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Differential evolution algorithm with multiple mutation strategies based on roulette wheel selection

  • Wuwen Qian
  • Junrui Chai
  • Zengguang Xu
  • Ziying Zhang
Article

Abstract

In this paper, we propose a differential evolution (DE) algorithm variant with a combination of multiple mutation strategies based on roulette wheel selection, which we call MMRDE. We first propose a new, reflection-based mutation operation inspired by the reflection operations in the Nelder–Mead method. We design an experiment to compare its performance with seven mutation strategies, and we prove its effectiveness at balancing exploration and exploitation of DE. Although our reflection-based mutation strategy can balance exploration and exploitation of DE, it is still prone to premature convergence or evolutionary stagnation when solving complex multimodal optimization problems. Therefore, we add two basic strategies to help maintain population diversity and increase the robustness. We use roulette wheel selection to arrange mutation strategies based on their success rates for each individual. MMRDE is tested with some improved DE variants based on 28 benchmark functions for real-parameter optimization that have been recommended by the Institute of Electrical and Electronics Engineers CEC2013 special session. Experimental results indicate that the proposed algorithm shows its effectiveness at cooperative work with multiple strategies. It can obtain a good balance between exploration and exploitation. The proposed algorithm can guide the search for a global optimal solution with quick convergence compared with other improved DE variants.

Keywords

Differential evolution Nelder–mead method New mutation operation Roulette wheel selection Multiple mutation strategies Global optimization 

Notes

Acknowledgments

We thank Miguel Leon (from the School of Innovation, Design and Engineering, Malardalen University) for his great help with this study. We greatly appreciate the reviewers for their thoughtful and encouraging comments on our manuscript, which we all think is helpful for improving the quality of our paper. This study was supported by program 2013KCT-15 of the Shanxi Provincial Key Innovative Research Team and the National Natural Science Foundation of China (51409206). We thank LetPub (www.letpub.com) for its linguistic assistance during the preparation of this manuscript.

References

  1. 1.
    Storn R, Price K (1997) Differential evolution – A simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Chang CF et al (2007) Robust searching hybrid differential evolution method for optimal reactive power planning in large-scale distribution systems. Electr Power Syst Res 77(5-6):430–437CrossRefGoogle Scholar
  3. 3.
    Dragoi EN et al (2013) Optimization methodology based on neural networks and self-adaptive differential evolution algorithm applied to an aerobic fermentation process. Appl Soft Comput 13(1):222–238CrossRefGoogle Scholar
  4. 4.
    Iorio AW, Li X (2004) Solving rotated multi-objective optimization problems using differential evolution. AI 2004: Advances in Artificial Intelligence 3339:861–872MathSciNetGoogle Scholar
  5. 5.
    Das S, Konar A, Chakraborty U K (2005) Two improved differential evolution schemes for faster global search. In: Genetic And Evolutionary Computation Conference, pp 991– 998Google Scholar
  6. 6.
    Chakraborty UK, Das S, Konar A (2006) Differential Evolution with Local Neighborhood. In: 2006 IEEE International Conference on Evolutionary Computation 2042–2049Google Scholar
  7. 7.
    Qin AK, Suganthan PN (2005) Self-adaptive differential evolution algorithm for numerical optimization. In: 2005 IEEE Congress on Evolutionary Computation 2:1785–1791Google Scholar
  8. 8.
    Brest J et al (2006) Self-adapting control parameters in differential evolution: A comparative study on numerical benchmark problems. IEEE Trans Evol Comput 10(5):646–657CrossRefGoogle Scholar
  9. 9.
    Zhang J, Sanderson A C (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958CrossRefGoogle Scholar
  10. 10.
    Mallipeddi R et al (2011) Differential evolution algorithm with ensemble of parameters and mutation strategies. Appl Soft Comput 11(2):1679–1696CrossRefGoogle Scholar
  11. 11.
    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
  12. 12.
    Tanabe R, Fukunaga A (2013) Success-history based parameter adaptation for differential evolution. In: 2013 IEEE Congress on Evolutionary Computation 71–78Google Scholar
  13. 13.
    Yi W et al (2015) A new differential evolution algorithm with a hybrid mutation operator and self-adapting control parameters for global optimization problems. Appl Intell 42(4):642–660CrossRefGoogle Scholar
  14. 14.
    Leon M, Xiong N (2016) Adapting differential evolution algorithms for continuous optimization via greedy adjustment of control parameters. J Artificial Intell Soft Comput Res 6(2):103–118CrossRefGoogle Scholar
  15. 15.
    Wu G et al (2016) Differential evolution with multi-population based ensemble of mutation strategies. Inf Sci 329(C):329– 345CrossRefGoogle Scholar
  16. 16.
    Leon M, Xiong N (2017) Alopex-based mutation strategy in differential evolution. In: 2017 IEEE Congress on Evolutionary Computation 1978–1984Google Scholar
  17. 17.
    Ronkkonen J, Kukkonen S, Price KV (2005) Real-parameter optimization with differential evolution. In: 2005 IEEE Congress on Evolutionary Computation, vol 1, pp 506–513Google Scholar
  18. 18.
    Price K, Storn RM, Lampinen JA (2005) Differential evolution: a practical approach to global optimization (natural computing series). Springer-Verlag, New York, pp 1–24MATHGoogle Scholar
  19. 19.
    Jia D, Zheng G, Khurram Khan M (2011) An effective memetic differential evolution algorithm based on chaotic local search. Inf Sci 181(15):3175–3187CrossRefGoogle Scholar
  20. 20.
    Ali MZ et al (2017) An Adaptive Multipopulation Differential Evolution with Dynamic Population Reduction. IEEE Trans Cybern 47(7):2768–2779CrossRefGoogle Scholar
  21. 21.
    Lampinen J (2002) A Fuzzy Adaptive Differential Evolution Algorithm. Soft Comput 9(5):448–462MATHGoogle Scholar
  22. 22.
    Ghosh A et al (2011) An improved differential evolution algorithm with fitness-based adaptation of the control parameters. Inf Sci 181(18):3749–3765MathSciNetCrossRefGoogle Scholar
  23. 23.
    Mezura-Montes E, Velazquez-Reyes J, Coello Coello CA (2006) A comparative study of differential evolution variants for global optimization. In: 8th Annual Genetic and Evolutionary Computation Conference 485–492Google Scholar
  24. 24.
    Dorronsoro B, Bouvry P (2011) Improving classical and decentralized differential evolution with new mutation operator and population topologies. IEEE Trans Evol Comput 15(1):67–98CrossRefGoogle Scholar
  25. 25.
    Islam SM et al (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. 26.
    Mohamed AW (2015) An improved differential evolution algorithm with triangular mutation for global numerical optimization. Comput Ind Eng 85(C):359–375CrossRefGoogle Scholar
  27. 27.
    Wang S et al (2017) Self-adaptive differential evolution algorithm with improved mutation strategy. Soft Computing, pp 1–15. Springer Berlin Heidelberg.  https://doi.org/10.1007/s00500-017-2588-5. Online ISSN: 1433-7479
  28. 28.
    Piotrowski AP (2013) Adaptive memetic differential evolution with global and local neighborhood-based mutation operators. Inf Sci 241(10):164–194CrossRefGoogle Scholar
  29. 29.
    Gong W et al (2011) Adaptive strategy selection in differential evolution for numerical optimization: An empirical study. Inf Sci 181(24):5364–5386MathSciNetCrossRefGoogle Scholar
  30. 30.
    Tasoulis DK, Plagianakos VP, Vrahatis MN (2005) Clustering in Evolutionary Algorithms to efficiently compute simultaneously local and global minima. In: 2005 IEEE Congress on Evolutionary Computation, vol 2, pp 1847–1854Google Scholar
  31. 31.
    Epitropakis MG, Plagianakos VP, Vrahatis MN (2008) Balancing the exploration and exploitation capabilities of the differential evolution algorithm. In: 2008 IEEE Congress on Evolutionary Computation 2686–2693Google Scholar
  32. 32.
    Ali MZ, Awad NH, Suganthan PN (2015) Multi-population differential evolution with balanced ensemble of mutation strategies for large-scale global optimization. Appl Soft Comput 33(C):304–327CrossRefGoogle Scholar
  33. 33.
    Piotrowski AP, Napiorkowski JJ, Kiczko A (2012) Differential Evolution algorithm with Separated Groups for multi-dimensional optimization problems. Eur J Oper Res 216(1):33–46MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    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
  35. 35.
    Das S et al (2009) Differential evolution using a neighborhood-based mutation operator. IEEE Trans Evol Comput 13(3):526–553CrossRefGoogle Scholar
  36. 36.
    Pencheva T, Atanassov K, Shannon A (2009) Modelling of a roulette wheel selection operator in genetic algorithms using generalized nets. Int J Bio 13(4):101–105Google Scholar
  37. 37.
    Lipowski A, Lipowska D (2012) Roulette-wheel selection via stochastic acceptance. Physica A: Stat Mech Appl 391(5):2193–2196CrossRefGoogle Scholar
  38. 38.
    Ho-Huu V et al (2018) An improved differential evolution based on roulette wheel selection for shape and size optimization of truss structures with frequency constraints. Neural Comput Applic 29(1):167–185CrossRefGoogle Scholar
  39. 39.
    Peng F et al (2009) Multi-start JADE with knowledge Transfer for numerical optimization. In: 2009 IEEE Congress on Evolutionary Computation 1889–1895Google Scholar
  40. 40.
    Liang J et al (2013) Problem definitions and evaluation criteria for the CEC 2013 Special Session on Real-Parameter OptimizationGoogle Scholar
  41. 41.
    Alcala-Fdez J et al (2009) KEEL: A software tool to assess evolutionary algorithms for data mining problems. Soft Comput 13(3):307–318CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Wuwen Qian
    • 1
  • Junrui Chai
    • 1
  • Zengguang Xu
    • 1
  • Ziying Zhang
    • 1
  1. 1.State Key Laboratory of Eco-hydraulics in Northwest Arid Region of China (Xi’an University of Technology)Xi’anChina

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