INFORMATION CHANGE THE WORLD

International Journal of Intelligent Systems and Applications(IJISA)

ISSN: 2074-904X (Print), ISSN: 2074-9058 (Online)

Published By: MECS Press

IJISA Vol.11, No.4, Apr. 2019

An Enhanced Differential Evolution Algorithm with Multi-mutation Strategies and Self-adapting Control Parameters

Full Text (PDF, 922KB), PP.26-38


Views:200   Downloads:30

Author(s)

M. A. Attia, M. Arafa, E. A. Sallam, M. M. Fahmy

Index Terms

Differential evolution;Global optimization;Multi-mutation strategies;Self-adapting control parameters;Evolutionary algorithms

Abstract

Differential evolution (DE) is a stochastic population-based optimization algorithm first introduced in 1995. It is an efficient search method that is widely used for solving global optimization problems. It has three control parameters: the scaling factor (F), the crossover rate (CR), and the population size (NP). As any evolutionary algorithm (EA), the performance of DE depends on its exploration and exploitation abilities for the search space. Tuning the control parameters and choosing a suitable mutation strategy play an important role in balancing the rate of exploration and exploitation. Many variants of the DE algorithm have been introduced to enhance its exploration and exploitation abilities. All of these DE variants try to achieve a good balance between exploration and exploitation rates. In this paper, an enhanced DE algorithm with multi-mutation strategies and self-adapting control parameters is proposed. We use three forms of mutation strategies with their associated self-adapting control parameters. Only one mutation strategy is selected to generate the trial vector. Switching between these mutation forms during the evolution process provides dynamic rates of  exploration and exploitation. Having different rates of exploration and exploitation through the optimization process enhances the performance of DE in terms of accuracy and convergence rate. The proposed algorithm is evaluated over 38 benchmark functions: 13 traditional functions, 10 special functions chosen from CEC2005, and 15 special functions chosen from CEC2013. Comparison is made in terms of the mean and standard deviation of the error with the standard "DE/rand/1/bin" and five state-of-the-art DE algorithms. Furthermore, two nonparametric statistical tests are applied in the comparison: Wilcoxon signed-rank and Friedman tests. The results show that the performance of the proposed algorithm is better than other DE algorithms for the majority of the tested functions.

Cite This Paper

M. A. Attia, M. Arafa, E. A. Sallam, M. M. Fahmy, "An Enhanced Differential Evolution Algorithm with Multi-mutation Strategies and Self-adapting Control Parameters", International Journal of Intelligent Systems and Applications(IJISA), Vol.11, No.4, pp.26-38, 2019. DOI: 10.5815/ijisa.2019.04.03

Reference

[1]R. Storn, and K. V. Price, "Differential evolution - a simple and efficient adaptive scheme for global optimization over continuous spaces," ICSI, TR-95-012, 1995.

[2]S. Das, S. S. Mullicka, and P.N. Suganthan, "Recent advances in differential evolution an updated survey," Swarm and Evolutionary Computation, vol. 27, pp. 1-30, 2016.

[3]A. K. Qin, and P. N. Suganthan, "Self adaptive differential evolution algorithm for numerical optimization," The 2005 IEEE Congress on Evolutionary Computation, vol. 2, pp. 1785-1791, 2005.

[4]R. Mallipeddia, P. N. Suganthana, Q. K. Panb, and M. F. Tasgetiren, "Differential evolution algorithm with ensemble of parameters and mutation strategies," Applied Soft Computing, vol. 11, no. 2, pp. 1679–1696, 2011. 

[5]Amara Prakasa Rao, N. V. Sarma, "Performance analysis of differential evolution algorithm based beamforming for smart antenna systems," International Journal of Wireless and Microwave Technologies (IJWMT), vol. 4, no. 1, pp. 1-9, 2014.

[6]Sahil Saharan, J. S. Lather, R. Radhakrishnan, "Optimization of different queries using optimization algorithm (DE)," International Journal of Computer Network and Information Security(IJCNIS), vol. 10, no. 3, pp. 52-59, 2018.

[7]O. Tolga Altinoz, A. Egemen Yilmaz, "Optimal PID design for control of active car suspension system," International Journal of Information Technology and Computer Science(IJITCS), vol. 10, no. 1, pp. 16-23, 2018.

[8]Meera Ramadas, Ajith Abraham, and Sushil Kumar, "Fsde-forced strategy differential evolution used for data clustering," Journal of King Saud University –Computer and Information Sciences, vol. 31,  pp. 52–61, 2019. 

[9]M. Crepinsek, S. Liu, and M. Mernik, "Exploration and exploitation in evolutionary algorithms: a survey," ACM Computing Surveys, vol. 45, no. 3, pp. 1 - 35, 2013.

[10]J. Zhang, and A. C. Sanderson, “JADE: Adaptive Differential Evolution with Optional External Archive," IEEE Transactions on Evolution Computation, vol. 13, no. 5, pp. 945 - 958, 2009.

[11]W. Yi, L. Gao, X Li, and Y. Zhou, "A New differential evolution algorithm with a hybrid mutation operator and self-adapting control parameters for global optimization problems," Applied Intelligence, vol. 42, no. 4, pp. 642–660, 2015.

[12]Mengnan Tian, Xingbao Gao, Cai Dai, "Differential evolution with improved individual-based parameter setting and selection strategy, "Applied Soft Computing Journal, vol. 56, pp. 286-297,  2017.

[13]Y. Zhou, W. Yi, L. Gao, and X. Li, "Adaptive differential evolution with sorting crossover rate for continuous optimization problems," IEEE Transactions on Cybernetics, vol. 47, no. 9, pp. 2742 - 2753, 2017.

[14]J. Liang, W.  Xu, C. Yue, K. Yu, H. Song, O. Crisalle, and B. Qu, "Multimodal multiobjective optimization with differential evolution," Swarm and Evolutionary Computation, vol. 44, pp. 1028-1059, 2019.

[15]D. J. Poole, and C. B. Allen, "Constrained niching using differential evolution," Swarm and Evolutionary Computation, vol. 44, pp. 74–100, 2019.

[16]R. Tanabe, and A. Fukunaga, "Evaluating the performance of shade on cec 2013 benchmark problems," in 2013 IEEE Congress on Evolutionary Computation, pp. 1952 – 1959, 2013.

[17]J. Tvrdík, and R. Polakova, "Competitive differential evolution applied to cec 2013 problems," in Proceedings of The IEEE Congress on Evolutionary Computation, México, pp. 1651–1657, 2013.

[18]L. d. Coelho, H. V. Ayala, and R. Z. Freire, "Population’s variance based adaptive differential evolution for real parameter optimization," in Proceedings of the IEEE Congress on Evolutionary Computation, México, pp. 20-23, 2013.

[19]S. M. Islam, S. Das, S. Ghosh, S. Roy, and P. N. Suganthan, "An Adaptive differential evolution algorithm with novel mutation and crossover strategies for global numerical optimization," IEEE Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics, vol. 42, no. 2, pp. 482 - 500,2012.

[20]M. Yang, C. Li, Z. Cai, and J. Guan, "Differential evolution with auto-enhanced population diversity," IEEE Transactions on Cybernetics, vol. 45, no. 2, pp. 302 - 315, 2015.

[21]X. Zhou, and G. Zhang, "Abstract convex underestimation assisted multistage differential evolution," IEEE Transactions on Cybernetics, vol. 47, no. 9, pp. 2730 - 2741, 2017.

[22]A. W. Mohamed, and P. N. Suganthan, "Real-parameter unconstrained optimization based on enhanced fitness-adaptive differential evolution algorithm with novel mutation," Soft Computing, vol. 22, no. 10, pp.  3215 - 3235, 2018.

[23]K .V.Price, "An Introduction to differential evolution," in New Ideas in Optimization, D. Corne, M. Dorigo, and F. Glover, Eds., London, U.K.: McGraw-Hill Publishing Company, 1999, ISBN: 0-07-709506-5, pp. 79-108.

[24]Meera Ramadas, and Ajith Abraham, "Metaheuristics for data clustering and image segmentation," Intelligent Systems Reference Library, springer, Switzerland, ISBN: 9783030040963, vol. 152, 2019.

[25]S. Das, and P. N. Suganthan, "Differential evolution: a survey of the state-of-the-art," IEEE Transactions on Evolutionary Computation, vol. 15, no. 1, pp. 4-31, 2011.

[26]K. Opara, and J. Arabas, "Comparison of mutation strategies in differential evolution – a probabilistic perspective," Swarm and Evolutionary Computation, vol. 39, pp. 53-69, 2018.

[27]G. Wu, X. Shen, H. Li, H. Chen, A. Lin, and P. N. Suganthan, "Ensemble of differential evolution variants",  Information Sciences, vol. 423, pp. 172–186, 2018.

[28]R. storn, "Differential evolution (de) for continuous function optimization (an algorithm by kenneth price and rainer storn)," 2014. [Online]. http://www.icsi.berkeley.edu/~storn/code.html (Last Accessed in Dec. 2018).

[29]Yun-Wei Shang, and Yu-Huang Qiu, "A Note on the extended rosenbrock function," Evolutionary Computation, vol. 14, no. 1, pp. 119-126, 2006.

[30]P. N. Suganthan, N. Hansen, J. J. Liang, K. Deb, Y. P. Chen, A. Auger, and S. Tiwari, "Problem definitions and evaluation criteria for cec 2005 special session on rreal-parameter optimization," Nanyang Technological University, Zhengzhou, China/Singapore, Technical Report, 2005. 

[31]P. N. Suganthan. [Online]. http://www3.ntu.edu.sg/home/epnsugan/index_files/CEC-benchmarking.htm.

[32]J. J. Liang, B. Y. Qin, P. N. Suganthan, and A. G. Diaz, "Problem definitions and evaluation criteria for the cec 2013 special session on real-parameter optimization," Nanyang Technological University, Zhengzhou, China/Singapore, Technical Report, 2013.

[33]J. Derrac, S. Garc´ıa, D. Molina, and F. Herrera, "A Practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms," Swarm and Evolutionary Computation, vol. 1, no. 1, pp. 3–18, 2011.

[34]M. Arafa, Elsayed A. Sallam, and M. M. Fahmy, "An Enhanced differential evolution optimization algorithm," in Fourth International Conference on Digital Information and Communication Technology and it's Applications (DICTAP2014), Bangkok, Thailand, pp. 216-225, 2014.