowledgements

This work was supported by the National Institute of Technology Jalandhar, and Northcap University Gurgaon, India.

Author information

Authors and Affiliations

  1. Department of Science and Humanities, Northcap University, Gurugram, Haryana, 122017, India

    Indu Bala

  2. Department of Mathematics, Dr. B. R. Ambedkar National Institute of Technology Jalandhar, Jalandhar, 144011, India

    Anupam Yadav

Authors
  1. Indu Bala
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anupam Yadav
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anupam Yadav.

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

Bala, I., Yadav, A. Niching comprehensive learning gravitational search algorithm for multimodal optimization problems. Evol. Intel. 15, 695–721 (2022). https://doi.org/10.1007/s12065-020-00547-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12065-020-00547-w

Keywords

Search

Navigation