Differential evolution with individual-dependent and dynamic parameter adjustment

Focus

Abstract

Differential evolution (DE) is a powerful and versatile evolutionary algorithm for global optimization over continuous search space, whose performance is significantly influenced by its mutation operator and control parameters (population size, scaling factor and crossover rate). In order to enhance the performance of DE, we adopt a new variant of classic mutation operator, a gradual decrease rule for population size, an individual-dependent and dynamic strategy to generate the required values of scaling factor and crossover rate during the evolutionary process, respectively. In the proposed variant of DE (denoted by IDDE), the adopted mutation operator merges the superiority of two classic mutation operators (DE/best/2 and DE/rand/2) together, and the adjustment mechanism of control parameters applies the fitness value information of each individual and dynamic fluctuation rule, which can provide a better balance between the exploration ability and exploitation ability. To verify the performance of proposed IDDE, a suite of thirty benchmark functions is applied to conduct the simulation experiment. The simulation results demonstrate that the proposed IDDE performs significantly better than five state-of-the-art DE variants and other two evolutionary algorithms.

Keywords

Differential evolution Individual-dependent strategy Dynamic parameter adjustment Evolutionary algorithms Global optimization 

Notes

Compliance with ethical standards

Conflict of interest

All authors have no conflict of interest.

Human participants or animals

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Biswas S, Kundu S, Das S (2015) Inducing niching behavior in differential evolution through local information sharing. IEEE Trans Evol Comput 19(2):246–263CrossRefGoogle Scholar
  2. Bose D, Biswas S, Vasilakos AW, Laha S (2014) Optimal filter design using an improved artificial bee colony algorithm. Inf Sci 281:443–461MathSciNetCrossRefGoogle Scholar
  3. Brest J, Greiner S, Bošković B, Mernik M, Žumer 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
  4. Brown C, Jin Y, Leach M, Hodgson M (2016) \(\mu \)JADE: adaptive differential evolution with a small population. Soft Comput 20:4111–4120CrossRefGoogle Scholar
  5. Cai Y, Wang J (2013) Differential evolution with neighborhood and direction information for numerical optimization. IEEE Trans Cybern 43(6):2202–2215CrossRefGoogle Scholar
  6. Cai Y, Wang J (2015) Differential evolution with hybrid linkage crossover. Inf Sci 320:244–287MathSciNetCrossRefGoogle Scholar
  7. Cai Y, Wang J, Chen Y, Wang T, Tian H, Luo W (2016) Differential evolution with neighborhood and direction information for numerical optimization. Soft Comput 20:465–494CrossRefGoogle Scholar
  8. Chen Y, Gao J, Yang G, Liu Y (2017) Solving equilibrium standby redundancy optimization problem by hybrid PSO algorithm. Comput Soft. doi: 10.1007/s00500-017-2552-4 Google Scholar
  9. Cuevas E, Zaldívar D, Pérez-Cisneros M, Oliva D (2013) Block-matching algorithm based on differential evolution for motion estimation. Eng Appl Artif Intell 26:488–498CrossRefGoogle Scholar
  10. Črepinšek M, Liu SH, Mernik M (2013) Exploration and exploitation in evolutionary algorithms: a survey. ACM Comput Surv 45(3):1–33MATHGoogle Scholar
  11. Das S, Suganthan PN (2011a) Differential evolution: a survey of the state-of-the-art. IEEE Trans Evol Comput 15(1):4–31CrossRefGoogle Scholar
  12. Das S, Suganthan PN (2011b) Problem definitions and evaluation criteria for CEC 2011 competition on testing evolutionary algorithms on real world optimization problems. Jadavpur University, Kolkata, India, and Nanyang Technological University, Singapore 2010Google Scholar
  13. Das S, Konar A, Chakraborty UK, Abraham A (2009) Differential evolution using a neighborhood based mutation operator. IEEE Trans Evol Comput 13(3):526–553CrossRefGoogle Scholar
  14. Das S, Mullick SS, Suganthan PN (2016) Recent advances in differential evolution—an updated survey. Swarm Evol Comput 27:1–30CrossRefGoogle Scholar
  15. Dorigo M, Blum C (2005) Ant colony optimization theory: a survey. Theor Comput Sci 344:243–278MathSciNetCrossRefMATHGoogle Scholar
  16. Draa A, Bouzoubia S, Boukhalfa I (2015) A sinusoidal differential evolution algorithm for numerical optimisation. Appl Soft Comput 27:99–126CrossRefGoogle Scholar
  17. Fan Q, Yan X (2016) Self-adaptive differential evolution algorithm with zoning evolution of control parameters and adaptive mutation strategies. IEEE Trans Cybern 46(1):219–232MathSciNetCrossRefGoogle Scholar
  18. García-Martínez C, Lozano M, Herrera F, Molina D, Sánchez A (2008) Global and local real-coded genetic algorithms based on parent-centric crossover operators. Eur J Oper Res 185(3):1088–1113CrossRefMATHGoogle Scholar
  19. Ghosh A, Das S, Chowdhury A, Giri R (2011) An improved differential evolution algorithm with fitness-based adaptation of the control parameters. Inf Sci 181(18):3749–3765MathSciNetCrossRefGoogle Scholar
  20. Goldberg D (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, New YorkMATHGoogle Scholar
  21. Gong WY, Cai ZH, Ling CX, Li H (2011a) Enhanced differential evolution with adaptive strategies for numerical optimization. IEEE Trans Syst Man Cybern B Cybern 41(2):397–413CrossRefGoogle Scholar
  22. Han MF, Liao SH, Chang JY, Lin CT (2013) Dynamic group-based differential evolution using a self-adaptive strategy for global optimization problems. Appl Intell 39(1):41–56CrossRefGoogle Scholar
  23. Herrera F, Lozano M (2000) Gradual distributed real-coded genetic algorithms. IEEE Trans Evol Comput 4(1):43–63CrossRefGoogle Scholar
  24. Idris I, Selamat A, Omatu S (2014) Hybrid email spam detection model with negative selection algorithm and differential evolution. Eng Appl Artif Intell 28:97–110CrossRefGoogle Scholar
  25. Islam SM, Das S, Ghosh S, Roy S, Suganthan PN (2012) An adaptive differential evolution algorithm with novel mutation and crossover strategies for global numerical optimization. IEEE Trans Syst Man Cybern B Cybern 42(2):482–500CrossRefGoogle Scholar
  26. Karafotias G, Hoogendoorn M, Eiben AE (2015) Parameter control in evolutionary algorithms: trends and challenges. IEEE Trans Evol Comput 19(2):167–187CrossRefGoogle Scholar
  27. Kennedy J, Eberhart R, Shi Y (2001) Swarm intelligence. Morgan Kaufman, San FranciscoGoogle Scholar
  28. Li XD, Yao X (2012) Cooperatively coevolving particle swarms for large scale optimization. IEEE Trans Evol Comput 16(2):210–224MathSciNetCrossRefGoogle Scholar
  29. Liang JJ, Qu BY, Suganthan PN (2013) Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization. Zhengzhou University, China, and Nanyang Technological University, SingaporeGoogle Scholar
  30. Lin L, Gen M (2009) Auto-tuning strategy for evolutionary algorithms: balancing between exploration and exploitation. Soft Comput 13(2):157–168CrossRefMATHGoogle Scholar
  31. Liu J, Lampinen J (2005) A fuzzy adaptive differential evolution algorithm. Soft Comput 9(6):448–462CrossRefMATHGoogle Scholar
  32. Mallipeddi R, Suganthan PN, Pan QK, Tasgetiren MF (2011) Differential evolution algorithm with ensemble of parameters and mutation strategies. Appl Soft Comput 11(2):1679–1696CrossRefGoogle Scholar
  33. Neri F, Tirronen V (2010) Recent advances in differential evolution: a survey and experimental analysis. Artif Intell Rev 33(1–2):61–106CrossRefGoogle Scholar
  34. Piotrowski AP (2017) Review of differential evolution population size. Swarm Evol Comput 32:1–24CrossRefGoogle Scholar
  35. 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
  36. Rao R, Savsani V, Vakharia D (2012) Teaching-learning-based optimization: an optimization method for continuous non-linear large scale problems. Inf Sci 183(1):1–15MathSciNetCrossRefGoogle Scholar
  37. Sarker R, Elsayed SM, Ray T (2014) Differential evolution with dynamic parameters selection for optimization problems. IEEE Trans Evol Comput 18(5):689–707CrossRefGoogle Scholar
  38. Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713CrossRefGoogle Scholar
  39. Storn R, Price K (1997) Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341–359MathSciNetCrossRefMATHGoogle Scholar
  40. Sun G, Liu Y, Lan Y (2011) Fuzzy two-stage material procurement planning problem. J Intell Manuf 22:319–331CrossRefGoogle Scholar
  41. Sun G, Zhao R, Lan Y (2016) Joint operations algorithm for large-scale global optimization. Appl Soft Comput 38:1025–1039CrossRefGoogle Scholar
  42. Tang LX, Dong Y, Liu J (2015) Differential evolution with an individual-dependent mechanism. IEEE Trans Evol Comput 19(4):560–574CrossRefGoogle Scholar
  43. Tang LX, Zhao Y, Liu JY (2014) An improved differential evolution algorithm for practical dynamic scheduling in steelmaking-continuous casting production. IEEE Trans Evol Comput 18(2):209–225CrossRefGoogle Scholar
  44. Tayarani-N M, Yao X, Xu H (2015) Meta-heuristic algorithms in car engine design: a literature survey. IEEE Trans Evol Comput 19(5):609–629CrossRefGoogle Scholar
  45. Wang S, Watada J (2012) A hybrid modified PSO approach to VaR-based facility location problems with variable capacity in fuzzy random uncertainty. Inf Sci 192(1):3–18CrossRefMATHGoogle Scholar
  46. Wang Y, Cai Z, Zhang Q (2011) Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans Evol Comput 15(1):55–66CrossRefGoogle Scholar
  47. Wang H, Rahnamayan S, Sun H, Omran MGH (2013) Gaussian bare-bones differential evolution. IEEE Trans Cybern 43(2):634–647CrossRefGoogle Scholar
  48. Wang J, Liao J, Zhou Y, Cai Y (2014) Differential evolution enhanced with multiobjective sorting based mutation operators. IEEE Trans Cybern 44(12):2792–2805CrossRefGoogle Scholar
  49. Yang M, Li C, Cai Z, Guan J (2015a) Differential evolution with auto-enhanced population diversity. IEEE Trans Cybern 45(2):302–315CrossRefGoogle Scholar
  50. Yang G, Liu Y, Yang K (2015b) Multi-objective biogeography-based optimization for supply chain network design under uncertainty. Comput Ind Eng 85:145–156CrossRefGoogle Scholar
  51. Yu W, Shen M, Chen W, Zhan Z, Gong Y, Lin Y, Liu O, Zhang J (2014) Differential evolution with two-level parameter adaptation. IEEE Trans Cybern 44(7):1080–1099CrossRefGoogle Scholar
  52. Zhai H, Liu Y, Yang K (2016) Modeling two-stage UHL problem with uncertain demands. Appl Math Model 40(4):3029–3048MathSciNetCrossRefGoogle Scholar
  53. Zhang J, Sanderson AC (2009) JADE: Adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958CrossRefGoogle Scholar
  54. Zhang J, Avasarala V, Subbu R (2010) Evolutionary optimization of transition probability matrices for credit decision-making. Eur J Oper Res 200(2):557–567CrossRefMATHGoogle Scholar
  55. Zhao J, Xu Y, Luo F, Dong Z, Peng Y (2014) Power system fault diagnosis based on history driven differential evolution and stochastic time domain simulation. Inf Sci 275:13–29MathSciNetCrossRefGoogle Scholar
  56. Zhu W, Tang Y, Fang J, Zhang W (2013) Adaptive population tuning scheme for differential evolution. Inf Sci 223:164–191CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.College of Economic and ManagementZhejiang Normal UniversityJinhuaChina
  2. 2.Institute of Uncertain SystemsHuanggang Normal UniversityHuanggangChina
  3. 3.Institute of Systems EngineeringTianjin UniversityTianjinChina

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