Real-Parameter Unconstrained Optimization Based on Enhanced AGDE Algorithm

  • Ali Khater Mohamed
  • Ali Wagdy MohamedEmail author
Part of the Studies in Computational Intelligence book series (SCI, volume 801)


Adaptive guided differential evolution algorithm (AGDE) is a differential evolution (DE) algorithm that utilizes the information of good and bad vectors in the population, it introduced a novel mutation rule in order to balance effectively the exploration and exploitation tradeoffs. It divided the population into three clusters (best, better and worst) with sizes 100p%, NP − 2 * 100% and 100% respectively. where p is the proportion of the partition with respect to the total number of individuals in the population (NP). AGDE selects three random individuals, one of each partition to implement the mutation process. Besides, a novel adaptation scheme was proposed in order to update the value of crossover rate without previous knowledge about the characteristics of the problems. This paper introduces enhanced AGDE (EAGDE) with non-linear population size reduction, which gradually decreases the population size according to a non-linear function. Moreover, a newly developed rule developed to determine the initial population size, that is related to the dimensionality of the problems. The performance of the proposed algorithm is evaluated using CEC2013 benchmarks and the results are compared with the state-of-art DE and non-DE algorithms, the results showed a great competitiveness for the proposed algorithm over the other algorithms, and the original AGDE.


Differential evolution Novel mutation Adaptive crossover Initial population Population reduction 


  1. 1.
    Storn, R., Price, K.: Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous spaces. International Computer Science Institute Technical Report, Tech. Rep. TR-95-012 (1995)Google Scholar
  2. 2.
    Storn, R., Price, K.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob. Optim. 11(4), 341–359 (1997)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Das, S., Abraham, A., Chakraborty, U.K., Konar, A.: Differential evolution using a neighborhood-based mutation operator. IEEE Trans. Evol. Comput. 13(3), 526–553 (2009)CrossRefGoogle Scholar
  4. 4.
    Zhang, J., Sanderson, A.C.: JADE: adaptive differential evolution with optional external archive. IEEE Trans. Evol. Comput. 13(5), 945–958 (2009)CrossRefGoogle Scholar
  5. 5.
    Qin, A.K., Huang, V.L., Suganthan, P.N.: Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans. Evol. Comput. 13(2), 398–417 (2009)CrossRefGoogle Scholar
  6. 6.
    Mohamed, A.W., Sabry, H.Z.: Constrained optimization based on modified differential evolution algorithm. Inf. Sci. 171–208 (2012)Google Scholar
  7. 7.
    Mohamed, A.W., Sabry, H.Z., Khorshid, M.: An alternative differential evolution algorithm for global optimization. J. Adv. Res. 3(2), 149–165 (2012)CrossRefGoogle Scholar
  8. 8.
    Mohamed, A.W., Sabry, H.Z., Farhat, A.: Advanced differential evolution algorithm for global numerical optimization. In: Proceedings of the IEEE International Conference on Computer Applications and Industrial Electronics (ICCAIE’11), Penang, Malaysia, pp. 156–161 (2011)Google Scholar
  9. 9.
    Li, X., Yin, M.: Modified differential evolution with self-adaptive parameters method. J. Comb. Optim. 31(2), 546–576 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Mohamed, A.W.: An improved differential evolution algorithm with triangular mutation for global numerical optimization. Comput. Ind. Eng. 85, 359–375 (2015)CrossRefGoogle Scholar
  11. 11.
    Mohamed, A.W., Suganthan, P.N.: Real-parameter unconstrained optimization based on enhanced fitness-adaptive differential evolution algorithm with novel mutation. Soft Comput. (2017).
  12. 12.
    Mohamed, A.W.: An efficient modified differential evolution algorithm for solving constrained non-linear integer and mixed-integer global optimization problems. Int. J. Mach. Learn. Cybernet. 8, 989 (2017). Scholar
  13. 13.
    Mohamed, A.W.: A novel differential evolution algorithm for solving constrained engineering optimization problems. J. Intell. Manuf. (2017).
  14. 14.
    Mohamed, A.W., Almazyad, A.S.: Differential evolution with novel mutation and adaptive crossover strategies for solving large scale global optimization problems. Appl. Comput. Intell. Soft Comput. (2017), Article ID 7974218, 18 pp.
  15. 15.
    Mohamed, A.W.: Solving stochastic programming problems using new approach to differential evolution algorithm. Egypt. Inf. J. 18(2), 75–86 (2017)CrossRefGoogle Scholar
  16. 16.
    Brest, J., Greiner, S., Bošković, B., Mernik, M., Zumer, V.: Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans. Evol. Comput. 10(6), 646–657 (2006)CrossRefGoogle Scholar
  17. 17.
    Noman, N., Iba, H.: Accelerating differential evolution using an adaptive local search. IEEE Trans. Evol. Comput. 12(1), 107–125 (2008)CrossRefGoogle Scholar
  18. 18.
    Peng, F., Tang, K., Chen, G., Yao, X.: Multi-start JADE with knowledge transfer for numerical optimization. In: IEEE CEC, pp. 1889–1895 (2009)Google Scholar
  19. 19.
    Montgomery, J., Chen, S.: An Analysis of the Operation of Differential Evolution at High and Low Crossover Rates, pp. 1–8. IEEE Congress on Evolutionary Computation, Barcelona (2010)Google Scholar
  20. 20.
    Mallipeddi, R., Suganthan, P.N., Pan, Q.K., Tasgetiren, M.F.: Differential evolution algorithm with ensemble of parameters and mutation strategies. Appl. Soft Comput. 11(2), 1679–1696 (2011)CrossRefGoogle Scholar
  21. 21.
    Wang, Y., Cai, Z., Zhang, Q.: Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans. Evol. Comput. 15(1), 55–66 (2011)CrossRefGoogle Scholar
  22. 22.
    Yong, W., Han-Xiong, L., Tingwen, H., Long, L.: Differential evolution based on covariance matrix learning and bimodal distribution parameter setting. Appl. Soft Comput. 18, 232–247 (2014)CrossRefGoogle Scholar
  23. 23.
    Draa, A., Bouzoubia, S., Boukhalfa, I.: A sinusoidal differential evolution algorithm for numerical optimization. Appl. Soft Comput. 27, 99–126 (2015)CrossRefGoogle Scholar
  24. 24.
    Das, S., Suganthan, P.N.: Differential evolution: a survey of the state-of-the-art. IEEE Trans. Evol. Comput. 15(1), 4–31 (2011)CrossRefGoogle Scholar
  25. 25.
    Das, S., Mullick, S.S., Suganthan, P.N.: Recent advances in differential evolution-an updated survey. Swarm Evol. Comput. 27, 1–30 (2016)CrossRefGoogle Scholar
  26. 26.
    Cheng, J.X., Zhang, G.X., Neri, F.: Enhancing distributed differential evolution with multicultural migration for global numerical optimization. Inf. Sci. 247, 72–93 (2013)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Gao, W.F., Pan, Z., Gao, J.: A new highly efficient differential evolution with self-adaptive strategy for multimodal optimization. IEEE Trans. Cybern. 44(8), 1314–1327 (2014)CrossRefGoogle Scholar
  28. 28.
    Mallipeddi, R., Suganthan, P.N.: Empirical study on the effect of population size on differential evolution algorithm. In: Proceedings of IEEE Congress on Evolutionary Computation, Hong Kong (2008)Google Scholar
  29. 29.
    Wang, H., Wang, W.J., Cui, Z.H., Sun, H., Ranhnamayan, S.: Heterogeneous differential evolution for numerical optimization. Sci. World J. Article ID 318063 (2014)Google Scholar
  30. 30.
    Gao, W.F., Yen, G.G., Liu, S.Y.: A dual differential evolution with coevolution for constrained optimization. IEEE Trans. Cybern. 45(5), 1094–1107 (2015)Google Scholar
  31. 31.
    Brest, J., Maucec, M.S.: Self-adaptive differential evolution algorithm using population size reduction and three strategies. Soft. Comput. 15(11), 2157–2174 (2011)CrossRefGoogle Scholar
  32. 32.
    Zamuda, A., Brest, J.: Self-adaptive control parameters’ randomization frequency and propagations in differential evolution. Swarm Evol. Comput. 25, 72–99 (2015)CrossRefGoogle Scholar
  33. 33.
    Piotrowski, A.P.: Review of differential evolution population size. Swarm Evol. Comput. 32, 1–24 (2017)CrossRefGoogle Scholar
  34. 34.
    Mohamed, A.W., Mohamed, A.K.: Adaptive guided differential evolution algorithm with novel mutation for numerical optimization. Int. J. Mach. Learn. Cybern. (2017).
  35. 35.
    Laredo, J.L.J., Fernandes, C., Guervós, J.J.M., Gagné, C.: Improving genetic algorithms performance via deterministic population shrinkage. In: GECCO, pp. 819–826 (2009)Google Scholar
  36. 36.
    Liang, J.J., Qin, B.Y., Suganthan, P.N., Hernandez-Diaz, A.G.: Problem Definitions and Evaluation Criteria for the CEC 2013 Special Session on Real-Parameter Optimization. Zhengzhou University/Nanyang Technological University, Zhengzhou, China/Singapore (2013)Google Scholar
  37. 37.
    García, S., Molina, D., Lozano, M., Herrera, F.: A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behavior: a case study on the CEC’2005 special session on real parameter optimization. J. Heurist. 15, 617–644 (2009). SpringerCrossRefGoogle Scholar
  38. 38.
    Hansen, N., Ostermeier, A.: Cma-es source code (2009).

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Business Administration, College of Sciences and HumanitiesMajmaah UniversityMajmaahSaudi Arabia
  2. 2.Operations Research DepartmentInstitute of Statistical Studies and Research, Cairo UniversityGizaEgypt

Personalised recommendations