Parameter optimization of chaotic system using Pareto-based triple objective artificial bee colony algorithm

Chaotic map is a kind of discrete chaotic system. The existing chaotic maps suffer from optimal parameters in terms of chaos measurements. In this study, a novel approach of optimization of parametric chaotic map (PCM) using triple objective optimization is presented for the first time. A PCM with s...

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Veröffentlicht in:	Neural computing & applications Jg. 35; H. 18; S. 13207 - 13223
Hauptverfasser:	Toktas, Abdurrahim, Erkan, Uğur, Ustun, Deniz, Wang, Xingyuan
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	London Springer London 01.06.2023 Springer Nature B.V
Schlagworte:	Algorithms Artificial Intelligence Chaos theory Computational Biology/Bioinformatics Computational Science and Engineering Computer Science Data Mining and Knowledge Discovery Design parameters Entropy Image Processing and Computer Vision Liapunov exponents Optimization Original Article Pareto optimum Probability and Statistics in Computer Science Search algorithms Swarm intelligence Pareto optimization Image encryption Multi-objective optimization Chaotic system
ISSN:	0941-0643, 1433-3058
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Abstract	Chaotic map is a kind of discrete chaotic system. The existing chaotic maps suffer from optimal parameters in terms of chaos measurements. In this study, a novel approach of optimization of parametric chaotic map (PCM) using triple objective optimization is presented for the first time. A PCM with six parameters is first conceived and then optimized using Pareto-based triple objective artificial bee colony (PT-ABC) algorithm. Pareto optimality is employed to catch the trade-off among the objectives: Lyapunov exponent (LE), sample entropy (SE), and Kolmogorov entropy (KE). A global optimal design including the six parameters is selected for minimizing the reciprocal of the three objectives independently. The chaotic performance of PCM is verified through an evaluation with bifurcation diagram, attractor, LE, SE, KE, and correlation dimension. The results are also validated by comparison with those of which reported elsewhere. Furthermore, the applicability of PCM is examined over image encryption and the results are compared with existing chaos-based IEs. Therefore, the PCM manifests the best ergodicity and complexity thanks to its PT-ABC algorithm.
AbstractList	Chaotic map is a kind of discrete chaotic system. The existing chaotic maps suffer from optimal parameters in terms of chaos measurements. In this study, a novel approach of optimization of parametric chaotic map (PCM) using triple objective optimization is presented for the first time. A PCM with six parameters is first conceived and then optimized using Pareto-based triple objective artificial bee colony (PT-ABC) algorithm. Pareto optimality is employed to catch the trade-off among the objectives: Lyapunov exponent (LE), sample entropy (SE), and Kolmogorov entropy (KE). A global optimal design including the six parameters is selected for minimizing the reciprocal of the three objectives independently. The chaotic performance of PCM is verified through an evaluation with bifurcation diagram, attractor, LE, SE, KE, and correlation dimension. The results are also validated by comparison with those of which reported elsewhere. Furthermore, the applicability of PCM is examined over image encryption and the results are compared with existing chaos-based IEs. Therefore, the PCM manifests the best ergodicity and complexity thanks to its PT-ABC algorithm.
Author	Wang, Xingyuan Ustun, Deniz Erkan, Uğur Toktas, Abdurrahim
Author_xml	– sequence: 1 givenname: Abdurrahim surname: Toktas fullname: Toktas, Abdurrahim organization: Department of Artificial Intelligence and Data Engineering, Engineering Faculty, Ankara University – sequence: 2 givenname: Uğur orcidid: 0000-0002-2481-0230 surname: Erkan fullname: Erkan, Uğur email: ugurerkan@kmu.edu.tr organization: Department of Computer Engineering, Faculty of Engineering, Karamanoglu Mehmetbey University – sequence: 3 givenname: Deniz surname: Ustun fullname: Ustun, Deniz organization: Department of Computer Engineering, Engineering Faculty, Tarsus University – sequence: 4 givenname: Xingyuan surname: Wang fullname: Wang, Xingyuan organization: School of Electrical and Automation Engineering, East China Jiaotong University
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Snippet	Chaotic map is a kind of discrete chaotic system. The existing chaotic maps suffer from optimal parameters in terms of chaos measurements. In this study, a...
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SubjectTerms	Algorithms Artificial Intelligence Chaos theory Computational Biology/Bioinformatics Computational Science and Engineering Computer Science Data Mining and Knowledge Discovery Design parameters Entropy Image Processing and Computer Vision Liapunov exponents Optimization Original Article Pareto optimum Probability and Statistics in Computer Science Search algorithms Swarm intelligence
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Title	Parameter optimization of chaotic system using Pareto-based triple objective artificial bee colony algorithm
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