Soft Computing

, Volume 22, Issue 2, pp 659–676 | Cite as

Evolutionary programming with a simulated-conformist mutation strategy

  • Han HuangEmail author
  • Shujin Ye
  • Zhun Fan
  • Zhiyong Lin
  • Liang Lv
  • Zhifeng Hao
Methodologies and Application


Evolutionary programming has been widely implemented as a continuous optimization algorithm. Prior studies have come to a bottleneck because most of the evolutionary programming algorithms are unable to robustly solve different types of optimization problems. We argue that such a bottleneck results from the existing mutation strategies’ making little use of the population information. Inspired by a psychological model which describes how a person optimizes his/her social activities by conformity behavior, this study proposes a variation vector of the mutation to simulate the conformity behavior with behavior-reference, majority-impact, and distinctive-impact factors. These factors, respectively, correspond with three types of population information for each mutated individual: heuristic information, optimal gradient, and population diversity. We use the proposed vector to design an improved evolutionary programming with a simulated-conformist mutation strategy. The results show that the population information produced by the three factors enhance the robustness of the performance of evolutionary programming in solving both uni- and multimodal functions. The finding is verified by empirical analyses of two sets of benchmark functions proposed in 1998 and 2013. The numerical results indicate that the proposed algorithm performs significantly better on average than the existing EPs and some other algorithms with similar strategies.


Continuous optimization Evolutionary programming Simulated-conformist mutation 



This work is supported by National Natural Science Foundation of China (61370102), Guangdong Natural Science Funds for Distinguished Young Scholar (2014A030306050), the Fundamental Research Funds for the Central Universities, SCUT (2015PT022), Guangdong High-Level Personnel of Special Support Program (2014TQ01X664), the Guangdong High-Level University Project Green Technologies for Marine Industries, the Science and Technology Planning Project of Guangdong Province (2013B011304002), and the Project of Educational Commission of Guangdong Province, China (2015KGJHZ014). The authors thank Mr. Changjian Xu for his help with the experiment.

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.


  1. Alam MS, Islam MM, Yao X, Murase K (2011) Recurring two-stage evolutionary programming: a novel approach for numeric optimization. IEEE Tran Syst Man Cybern Part B Cybern 41(5):1352–1365CrossRefGoogle Scholar
  2. Alam MS, Islam MM, Yao X, Murase K (2012) Diversity guided evolutionary programming: a novel approach for continuous optimization. Appl Soft Comput 12(6):1693–1707CrossRefGoogle Scholar
  3. Alipouri Y, Poshtan J, Alipouri Y, Alipour MR (2012) Momentum coefficient for promoting accuracy and convergence speed of evolutionary programming. Appl Soft Comput 12(6):1765–1786CrossRefGoogle Scholar
  4. Anik M, Alam T, Ahmed S, Noman ASM, Rakibul Islam KM (2013) A dual mutation strategy embedded evolutionary programming for continuous optimization. In: World Congress on Nature and Biologically Inspired Computing (NABIC). IEEE, pp 84–91Google Scholar
  5. Asch SE (1956) Studies of independence and conformity: I. A minority of one against a unanimous majority. Psychol Monogr Gen Appl 70(9):1–70CrossRefGoogle Scholar
  6. Bäck T, Schwefel H-P (1993) An overview of evolutionary algorithms for parameter optimization. Evol Comput 1(1):1–23CrossRefGoogle Scholar
  7. Bratton D, Kennedy J (2007) Defining a standard for particle swarm optimization. In: Swarm intelligence symposium. IEEE, pp 120–127Google Scholar
  8. Brest J, Greiner S, Boskovic B, Mernik M, Zumer V (2006) Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans Evol Comput 10(6):646–657CrossRefGoogle Scholar
  9. Chellapilla K (1998) Combining mutation operators in evolutionary programming. IEEE Trans Evol Comput 2(3):91–96CrossRefGoogle Scholar
  10. Chen G, Low CP, Yang Z (2009) Preserving and exploiting genetic diversity in evolutionary programming algorithms. IEEE Trans Evol Comput 13(3):661–673CrossRefGoogle Scholar
  11. Chung CY, Liang CH, Wong KP, Duan XZ (2010) Hybrid algorithm of differential evolution and evolutionary programming for optimal reactive power flow. IET Gener Transm Distrib 4(1):84–93CrossRefGoogle Scholar
  12. Dong H, He J, Huang H, Hou W (2007) Evolutionary programming using a mixed mutation strategy. Inf Sci 177(1):312–327MathSciNetCrossRefzbMATHGoogle Scholar
  13. Dong H, Dong Y, Zhou C, Yin G, Hou W (2009) A fuzzy clustering algorithm based on evolutionary programming. Expert Syst Appl 36(9):11792–11800CrossRefGoogle Scholar
  14. Duo H, Sasaki H, Nagata T, Fujita H (1999) A solution for unit commitment using lagrangian relaxation combined with evolutionary programming. Electr Power Syst Res 51(1):71–77CrossRefGoogle Scholar
  15. El-Sharkh MY, El-Keib AA, Chen H (2003) A fuzzy evolutionary programming-based solution methodology for security-constrained generation maintenance scheduling. Electr Power Syst Res 67(1):67–72CrossRefGoogle Scholar
  16. Fogel DB (1991) System identification through simulated evolution: a machine learning approach to modeling. Ginn Press, BratislavaGoogle Scholar
  17. Fogel DB (1993) Applying evolutionary programming to selected traveling salesman problems. Cybern Syst 24(1):27–36MathSciNetCrossRefGoogle Scholar
  18. Fogel D (2009) Artificial intelligence through simulated evolution. Wiley-IEEE Press, LondonCrossRefzbMATHGoogle Scholar
  19. Fogel DB (1992) Evolving artificial intelligence. PhD dissertation, La Jolla, CA, USA. UMI order no. GAX93-03240Google Scholar
  20. Gämperle R, Müller SD, Koumoutsakos P (2002) A parameter study for differential evolution. Adv Intell Syst Fuzzy Syst Evol Comput 10:293–298Google Scholar
  21. Hansen N (2006) The CMA evolution strategy: a comparing review. In: Lozano J, Larranaga P, Inza I, Bengoetxea E (eds) Towards a new evolutionary computation. Advances on Estimation of Distribution Algorithms. Springer, Berlin, pp 75–102Google Scholar
  22. Hansen N, Müller SD, Koumoutsakos P (2003) Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evol Comput 11(1):1–18CrossRefGoogle Scholar
  23. Hedar A-R, Fukushima M (2006) Directed evolutionary programming: towards an improved performance of evolutionary programming. In: IEEE Congress on Evolutionary Computation, 2006. CEC 2006. IEEE, pp 1521–1528Google Scholar
  24. Hershkovitz S, Baltianski S, Tsur Y (2011) Harnessing evolutionary programming for impedance spectroscopy analysis: a case study of mixed ionic-electronic conductors. Solid State Ion 188(1):104–109CrossRefGoogle Scholar
  25. Hong L, Drake JH, Özcan E (2014) A step size based self-adaptive mutation operator for evolutionary programming. In: Proceedings of the 2014 conference companion on genetic and evolutionary computation companion. ACM, pp 1381–1388Google Scholar
  26. Jung SH (2003) Queen-bee evolution for genetic algorithms. Electron Lett 39(6):575–576CrossRefGoogle Scholar
  27. Khatib W, Fleming PJ (1998) The Stud GA: a mini revolution? In: Parallel problem solving from nature-PPSN V. Springer, pp 683–691Google Scholar
  28. Lee CY, Yao X (2004) Evolutionary programming using mutations based on the Lévy probability distribution. IEEE Trans Evol Comput 8(1):1–13CrossRefGoogle Scholar
  29. Liang K-H, Yao X, Newton CS (2001) Adapting self-adaptive parameters in evolutionary algorithms. Appl Intell 15(3):171–180CrossRefzbMATHGoogle Scholar
  30. Liang JJ, Kai Qin A, Suganthan PN, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10(3):281–295CrossRefGoogle Scholar
  31. Liang JJ, Qu BY, Suganthan PN, Hernández-Dıaz AG (2013) Problem definitions and evaluation criteria for the CEC 2013 special session on real-parameter optimization. Zhengzhou University, Zhengzhou, China and Nanyang Technological University, Singapore, Technical report, Computational Intelligence Laboratory 201212Google Scholar
  32. Mallipeddi R, Mallipeddi S, Suganthan PN (2010) Ensemble strategies with adaptive evolutionary programming. Inf Sci 180(9):1571–1581CrossRefzbMATHGoogle Scholar
  33. Nguyen QH, Ong Y-S, Lim MH (2009) A probabilistic memetic framework. IEEE Trans Evol Comput 13(3):604–623CrossRefGoogle Scholar
  34. Rajan A, Christober C (2011) Hydro-thermal unit commitment problem using simulated annealing embedded evolutionary programming approach. Int J Electr Power Energy Syst 33(4):939–946CrossRefGoogle Scholar
  35. Ratnaweera A, Halgamuge SK, Watson HC (2004) Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Trans Evol Comput 8(3):240–255CrossRefGoogle Scholar
  36. Rozenberg G, Thomas B, Kok JN (2011) Handbook of natural computing. Springer, BerlinGoogle Scholar
  37. Schwefel H-PP (1993) Evolution and optimum seeking: the sixth generation. Wiley, LondonGoogle Scholar
  38. Sinha N, Chakrabarti R, Chattopadhyay PK (2003) Evolutionary programming techniques for economic load dispatch. IEEE Trans Evol Comput 7(1):83–94CrossRefGoogle Scholar
  39. Tan Q, He Q, Zhao W, Shi Z, Lee ES (2011) An improved fcmbp fuzzy clustering method based on evolutionary programming. Compu Math Appl 61(4):1129–1144MathSciNetCrossRefzbMATHGoogle Scholar
  40. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82CrossRefGoogle Scholar
  41. Yao X, Liu Y (1998) Scaling up evolutionary programming algorithms. Evolutionary programming VII. Proc. of the seventh annual conference on evolutionary programming (EP98), Lecture Notes in Computer Science. Springer, Berlin, pp 103–112Google Scholar
  42. Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3(2):82–102CrossRefGoogle Scholar
  43. Zhang H, Lu J (2008) Adaptive evolutionary programming based on reinforcement learning. Inf Sci 178(4):971–984MathSciNetCrossRefzbMATHGoogle Scholar
  44. Zhao X, Gao X-S, Ze-Chun H (2007) Evolutionary programming based on non-uniform mutation. Appl Math Comput 192(1):1–11MathSciNetCrossRefzbMATHGoogle Scholar
  45. Zhao S-Z, Suganthan PN, Das S (2011) Self-adaptive differential evolution with multi-trajectory search for large-scale optimization. Soft Comput 15(11):2175–2185CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Han Huang
    • 1
    Email author
  • Shujin Ye
    • 1
  • Zhun Fan
    • 1
  • Zhiyong Lin
    • 1
  • Liang Lv
    • 1
  • Zhifeng Hao
    • 1
  1. 1.School of Software EngineeringSouth China University of TechnologyGuangzhouChina

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