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On the Tuning of Complex Dynamics Embedded into Differential Evolution

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Book cover Artificial Intelligence and Soft Computing (ICAISC 2015)

Abstract

This research deals with the hybridization of the two softcomputing fields, which are chaos theory and evolutionary computation. This paper aims on the experimental investigations on the chaos-driven evolutionary algorithm Differential Evolution (DE) concept. This research represents the continuation of the satisfactory results obtained by means of chaos embedded (driven) DE, which utilizes the chaotic dynamics in the place of pseudorandom number generators This work is aimed at the tuning of the complex chaotic dynamics directly injected into the DE. To be more precise, this research investigates the influence of different parameter settings for discrete chaotic systems to the performance of DE. Repeated simulations were performed on the IEEE CEC 13 benchmark functions set in dimension of 30. Finally, the obtained results are compared with canonical DE and jDE.

This work was supported by Grant Agency of the Czech Republic - GACR P103/15/06700S, further by financial support of research project NPU I No. MSMT-7778/2014 by the Ministry of Education of the Czech Republic and also by the European Regional Development Fund under the Project CEBIA-Tech No. CZ.1.05/2.1.00/03.0089, partially supported by Grant of SGS No. SP2015/142 and SP2015/141 of VSB - Technical University of Ostrava, Czech Republic and by Internal Grant Agency of Tomas Bata University under the project No. IGA/FAI/2015/057.

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References

  1. Price, K.V.: An Introduction to Differential Evolution. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, pp. 79–108. McGraw-Hill Ltd. (1999)

    Google Scholar 

  2. Qin, A.K., Huang, V.L., Suganthan, P.N.: Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization. IEEE Transactions on Evolutionary Computation 13(2), 398–417 (2009)

    Article  Google Scholar 

  3. Mallipeddi, R., Suganthan, P.N., Pan, Q.K., Tasgetiren, M.F.: Differential evolution algorithm with ensemble of parameters and mutation strategies. Applied Soft Computing 11(2), 1679–1696 (2011)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  6. Neri, F., Iacca, G., Mininno, E.: Disturbed Exploitation compact Differential Evolution for limited memory optimization problems. Information Sciences 181(12), 2469–2487 (2011)

    Article  MathSciNet  Google Scholar 

  7. Iacca, G., Caraffini, F., Neri, F.: Compact Differential Evolution Light: High Performance Despite Limited Memory Requirement and Modest Computational Overhead. J. Comput. Sci. Technol. 27(5), 1056–1076 (2012)

    Article  MathSciNet  Google Scholar 

  8. Aydin, I., Karakose, M., Akin, E.: Chaotic-based hybrid negative selection algorithm and its applications in fault and anomaly detection. Expert Systems with Applications 37(7), 5285–5294 (2010)

    Article  Google Scholar 

  9. Liang, W., Zhang, L., Wang, M.: The chaos differential evolution optimization algorithm and its application to support vector regression machine. Journal of Software 6(7), 1297–1304 (2011)

    Article  Google Scholar 

  10. Zhenyu, G., Bo, C., Min, Y., Binggang, C.: Self-Adaptive Chaos Differential Evolution. In: Jiao, L., Wang, L., Gao, X.-B., Liu, J., Wu, F. (eds.) ICNC 2006. LNCS, vol. 4221, pp. 972–975. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  11. Davendra, D., Zelinka, I., Senkerik, R.: Chaos driven evolutionary algorithms for the task of PID control. Computers & Mathematics with Applications 60(4), 1088–1104 (2010)

    Article  MathSciNet  Google Scholar 

  12. dos Santos Coelho, L., Mariani, V.C.: A novel chaotic particle swarm optimization approach using Henon map and implicit filtering local search for economic load dispatch. Chaos, Solitons & Fractals 39(2), 510–518 (2009)

    Article  Google Scholar 

  13. Davendra, D., Bialic-Davendra, M., Senkerik, R.: Scheduling the Lot-Streaming Flowshop scheduling problem with setup time with the chaos-induced Enhanced Differential Evolution. In: 2013 IEEE Symposium on Differential Evolution (SDE), April 16-19, pp. 119–126 (2013)

    Google Scholar 

  14. Pluhacek, M., Senkerik, R., Davendra, D., Kominkova Oplatkova, Z., Zelinka, I.: On the behavior and performance of chaos driven PSO algorithm with inertia weight. Computers & Mathematics with Applications 66(2), 122–134 (2013)

    Article  MathSciNet  Google Scholar 

  15. Pluhacek, M., Senkerik, R., Zelinka, I., Davendra, D.: Chaos PSO algorithm driven alternately by two different chaotic maps - An initial study. In: 2013 IEEE Congress on Evolutionary Computation (CEC), June 20-23, pp. 2444–2449 (2013)

    Google Scholar 

  16. Gandomi, A.H., Yang, X.S., Talatahari, S., Alavi, A.H.: Firefly algorithm with chaos. Communications in Nonlinear Science and Numerical Simulation 18(1), 89–98 (2013)

    Article  MathSciNet  Google Scholar 

  17. Senkerik, R., Pluhacek, M., Zelinka, I., Oplatkova, Z.K., Vala, R., Jasek, R.: Performance of Chaos Driven Differential Evolution on Shifted Benchmark Functions Set. In: Herrero, A., et al. (eds.) International Joint Conference SOCO 2013-CISIS 2013-ICEUTE 2013. AISC, vol. 239, pp. 41–50. Springer, Heidelberg (2014)

    Google Scholar 

  18. Senkerik, R., Davendra, D., Zelinka, I., Pluhacek, M., Kominkova Oplatkova, Z.: On the Differential Evolution Driven by Selected Discrete Chaotic Systems: Extended Study. In: 19th International Conference on Soft Computing, MENDEL 2013, pp. 137–144 (2013)

    Google Scholar 

  19. Lozi, R.: Engineering of Mathematical Chaotic Circuits. In: Zelinka, I., Chen, G., Rössler, O.E., Snasel, V., Abraham, A. (eds.) Nostradamus 2013: Prediction, Model. & Analysis. AISC, vol. 210, pp. 17–29. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  20. Price, K.V., Storn, R.M., Lampinen, J.A.: Differential Evolution - A Practical Approach to Global Optimization. Natural Computing Series. Springer, Heidelberg (2005)

    Google Scholar 

  21. Sprott, J.C.: Chaos and Time-Series Analysis. Oxford University Press (2003)

    Google Scholar 

  22. Brest, J., Greiner, S., Boskovic, B., Mernik, M., Zumer, V.: Self-adapting control parameters in differential evolution: A comparative study on numerical benchmark problems. IEEE Transactions on Evolutionary Computation 10, 646–657 (2006)

    Article  Google Scholar 

  23. Liang, J.J., Qu, B.-Y., Suganthan, P.N., Hernandez-Diaz, A.G.: Problem Definitions and Evaluation Criteria for the CEC 2013 Special Session and Competition on Real-Parameter Optimization, Technical Report 201212, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, Singapore (2013)

    Google Scholar 

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Correspondence to Roman Senkerik .

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Senkerik, R., Pluhacek, M., Zelinka, I., Davendra, D., Oplatkova, Z.K., Jasek, R. (2015). On the Tuning of Complex Dynamics Embedded into Differential Evolution. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2015. Lecture Notes in Computer Science(), vol 9119. Springer, Cham. https://doi.org/10.1007/978-3-319-19324-3_36

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  • DOI: https://doi.org/10.1007/978-3-319-19324-3_36

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19323-6

  • Online ISBN: 978-3-319-19324-3

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