Table 1.
Parameters settings for involved chaotic PSO algorithms.
Table 2.
Selected analytic benchmark functions for performance testing of diverse chaotic PSO algorithms.
Fig 1.
The 3-D maps for 2-D test functions f3, f5 and f6.
(a) Shifted Rastrigin’s Function. (b) Shifted Rotated Weierstrass Function. (c) Schwefel’s Problem 2.13.
Fig 2.
The median convergence characteristics of diverse chaotic PSO algorithms for the 5-D test functions.
(a) Shifted Rosenbrock’s function. (b) Shifted rotated Ackley’s function with global optimum on bounds. (c) Shifted Rastrigin’s function. (d) Shifted rotated Rastrigin’s function. (e) Shifted rotated Weierstrass function. (f) Schwefel’s problem 2.13. (g) Expanded extended Griewank’s plus Rosenbrock’s function (G(R(x))). (h) Shifted rotated expanded Scaffer’s SF(x) function. (i) Hybrid composition function 1. (j) Rotated hybrid composition function 1.
Fig 3.
The median convergence characteristics of diverse CPSO algorithms for the 15-D test functions.
(a) Shifted Rosenbrock’s function. (b) Shifted rotated Ackley’s function with global optimum on bounds. (c) Shifted Rastrigin’s function. (d) Shifted rotated Rastrigin’s function. (e) Shifted rotated Weierstrass function. (f) Schwefel’s problem 2.13. (g) Expanded extended Griewank’s plus Rosenbrock’s function (G(R(x))). (h) Shifted rotated expanded Scaffer’s SF(x) function. (i) Hybrid composition function 1. (j) Rotated hybrid composition function 1.
Fig 4.
The median convergence characteristics of diverse CPSO algorithms for the 100-D test functions.
(a) Shifted Rosenbrock’s function. (b) Shifted rotated Ackley’s function with global optimum on bounds. (c) Shifted Rastrigin’s function. (d) Shifted rotated Rastrigin’s function. (e) Shifted rotated Weierstrass function. (f) Schwefel’s problem 2.13. (g) Expanded extended Griewank’s plus Rosenbrock’s function (G(R(x))). (h) Shifted rotated expanded Scaffer’s SF(x) function. (i) Hybrid composition function 1. (j) Rotated hybrid composition function 1.
Table 3.
Computed global minimum results of diverse chaotic PSO algorithms for the 5-D multimodal problems.
Table 4.
Computed global minimum results of diverse chaotic PSO algorithms for the 15-D multimodal problems.
Table 5.
Computed global minimum results of diverse chaotic PSO algorithms for the 100-D multimodal problems.
Table 6.
Fixed accuracy level of the selected analytic test functions in Table 2.
Table 7.
Success rates and success performances of diverse chaotic PSO algorithms for the 5-D test functions in Table 2.
Table 8.
The average computational cost time (seconds) of diverse chaotic PSO algorithms for the test functions f1 − f10 with 100-D size.
Fig 5.
The input signal and its output are shown in the course of the estimation procedure.
(a) The pseudo-random binary sequence. (b) The testing samples.
Table 9.
Parameters settings for the involved optimization algorithms.
Table 10.
Results of diverse evolutionary optimization algorithms for the 4-D identification problem.
Table 11.
The average computational cost time (seconds) of diverse chaotic PSO algorithms for the 4-D identification problem.
Fig 6.
The median convergence and identification characteristics of diverse evolutionary optimization algorithms for 4-D identification problem above.
(a) The median convergence characteristics of diverse evolutionary optimization algorithms. (b) The median identification characteristics of diverse evolutionary optimization algorithms for K. (c) The median identification characteristics of diverse evolutionary optimization algorithms for T1. (d) The median identification characteristics of diverse evolutionary optimization algorithms for T2. (e) The median identification characteristics of diverse evolutionary optimization algorithms for T3.
Fig 7.
The output results and their errors of diverse evolutionary optimization algorithms for the 4-D identification problem are shown.
(a) The output of diverse evolutionary optimization algorithms. (b) The output errors of the nonlinear dynamic system of diverse evolutionary optimization algorithms.
Table 12.
The absolute accumulated errors and parameter values of diverse evolutionary optimization algorithms for the 4-D identification problem.