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 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.