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

  • Pinar Civicioglu
  • Erkan BesdokEmail author
  • Mehmet Akif Gunen
  • Umit Haluk Atasever
Original Article


In this paper, weighted differential evolution algorithm (WDE) has been proposed for solving real-valued numerical optimization problems. When all parameters of WDE are determined randomly, in practice, WDE has no control parameter but the pattern size. WDE can solve unimodal, multimodal, separable, scalable, and hybrid problems. WDE has a very fast and quite simple structure, in addition, it can be parallelized due to its non-recursive nature. WDE has a strong exploration and exploitation capability. In this paper, WDE’s success in solving CEC’ 2013 problems was compared to 4 different EAs (i.e., CS, ABC, JADE, and BSA) statistically. One 3D geometric optimization problem (i.e., GPS network adjustment problem) and 4 constrained engineering design problems were used to examine the WDE’s ability to solve real-world problems. Results obtained from the performed tests showed that, in general, problem-solving success of WDE is statistically better than the comparison algorithms that have been used in this paper.


Cuckoo search algorithm Artificial bee colony algorithm Differential evolution algorithm Backtracking search optimization Particle swarm optimization 


Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.


The authors would like to thank the editor and the referees for their contribution in enhancing the technical quality of this paper. Some parts of this paper were supported by the below mentioned projects: Erciyes University BAP FDA-2013-4530, FBA-10-3067, FBA-9-1131, FBA-2013-4525, 06-AY-15 and Tubitak 115Y235.


  1. 1.
    Karaboga D, Akay B (2009) A comparative study of artificial bee colony algorithm. Appl Math Comput 214(12):108–132MathSciNetzbMATHGoogle Scholar
  2. 2.
    Civicioglu P (2013) Artificial cooperative search algorithm for numerical optimization problems. Inform Syst 229:58–76zbMATHGoogle Scholar
  3. 3.
    Yang XS, Deb S (2009) Cuckoo search via levy flights. World congress on nature and biologically inspired computing-Nabic’2009. Coimbatore, India, vol 4, pp 210–214Google Scholar
  4. 4.
    Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713CrossRefGoogle Scholar
  5. 5.
    Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417CrossRefGoogle Scholar
  6. 6.
    Yong W, Han-Xion L, Tingwen H, Long L (2014) Differential evolution based on covariance matrix learning and bimodal distribution parameter setting. Appl Soft Comput 218:232–247Google Scholar
  7. 7.
    Civicioglu P (2013) Backtracking search optimization algorithm for numerical optimization problems. Appl Math Comput 219:8121–8144MathSciNetzbMATHGoogle Scholar
  8. 8.
    Civicioglu P, Beşdok E (2013) A conceptual comparison of the Cuckoo-search, particle swarm optimization, differential evolution and artificial bee colony algorithms. Artif Intell Rev 39(4):315–346CrossRefGoogle Scholar
  9. 9.
    Civicioglu P (2012) Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm. Comput Geosci 46:229–247CrossRefGoogle Scholar
  10. 10.
    Bratton D, Kennedy J (2007) Defining a standard for particle swarm optimization. In: IEEE swarm intelligence symposium, Honolulu 1-4244-0708-7Google Scholar
  11. 11.
    Liang JJ, Qin AK, Suganthan PN, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10:281–295CrossRefGoogle Scholar
  12. 12.
    Clerc M, Kennedy J (2002) The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6(1):58–73CrossRefGoogle Scholar
  13. 13.
    Omran MGH, Clerc M (2015) Accessed 20 Feb 2018
  14. 14.
    Hansen N, Ostermeier A (2001) Completely derandomized self-adaptation in evolution strategies. Evol Comput 9(2):159–195CrossRefGoogle Scholar
  15. 15.
    Price KV, Storn R, Lampinen J (2005) Differential evolution: a practical approach to global optimization. Springer, BerlinzbMATHGoogle Scholar
  16. 16.
    Salimi H (2015) Stochastic fractal search: a powerful metaheuristic algorithm. Knowl-Based Syst 75:1–18CrossRefGoogle Scholar
  17. 17.
    Cheng MY, Prayogo D (2014) Symbiotic organisms search: a new metaheuristic optimization algorithm. Comput Struct 139:98–112CrossRefGoogle Scholar
  18. 18.
    Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 13:2232–2248CrossRefGoogle Scholar
  19. 19.
    Sadollah A, Bahreininejad A, Eskandar H, Hamdi M (2013) Mine blast algorithm: a new population based algorithm for solving constrained engineering optimization problems. Appl Soft Comput 13:2592–2612CrossRefGoogle Scholar
  20. 20.
    Wang D, Wua Z, Fei Y, Zhang W (2014) Structural design employing a sequential approximation optimization approach. Comput Struct 134:75–87CrossRefGoogle Scholar
  21. 21.
    Maheri MR, Narimani MM (2014) An enhanced harmony search algorithm for optimum design of side sway steel frames. Comput Struct 136:78–89CrossRefGoogle Scholar
  22. 22.
    Civicioglu P, Alcı M (2004) Edge detection of highly distorted images suffering from impulsive noise. AEU Int J Electron C 58(6):413–419CrossRefGoogle Scholar
  23. 23.
    Wu X, Yang Z (2013) Nonlinear speech coding model based on genetic programming. Appl Soft Comput 13(7):3314–3323CrossRefGoogle Scholar
  24. 24.
    Yoon Y, Kim YH (2013) An efficient genetic algorithm for maximum coverage deployment in wireless sensor networks. IEEE Trans Cybern 43(5):1473–1483CrossRefGoogle Scholar
  25. 25.
    Civicioglu P, Alcı M, Besdok E (2004) Using an exact radial basis function artificial neural network for impulsive noise suppression from highly distorted image databases. LNCS 3261:383–391zbMATHGoogle Scholar
  26. 26.
    Chauhan RS, Arya SK (2013) An optimal design of IIR digital filter using particle swarm optimization. Appl Artif Intell 27(6):429–440CrossRefGoogle Scholar
  27. 27.
    Yan Y, He Y, Hu Y, et al (2014) Video superresolution via parameter-optimized particle swarm optimization. Math Probl Eng 373425Google Scholar
  28. 28.
    Moezi SA, Zakeri E, Zare A, Nedaei M (2015) On the application of modified cuckoo optimization algorithm to the crack detection problem of cantilever Euler–Bernoulli beam. Comput Struct 157:42–50CrossRefGoogle Scholar
  29. 29.
    Wang GG, Gandomi AH, Alavi AH, Deb S (2016) A hybrid method based on krill herd and quantum-behaved particle swarm optimization. Neural Comput Appl 4(27):989–1006CrossRefGoogle Scholar
  30. 30.
    Heidari AA, Abbaspour RA, Jordehi AR (2017) An efficient chaotic water cycle algorithm for optimization tasks. Neural Comput Appl 1(28):57–85CrossRefGoogle Scholar
  31. 31.
    Faris H, Aljarah I, Azmi Al-Betar M, Mirjalili S (2017) Grey wolf optimizer: a review of recent variants and applications. Neural Comput Appl 30:413–435CrossRefGoogle Scholar
  32. 32.
    Aljarah I, Faris H, Mirjalili S, Al-Madi N (2018) Training radial basis function networks using biogeography-based optimizer. Neural Comput Appl 7(29):529–553CrossRefGoogle Scholar
  33. 33.
    Wang GG, Gandomi AH, Alavi AH, Hao GS (2014) Hybrid krill herd algorithm with differential evolution for global numerical optimization. Neural Comput Appl 2(25):297–308CrossRefGoogle Scholar
  34. 34.
    Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 4(27):1053–1073CrossRefGoogle Scholar
  35. 35.
    Alweshah M (2018) Construction biogeography-based optimization algorithm for solving classification problems. Neural Comput Appl.
  36. 36.
    Liang JJ, Qu BY, Suganthan PN, Hernandez-Diaz AG (2013) Problem definitions and evaluation criteria for the CEC 2013 special session on real-parameter optimization. Technical report 201212, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, Singapore, January 2013Google Scholar
  37. 37.
    Zhang J, Sanderson AC (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958CrossRefGoogle Scholar
  38. 38.
    Wang Y, Liu ZZ, Li J et al (2016) Utilizing cumulative population distribution information in differential evolution. Appl Soft Comput 48:329–346CrossRefGoogle Scholar
  39. 39.
    Civicioglu P, Besdok E (2018) A+ Evolutionary search algorithm and QR decomposition based rotation invariant crossover operator. Expert Syst Appl 103:49–62CrossRefGoogle Scholar
  40. 40.
  41. 41.
    Ghilani CD, Wolf PR (2006) Adjustment computations, spatial data analysis, Forth edn. Wiley, New JerseyCrossRefGoogle Scholar
  42. 42.
    Yetkin M, Berber M (2014) Implementation of robust estimation in GPS networks using the Artificial Bee Colony algorithm. Earth Sci Inform 7:39–46. CrossRefGoogle Scholar
  43. 43.
    Yetkin M (2018) Application of robust estimation in geodesy using the harmony search algorithm. J Spat Sci 63(1):63–73. MathSciNetCrossRefGoogle Scholar
  44. 44.
    Derrac J, Garca 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 1:3–18CrossRefGoogle Scholar
  45. 45.
    Matsumoto M, Nishimura T (1998) Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans Model Comput Sci 8(1):3–30CrossRefGoogle Scholar
  46. 46.
    Mezura-Montesa E, Coellob CAC (2011) Constraint-handling in nature-inspired numerical optimization: past, present and future. Swarm Evol Comput 1(4):173–194CrossRefGoogle Scholar
  47. 47.
    Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Engrg 186:311–338CrossRefGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2018

Authors and Affiliations

  • Pinar Civicioglu
    • 1
  • Erkan Besdok
    • 2
    Email author
  • Mehmet Akif Gunen
    • 2
  • Umit Haluk Atasever
    • 2
  1. 1.Department of Aircraft Electrics and Electronics, Faculty of Aeronautics and AstronauticsErciyes UniversityKayseriTurkey
  2. 2.Department of Geomatics Engineering, Engineering FacultyErciyes UniversityKayseriTurkey

Personalised recommendations