Abstract
This research deals with the hybridization of the two softcomputing fields, which are chaos theory and evolutionary computation. This paper aims on the deeper investigations on the multi-chaos-driven evolutionary algorithm Differential Evolution (DE) concept. This research is aimed at the embedding and alternating of set of two discrete dissipative chaotic systems in the form of chaos pseudo random number generators for the DE. In this paper the novel initial concept of DE/rand/1/bin strategy driven alternately by two chaotic maps (systems) is deeply investigated in terms of determining the optimal switching moment of two different chaotic systems. From the previous research, it follows that very promising results were obtained through the utilization of different chaotic maps, which have unique properties with connection to DE. The idea is then to connect these two different influences to the performance of DE into the one multi-chaotic concept. Repeated simulations were performed on the selected shifted benchmark function in higher dimensions. Finally, the obtained results are compared with canonical DE.
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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)
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)
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)
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)
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)
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)
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)
dos Santos Coelho, L., Mariani, V.C.: A novel chaotic particle swarm optimization approach using Hénon map and implicit filtering local search for economic load dispatch. Chaos, Solitons & Fractals 39(2), 510–518 (2009)
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)
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)
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)
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)
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’13-CISIS’13-ICEUTE’13. AISC, vol. 239, pp. 41–50. Springer, Heidelberg (2014)
Senkerik, R., Davendra, D., Zelinka, I., Pluhacek, M., Kominkova Oplatkova, Z.: On the Differential Evolution Drivan by Selected Discrete Chaotic Systems: Extended Study. In: 19th International Conference on Soft Computing, MENDEL 2013, pp. 137–144 (2013)
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)
Price, K.V., Storn, R.M., Lampinen, J.A.: Differential Evolution - A Practical Approach to Global Optimization. Natural Computing Series. Springer, Heidelberg (2005)
Sprott, J.C.: Chaos and Time-Series Analysis. Oxford University Press (2003)
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Senkerik, R., Pluhacek, M., Zelinka, I., Davendra, D., Kominkova Oplatkova, Z. (2014). Multi-chaotic Differential Evolution: Determining the Switching Time. In: Zelinka, I., Suganthan, P., Chen, G., Snasel, V., Abraham, A., Rössler, O. (eds) Nostradamus 2014: Prediction, Modeling and Analysis of Complex Systems. Advances in Intelligent Systems and Computing, vol 289. Springer, Cham. https://doi.org/10.1007/978-3-319-07401-6_10
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DOI: https://doi.org/10.1007/978-3-319-07401-6_10
Publisher Name: Springer, Cham
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