Skip to main content

Advertisement

SpringerLink
Log in

Bernstein-Levy differential evolution algorithm for numerical function optimization

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Differential evolutionary (DE) algorithm is one of the most frequently used evolutionary computation method for the solution of non-differentiable, complex and discontinuous real value numerical problems. The analytical structure of the mutation and crossover operators used by DE and the initial values of the parameters of the relevant operators affect the problem-solving ability of DE. Unfortunately, there is no analytical method for selecting and initializing the best artificial genetic operators that DE can use to solve a problem. Therefore, there is a need to develop new evolutionary search methods that are parameter-free and insensitive to the artificial genetic operators they use. In this paper, the Bernstein–Levy differential evolution (BDE) algorithm, which has a unique elitist-mutation operator and a Bernstein polynomials-based stochastic parameter-free crossover operator, is introduced. The numerical problem-solving success of BDE is statistically evaluated by using 30 benchmark problems of CEC2014 in the numerical experiments presented. BDE's success in solving the related benchmark problems is statistically compared with six state-of-the-art comparison algorithms. In this paper, three real-world optimization problems are also solved by using the proposed algorithm, BDE. According to statistics generated from the experimental results, BDE is statistically better than comparison methods in solving the related real-world 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
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Code availability

Name of the code/library: ReadMe.m; algo_bde.m; fncdata.mat; kowalik.m; rastring.m; rosenbrock.m, license.txt. Contact: ebesdok@erciyes.edu.tr, + 90-352-207 66 66 (32650). Hardware requirements: Windows 10 OS. Program language: Matlab 2022a. Software required: Matlab 2022a. Program size: ReadMe.m 1 KB; algo_bde.m 5 KB; fncdata.mat 1 KB; kowalik.m 1 KB; rastring.m 1 KB; rosenbrock.m 1 KB, license.txt 2 KB. The source codes are available for downloading at the link: Github, 2022. https://github.com/BESDOK/Bernstein-Levy-Differential-Evolution-Algorithm-BDE-.

References

  1. Das S, Suganthan PN (2011) Differential evolution: a survey of the state-of-the-art. IEEE T Evolut Comput 15:4–31

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  3. Civicioglu P (2012) Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm. Comput Geosci 46:229–247

    Article  Google Scholar 

  4. Civicioglu P (2013) Artificial cooperative search algorithm for numerical optimization problems. Inform Sci 229:58–76

    Article  MATH  Google Scholar 

  5. Civicioglu P (2013) Backtracking search optimization algorithm for numerical optimization problems. Appl Math Comput 219:8121–8144

    MathSciNet  MATH  Google Scholar 

  6. Peng H, Qian JY, Kong FR, Fan DB, Shao P, Wu ZJ (2022) Enhancing firefly algorithm with sliding window for continuous optimization problems. Neural Comput Appl. https://doi.org/10.1007/s00521-022-07193-6

    Article  Google Scholar 

  7. Civicioglu P, Besdok E (2013) A conceptual comparison of the Cuckoo-search, particle swarm optimization, differential evolution and artificial bee colony algorithms. Artif Intell Rev 39:315–346

    Article  Google Scholar 

  8. Civicioglu P, Besdok E (2018) A plus evolutionary search algorithm and QR decomposition based rotation invariant crossover operator. Expert Syst Appl 103:49–62

    Article  Google Scholar 

  9. Civicioglu P, Besdok E (2019) Bernstain-search differential evolution algorithm for numerical function optimization. Expert Syst Appl 138:18

    Article  Google Scholar 

  10. Civicioglu P, Besdok E (2021) Bezier search differential evolution algorithm for numerical function optimization a comparative study with CRMLSP, MVO, WA. SHADE and LSHADE Expert Syst Appl 165:14

    Google Scholar 

  11. Civicioglu P, Besdok E, Gunen MA, Atasever UH (2020) Weighted differential evolution algorithm for numerical function optimization: a comparative study with Cuckoo search, artificial bee colony, adaptive differential evolution, and backtracking search optimization algorithms. Eural Comput Appl 32:3923–3937

    Article  Google Scholar 

  12. Eltaeib T, Mahmood A (2018) Differential evolution: a survey and analysis. Appl Sci 8:25

    Article  Google Scholar 

  13. Civicioglu P, Besdok E (2022) Contrast stretching based pansharpening by using weighted differential evolution algorithm. Expert Syst Appl 208:118144

    Article  Google Scholar 

  14. Wu GH, Shen X, Li HF, Chen HK, Lin AP, Suganthan PN (2018) Ensemble of differential evolution variants. Inf Sci 423:172–186

    Article  MathSciNet  Google Scholar 

  15. Gunen MA (2021) Weighted differential evolution algorithm based pansharpening. Int J Remote Sens 42:8468–8491

    Article  Google Scholar 

  16. Gunen MA, Besdok E, Civicioglu P, Atasever UH (2020) Camera calibration by using weighted differential evolution algorithm: a comparative study with ABC, PSO, COBIDE, DE, CS, GWO, TLBO, MVMO, FOA, LSHADE ZHANG and BOUGUET. Neural Comput Appl 32:17681–17701

    Article  Google Scholar 

  17. Choi TJ, Ahn CW (2014) An adaptive cauchy differential evolution algorithm with bias strategy adaptation mechanism for global numerical optimization. J Comput 9:2139–2145

    Article  Google Scholar 

  18. Zhan ZH, Wang ZJ, Jin H, Zhang J (2020) Adaptive distributed differential evolution. IEEE T Cybern 50:4633–4647

    Article  Google Scholar 

  19. Zhang YX, Gou J (2019) Adaptive differential evolution algorithm based on restart mechanism and direction information. IEEE Access 7:166803–166814

    Article  Google Scholar 

  20. Karaboga D, Akay B (2009) A comparative study of artificial bee colony algorithm. Appl Math Comput 214:108–132

    MathSciNet  MATH  Google Scholar 

  21. Yang XS, Deb S (2014) Cuckoo search: recent advances and applications. Neural Comput Appl 24:169–174

    Article  Google Scholar 

  22. Brown C, Jin YC, Leach M, Hodgson M (2016) JADE: adaptive differential evolution with a small population. Soft Comput 20:4111–4120

    Article  Google Scholar 

  23. Wang Y, Li HX, Huang TW, Li L (2014) Differential evolution based on covariance matrix learning and bimodal distribution parameter setting. Appl Soft Comput 18:232–247

    Article  Google Scholar 

  24. Awad NH, Ali MZ, Suganthan PN, Reynolds RG (2016). An ensemble sinusoidal parameter adaptation incorporated with L-SHADE for solving CEC2014 benchmark problems. In: IEEE congress on evolutionary computation CEC held as part of IEEE world congress on computational intelligence IEEE WCCI pp. 2958–2965. Vancouver, Canada, IEEE

  25. Elsayed SM, Sarker RA, Essam DL, Hamza NM (2014) Testing united multi-operator evolutionary algorithms on the CEC2014 real-parameter numerical optimization. In: IEEE Congress on evolutionary computation CEC. pp 1650–1657. Beijing, IEEE

  26. Liang JQB, Suganthan P (2013) Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization, technical report 201311. In: Computational intelligence laboratory, Zhengzhou University, Zhengzhou, China and technical report, Nanyang Technological University, Singapore

  27. Besdok E (2022) https://www.mathworks.com/matlabcentral/fileexchange/115155-bernstein-levy-differential-evolution-algorithm-bde

  28. Github (2022) https://github.com/BESDOK/Bernstein-Levy-Differential-Evolution-Algorithm-BDE-

  29. Abdelfatah RI (2020) A color image authenticated encryption using conic curve and Mersenne twister. Multimed Tools Appl 79:24731–24756

    Article  Google Scholar 

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

    Article  Google Scholar 

  31. Atlasus (2022) https://3dgradgeo.com/tr/urunler/hava-ekipman-satis/atlasus-uav/

  32. Turef (2022) https://www.tusaga-aktif.gov.tr/

  33. Civicioglu P, Alci M (2004) Impulsive noise suppression from highly distorted images with triangular interpolants. AEU-Int J Electron C 58:311–318

    Article  MATH  Google Scholar 

  34. Besdok E, Civicioglu P, Alci M (2004) Impulsive noise suppression from highly corrupted images by using resilient neural networks. Artif Intell Soft Comput ICAISC 2004(3070):670–675

    MATH  Google Scholar 

  35. Civicioglu P, Alci M, Besdok E (2004) Using an exact radial basis function artificial neural network for impulsive noise suppression from highly distorted image databases. Adv Inf Syst Proceed 3261:383–391

    MATH  Google Scholar 

  36. Civicioglu P, Alci M, Besdok E (2004) Impulsive noise suppression from images with the noise exclusive filter. EURASIP JASP 2004(16):2434–2440

    MATH  Google Scholar 

  37. Gunen MA, Civicioglu P, Besdok E (2016) Differential search algorithm based edge detection. XXIII ISPRS Congress Commission VII 41(B7):667–670

    Google Scholar 

  38. Chauhan D, Unnikrishnan A, Figliozzi M (2019) Maximum coverage capacitated facility location problem with range constrained drones. Transport Res C-Emer 99:1–18

    Article  Google Scholar 

  39. Vazquez-Carmona EV, Vasquez-Gomez JI, Herrera-Lozada JC, Antonio-Cruz M, Coverage path planning for spraying drones (2022) Comput Ind Eng. 168: 108125

  40. Zorbas D, Pugliese LDP, Razafindralambo T, Guerriero F (2016) Optimal drone placement and cost-efficient target coverage. J Netw Comput Appl 75:16–31

    Article  MATH  Google Scholar 

  41. Zhang B, Song J, Liu Z, Yang K (2021) Genetic algorithm enabled particle swarm optimization for aerial base station deployment. In: IEEE 94th Vehicular Technology Conference. VTC2021-Fall. https://doi.org/10.1109/VTC2021-FALL52928.2021.9625338

  42. Wang H, Li H, Zhang C, He S, Liu J (2017) A 3D coverage path planning approach for flying cameras in nature environment under photogrammetric constraints. In: Proceedings of the 36th Chinese control conference July 26–28, Dalian, China. https://doi.org/10.23919/ChiCC.2017.8028424

  43. Huang Y, Xu J, Shi M, Liu L. (2022). Time-Efficient Coverage Path Planning for Energy-Constrained UAV. Wirel Commun Mob Com. 5905809. https://doi.org/10.1155/2022/5905809

  44. Liu C, Zhang S, Akbar A (2019) Ground feature oriented path planning for unmanned aerial vehicle mapping. IEEE J Sel Top Appl 12(4):1175–1187

    Google Scholar 

  45. NASA (2022) https://speclib.jpl.nasa.gov/

  46. RSLAB (2022) https://rslab.ut.ac.ir/-/remote-sensing-datasets (Urban_R162.mat)

  47. Sun S, Rappaport TS, Thomas TA, Ghosh A, Nguyen HC, Kovacs IZ, Rodriguez I, Koymen O, Partyka A (2016) Investigation of prediction accuracy, sensitivity, and parameter stability of large-scale propagation path loss models for 5G wireless communications. IEEE T Veh Technol 65(5):2843–2860

    Article  Google Scholar 

  48. Seybold JS (2005) Introduction to RF propagation. Wiley, Hoboken

    Book  Google Scholar 

  49. Yun Z, Iskander MF (2015) Ray tracing for radio propagation modeling: principles and applications. IEEE Access 3:1089–1100

    Article  Google Scholar 

  50. Schaubach KR, Davis NJ, Rappaport TS (1992) A ray tracing method for predicting path loss and delay spread in microcellular environments. In: Vehicular technology society 42nd VTS conference-frontiers of technology, 932–935. Denver, CO, USA: IEEE, 1992

  51. Zuliang W, Mao Z, Juan W, Linhua Z (2008) Improved algorithm of atmospheric refraction error in Longley-Rice channel model. J Syst Eng Electron 19(4):683–687

    Article  Google Scholar 

  52. Friis HT (1946) A note on a simple transmission formula. IRE Proc 34(5):254–256

    Article  Google Scholar 

  53. Hufford G (2002) The ITS Irregular Terrain Model, version 1.2.2, itm.alg.pdf . https://www.its.bldrdoc.gov/resources/radio-propagationsoftware/itm/itm.aspx

  54. Longley AG, Rice PL (1968) Prediction of tropospheric radio transmission loss over irregular terrain: a computer method-1968. Institute for telecommunication sciences (ITS). NTIA

  55. Marianov V, Eiselt HA (2012) Transmitter location for maximum coverage and constructive-destructive interference management. Comput Oper Res 39:1441–1449

    Article  MathSciNet  MATH  Google Scholar 

  56. Cgiar (2022) https://srtm.csi.cgiar.org/download (Product: SRTM 90m DEM Version 4, Data File Name: srtm_44_05.zip)

  57. Mathworks (2022) https://www.mathworks.com/products/antenna.html (please see the ‘coverage’ and ‘txsite’ commands of related toolbox of Matlab 2022a)

Download references

Author information

Authors and Affiliations

  1. Faculty of Aeronautics and Astronautics, Department of Aircraft Electrics and Electronics, Erciyes University, Kayseri, Türkiye

    Pinar Civicioglu

  2. Faculty of Engineering, Department of Geomatics Engineering, Erciyes University, Kayseri, Türkiye

    Erkan Besdok

Authors
  1. Pinar Civicioglu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Erkan Besdok
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Erkan Besdok.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest. This manuscript does not contain any studies with human participants or animals performed by any of the authors. Authors have carefully checked the “Instructions for Authors” and certify that the manuscript complies with the ethical rules applicable for this journal.

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 (e.g. a society or other partner) 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

Civicioglu, P., Besdok, E. Bernstein-Levy differential evolution algorithm for numerical function optimization. Neural Comput & Applic 35, 6603–6621 (2023). https://doi.org/10.1007/s00521-022-08013-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-022-08013-7

Keywords

Search

Navigation