Skip to main content
SpringerLink
Log in

Logistic map and wavelet transform based differential evolution

  • Original Article
  • Published:
International Journal of System Assurance Engineering and Management Aims and scope Submit manuscript

Abstract

Differential evolution (DE) is a popular evolutionary technique which can be applied in various constrained and unconstrained optimization problems along with the real time problems by modifying its operators like mutation, crossover and selection. In this paper initialization process of population along with the mutation rate is modified using the concept of logistic map and wavelet transformation in DE respectively. This modification increases the convergence rate. The modified proposal is tested on various benchmark problems. Also the evaluated results are compared for performance with state of the art algorithms, along with three real time non linear engineering problems, which dictates that the modified DE is easily applicable to the real time optimization problems.

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

Similar content being viewed by others

References

  • Abderazek H, Ferhat D, Atanasovska I, Boualem K (2015) A differential evolution algorithm for tooth profile optimization with respect to balancing specific sliding coefficients of involute cylindrical spur and helical gears. Adv Mech Eng 7:1–11

    Article  Google Scholar 

  • Ali M, Pant M, Singh VP (2010) Two modified differential evolution algorithms and their applications to engineering design problems. World J Model Simul 6(1):72–80

    Google Scholar 

  • Anh P (2016) Engineering optimization by constrained differential evolution with nearest neighbour comparison. Vietnam J Mech 38(2):89–101

    Article  Google Scholar 

  • Biswas P, Suganthan P, Mallipeddi R, Amaratunga G (2018) Optimal power flow solutions using differential evolution algorithm integrated with effective constraint handling techniques. Eng Appl Artif Intell 68:81–100

    Article  Google Scholar 

  • Brest J, Greiner S et al (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 

  • Cai Y, Chen Y, Wang T, Tian H (2016) Improving differential evolution with a new selection method of parents for mutation. Front Comput Sci 10(2):246–269

    Article  Google Scholar 

  • Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: 6th international symposium on machine and human science, pp 39–43

  • Fu C, Xu Y, Jiang C, Han X, Huang Z (2017) Improved differential evolution with shrinking space technique for constrained optimization. Chin J Mech Eng 30(3):553–565

    Article  Google Scholar 

  • Hamza F, Abderazek H, Lakhdar S, Ferhat D, Yıldız A (2018) Optimum design of cam-roller follower mechanism using a new evolutionary algorithm. Int J Adv Manuf Technol 99(5–8):1267–1282

    Article  Google Scholar 

  • Holland JH (1975) Adaptive in natural and artificial systems. University of Michigan Press, Ann Arbor

    Google Scholar 

  • Jigang H, Hui F, Jie W (2019) A PI controller optimized with modified differential evolution algorithm for speed control of BLDC motor. Automatika 60(2):135–148

    Article  Google Scholar 

  • Knobloch R, Mlýnek J, Srb R (2017) The classic differential evolution algorithm and its convergence properties. Appl Math 62(2):197–208

    Article  MathSciNet  Google Scholar 

  • Kumar P, Pant M (2014) Modified random localization based DE for static economic power dispatch with generator constraints. Int J Bio-Inspired Comput 6(4):250–261

    Article  Google Scholar 

  • Kumar P, Pant M (2016) Recognition of noise source in multi sounds field by modified random localized based DE algorithm. Int J Syst Assur Eng Manag 9(1):245–261

    Article  Google Scholar 

  • Kumar P, Pant M (2012) Enhanced mutation strategy for differential evolution. In Proceedings of IEEE congress of evolutionary computing (CEC-12), pp 1–6.

  • Kumar S, Pant M, Ray AK (2018) DE-IE: differential evolution for color image enhancement. Int J Syst Assur Eng Manag 9(3):577–588

    Article  Google Scholar 

  • Kuo R, Zulvia F (2018) An improved differential evolution with cluster decomposition algorithm for automatic clustering. Soft Comput

  • Lei Y, Gou J, Wang C, Luo W, Cai Y (2017) Improved differential evolution with a modified orthogonal learning strategy. IEEE Access 5:9699–9716

    Article  Google Scholar 

  • Li X, Zhang H (2018) Enhanced differential evolution with modified parent selection technique for numerical optimisation. Int J Comput Sci Eng 17(1):98

    Google Scholar 

  • Li Y, Zhan Z, Gong Y, Chen W, Zhang J, Li Y (2014) Differential evolution with an evolution path: A DEEP evolutionary algorithm. IEEE Trans Cybern 45(9):1798–1810

    Article  Google Scholar 

  • Mohamed A, Sabry H, Abd-Elaziz T (2013) Real parameter optimization by an effective differential evolution algorithm. Egypt Inf J 14:37–53

    Article  Google Scholar 

  • Price KV, Storn RM, Lampinen JA (2005) Differential evolution: a practical approach to global optimization Natural Computing Series. Springer, Berlin

    MATH  Google Scholar 

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

    Article  Google Scholar 

  • Qiu X, Li B, Cui Z, Li J (2014) A fractal mutation factor modified differential evolution algorithm. Appl Mech Mater 598:418–423

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Rajpurohit J, Sharma TK, Abraham A, Vaishali A (2017) Glossary of metaheuristic algorithms. Int J Comput Inf Syst Ind Manag Applic 9:181–205

    Google Scholar 

  • Rout BD, Pati BB, Panda S (2018) A hybrid modified differential evolution-pattern search approach for SSSC based damping controller design under communication constraints. Int J Syst Assur Eng Manag 9(4):962–971

    Article  Google Scholar 

  • Singh P, Chaturvedi P, Kumar P (2018) A novel differential evolution approach for constraint optimization. Int J Bio-Inspired Comput 12(4):254–265

    Article  Google Scholar 

  • Storn R, Price K (1995) Differential evolution: a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical report TR-95–012, International Computer Science Institute, Berkeley, USA

  • Suganthan PN, Hansen N, Liang JJ, Deb K, Chen YP, Auger A, Tiwari S (2005) Problem definition and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Technical report, Nanyang Technological University, Singapore

  • Vesterstrom J, Thomsen R (2004) A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems. Proc Cong Evolut Comput 2:1980–1987

    Google Scholar 

  • Yao X, Liu Y, Liang K-H, Lin G (2003) Fast evolutionary algorithms. In: Ghosh A, Tsutsui S (eds) Advances in Evolutionary Computing. Natural Computing Series. Springer, Berlin, Heidelberg, pp 45–94. https://doi.org/10.1007/978-3-642-18965-4_2

    Chapter  Google Scholar 

  • Yi W, Li X, Gao L, Zhou Y (2015) ε Constrained differential evolution algorithm with a novel local search operator for constrained optimization problems. In: Proceedings in adaptation, learning and optimization, pp 495–507

  • Zaheer H, Pant M, Kumar S (2018) A new guiding force strategy for differential evolution. Int J Syst Assur Eng Manag 8(4):2170–2183

    Google Scholar 

  • Zhang J, Sanderson A (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958

    Article  Google Scholar 

  • Zou D, Wu J, Gao L, Li S (2013) A modified differential evolution algorithm for unconstrained optimization problems. Neurocomputing 120:469–481

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Amity University Rajasthan, Jaipur, India

    Katyayani Kashyap & Jitendra Rajpurohit

  2. Shobhit University Gangoh, Saharanpur, India

    Tarun K. Sharma

Authors
  1. Katyayani Kashyap
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tarun K. Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jitendra Rajpurohit
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tarun K. Sharma.

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

Kashyap, K., Sharma, T.K. & Rajpurohit, J. Logistic map and wavelet transform based differential evolution. Int J Syst Assur Eng Manag 11, 506–514 (2020). https://doi.org/10.1007/s13198-019-00920-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13198-019-00920-8

Keywords

Search

Navigation