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Cellular direction information based differential evolution for numerical optimization: an empirical study

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Abstract

Differential evolution (DE) is a well-known evolutionary algorithm which has been successfully applied in many scientific and engineering fields. In most DE algorithms, the base and difference vectors for mutation are randomly selected from the current population. That is, the useful population information cannot be fully exploited to guide the search of DE through mutation. Furthermore, the selection of parents in mutation has been verified to be critical for the DE performance. Therefore, to alleviate this drawback and improve the performance of DE, a novel DE algorithm with a directional mutation based on cellular topology is proposed in this study. This proposed algorithm is named as Cellular Direction Information based DE (DE-CDI). In DE-CDI, the cellular topology is employed first to define a neighborhood for each individual of population and then the direction information based on the neighborhood is incorporated into the mutation operator. In this way, DE-CDI not only utilizes the neighborhood information to exploit the regions of better individuals and accelerate convergence, but also introduces the direction information to guide the search to the promising area. To evaluate the performance of the proposed method, DE-CDI is applied to the original DE algorithms, as well as several advanced DE variants. Experimental results demonstrate the high performance of DE-CDI for most DE algorithms studied.

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References

  • Alcalá-Fdez J, Sánchez L, García S (2015) KEEL: a software tool to assess evolutionary algorithms for data mining problems (online). http://www.keel.es/

  • Bi XJ, Xiao J (2011) Classification-based self-adaptive differential evolution with fast and reliable convergence performance. Soft Comput 15(8):1581–1599

    Article  Google Scholar 

  • 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):646–657

    Article  Google Scholar 

  • Cai Y, Wang J (2013) Differential evolution with neighborhood and direction information for numerical optimization. IEEE Trans Cybern 43(6):2202–2215

    Article  Google Scholar 

  • Cai Y, Wang J, Yin J (2012) Learning-enhanced differential evolution for numerical optimization. Soft Comput 16(2):303–330

    Article  Google Scholar 

  • Cai Y, Wang J, Chen Y et al (2015) Adaptive direction information in differential evolution for numerical optimization. Soft Comput (in press)

  • Das S, Konar A (2006) Design of two dimensional IIR filters with modern search heuristics: a comparative study. Int J Comput Intell Appl 6(3):329–355

    Article  MATH  Google Scholar 

  • Das S, Suganthan PN (2010) Problem definitions and evaluation criteria for CEC 2011 competition on testing evolutionary algorithms on real world optimization problems. In: Technical report, Jadavpur University, West Bengal. Nanyang Technological University, Singapore

  • Das S, Suganthan PN (2011) Differential evolution: a survey of the state-of-the-art. IEEE Trans Evol Comput 15(1):4–31

    Article  Google Scholar 

  • Das S, Abraham A, Konar A (2008) Adaptive clustering using improved differential evolution algorithm. IEEE Trans Syst Man Cybern A 38(1):218–237

    Article  Google Scholar 

  • Das S, Abraham A, Chakraborty UK, Konar A (2009) Differential evolution using a neighborhood-based mutation operator. IEEE Trans Evolut Comput 13(3):526–553

    Article  Google Scholar 

  • De Falco I, Della Cioppa A, Maisto D, Scafuri U, Taranino E (2014) Impact of the topology on the performance of distributed differential evolution. Appl Evol Comput 8602:75–85

    Google Scholar 

  • Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18

    Article  Google Scholar 

  • Dorronsoro B, Bouvry P (2010) Differential evolution algorithms with cellular populations. In: Proceedings of the 11th PPSN, pp 320–330

  • Dorronsoro B, Bouvry P (2011) Improving classical and decentralized differential evolution with new mutation operator and population topologies. IEEE Trans Evol Comput 15(1):67–98

    Article  Google Scholar 

  • Epitropakis MG, Tasoulis DK, Pavlidis NG, Plagianakos VP, Vrahatis MN (2011) Enhancing differential evolution utilizing proximity based mutation operators. IEEE Trans Evol Comput 15(1):99–119

    Article  Google Scholar 

  • Eshelman LJ, Mathias KE, Schaffer JD (1997) Convergence controlled variation. In: Belew R, Vose M (eds) Foundations of genetic algorithms 4. Morgan Kaufmann, SanMateo, pp 203–224

    Google Scholar 

  • Fan H, Lampinen J (2003) A trigonometric mutation operation to differential evolution. J Global Optim 27(1):105–129

    Article  MathSciNet  MATH  Google Scholar 

  • García S, Fernandez A, Luengo J, Herrera F (2009) A study of statistical techniques and performance measures for genetics-based machine learning: accuracy and interpretability. Soft Comput 13(10):959–977

    Article  Google Scholar 

  • Gou J, Guo W, Hou F, Wang C, Cai Y (2015) Adaptive differential evolution with directional strategy and cloud model. Appl Intell 42(2):369–388

    Article  Google Scholar 

  • Hu Z, Cai X, Fan Z (2014) An improved memetic algorithm using ring neighborhood topology for constrained optimization. Soft Comput 18:2023–2041

    Article  Google Scholar 

  • Hui S, Suganthan PN (2013) Ensemble crowding differential evolution with neighborhood mutation for multimodal optimization. In: Proceedings of the IEEE symposium on differential evolution (SDE), pp 135–142. IEEE, New York

  • Iorio A, Li X (2006) Incorporating directional information within a differential evolution algorithm for multi-objective optimization. In: Proceedings of the 8th annual conference on genetic evolutionary computational, pp 691–698

  • 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):482–500

    Article  Google Scholar 

  • Joshi R, Sanderson AC (1999) Minimal representation multi-sensor fusion using differential evolution. IEEE Trans Syst Man Cybern Part A 29(1):63–76

    Article  Google Scholar 

  • Lampinen J (1999) A bibliography of differential evolution algorithm. In: Technical report, Laboratory of Information Processing, Department of Information Technology, Lappeenranta University of Technology. http://www.lut.fi/jlampine/debiblio.htm (online)

  • Liang JJ, Qu B-Y, Mao X, Niu B, Wang D (2014) Differential evolution based on fitness Euclidean-distance ratio for multimodal optimization. Neurocomputing 137(5):252–260

    Article  Google Scholar 

  • Liu J, Fan Z, Goodman E (2009) SRDE: an improved differential evolution based on stochastic ranking. In: Proceedings of the 1st ACM/SIGEVO, pp 345–352

  • Neri F, Tirronen V (2010) Recent advances in differential evolution: a survey and experimental analysis. Artif Intell Rev 33(1/2):61–106

    Article  Google Scholar 

  • Neri F, Iacca G, Mininno E (2011) Disturbed exploitation compact differential evolution for limited memory optimization problems. Inf Sci 181(12):2469–2487

    Article  MathSciNet  Google Scholar 

  • Noman N, Iba H (2011) Cellular differential evolution algorithm. In: Proceedings of the AII advanced artificial intelligence, pp 293–302

  • Noroozi V, Hashemi A, Meybodi M (2011) CellularDE: a cellular based differential evolution for dynamic optimization problems. In: Proceedings of the adapting natural computational algorithms, pp 340–349

  • Omran M, Engelbrecht AP, Salman A (2005) Differential evolution methods for unsupervised image classification. In: Proceedings of the 7th congress on evolutionary computation (CEC-2005), vol 2, pp 966–973. IEEE Press, Piscataway

  • Omran M, Engelbrecht A, Salman A (2006) Using the ring neighborhood topology with self-adaptive differential evolution. In: Jiao L, Wang L, Gao X-B, Liu J, Wu F (eds) Advances in natural computation. Springer, Berlin, pp 976–979

    Chapter  Google Scholar 

  • Omran M, Engelbrecht A, Salman A (2009) Bare bones differential evolution. Eur J Oper Res 196(1):128–139

    Article  MathSciNet  MATH  Google Scholar 

  • Piotrowski AP (2013) Adaptive memetic differential evolution with global and local neighborhood-based mutation operators. Inf Sci 241(20):164–194

    Article  Google Scholar 

  • Qin A, Huang V, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417

    Article  Google Scholar 

  • Rahnamayan S, Tizhoosh HR, Salama MMA (2008) Opposition based differential evolution. IEEE Trans Evol Comput 12(1):64–79

    Article  Google Scholar 

  • Rogalsky T, Derksen RW, Kocabiyik S (1999) Differential evolution in aerodynamic optimization. In: Proceedings of the 46th annual conference on Canadian Aeronautics and Space Institute, pp 29–36

  • Sarkar S, Mukherjee R, Biswas S, Kundu R, Das S (2015) An adaptive clustering and re-clustering based crowding differential evolution for continuous multi-modal optimization. In: Proceedings of the 18th Asia Pacific symposium on intelligent and evolutionary systems, vol 1, pp 373–388. Springer, New York

  • Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341–359

    Article  MathSciNet  MATH  Google Scholar 

  • Storn R, Price KV, Lampinen J (2005) Differential evolution—a practical approach to global optimization. Springer, Berlin

    MATH  Google Scholar 

  • Suganthan PN, Hansen N, Liang JJ, Deb K, Chen Y-P, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. In: KanGAL Report No. 2005005, Nanyang Technological University, Singapore. IIT Kanpur, India

  • Sun J, Zhang Q, Tsang EPK (2005) DE/EDA: a new evolutionary algorithm for global optimization. Inf Sci 169(3):249–262

    Article  MathSciNet  Google Scholar 

  • Tang L, Dong Y, Liu J (2015) Differential evolution with an individual-dependent mechanism. IEEE Trans Evol Comput (in press)

  • Wang F-S, Jang H-J (2000) Parameter estimation of a bio-reaction model by hybrid differential evolution. In: Proceedings of the IEEE congress on evolutionary computation, vol 1, pp 410–417. IEEE Press, Piscataway

  • Wang YX, Xiang QL (2008) Exploring new learning strategies in differential evolution algorithm. In: Proceedings of the IEEE congress on evolutionary computational, pp 204–209

  • Wang J, Cai Y (2015) Multiobjective evolutionary algorithm for frequency assignment problem in satellite communications. Soft Comput 19(5):1229–1253

    Article  Google Scholar 

  • Wang Y, Cai Z, Zhang Q (2011) Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans Evol Comput 15(1):55–66

    Article  MathSciNet  Google Scholar 

  • Wang J, Liao J, Zhou Y, Cai Y (2014) Differential evolution enhanced with multiobjective sorting based mutation operators. IEEE Trans Cybern 46(12):2792–2805

    Article  Google Scholar 

  • Weber M, Tirronen V, Neri F (2010) Scale factor inheritance mechanism in distributed differential evolution. Soft Comput 14(11):1187–1207

    Article  Google Scholar 

  • Weber M, Neri F, Tirronen V (2011) A study on scale factor in distributed differential evolution. Inf Sci 181(12):2488–2511

    Article  Google Scholar 

  • Yang M, Li C, Cai Z, Guan J (2015) Differential evolution with auto-enhanced population diversity. IEEE Trans Cybern (in press)

  • Zhang J, Sanderson A (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958

    Article  Google Scholar 

  • Zhang X, Yuen SY (2015) A directional mutation operator for differential evolution algorithms. Appl Soft Comput 30:529–548

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China (61305085, 61202468), the Natural Science Foundation of Fujian Province of China (2014J05074, 2014J01240), the Support Program for Innovative Team and Leading Talents of Huaqiao University (2014KJTD13) and the Fundamental Research Funds for the Central Universities (12BS216).

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Authors and Affiliations

  1. College of Computer Science and Technology, Huaqiao University, Xiamen, 361021, China

    Jingliang Liao, Yiqiao Cai, Tian Wang, Hui Tian & Yonghong Chen

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  1. Jingliang Liao
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  2. Yiqiao Cai
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  3. Tian Wang
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  4. Hui Tian
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  5. Yonghong Chen
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Correspondence to Yiqiao Cai.

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Communicated by V. Loia.

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Liao, J., Cai, Y., Wang, T. et al. Cellular direction information based differential evolution for numerical optimization: an empirical study. Soft Comput 20, 2801–2827 (2016). https://doi.org/10.1007/s00500-015-1682-9

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