Advanced Metaheuristics-Based Approach for Fuzzy Control Systems Tuning - Complex System Modelling and Control Through Intelligent Soft Computations - page 632

c 1 =2; c 2 =2
c 1 =0.2; c 2 =1.3
c 1 =2.9; c 2 =0.1
c 1 =1.19; c 2 =1.19

0.3

0.25

0.2

0.15

0 20 40 60 80 100

Iteration

Fig. 8 Robustness convergence under control parameters variation of the PSO-based approach:
ISE criterion case

Both for the MO and ISE criteria, the robustness on convergence of the proposed
algorithms is guaranteed under their main control parameters variation. The qual-
ities of the obtained solution, the fast convergence as well as the simple software
implementation are comparable with the standard GAO-based approach. According
to the convergence plots of the implemented metaheuristics, i.e., results of Figs. 5 ,
6 , 7 and 8 , the exploitation and exploration capabilities of these algorithms are ever
guaranteed.
In this study, only simulation results from the ISE criterion case are illustrated.
The main difference between performances of the implemented metaheuristics is
their relative quickness or slowness in terms of CPU computation time. For this
particular optimization problem, the quickness of DSA and PSO is specially marked
in comparison with other techniques. Indeed, while using a Pentium IV, 1.73 GHz
and MATLAB 7.7.0, the CPU computation times for the PSO algorithm are about
328 and 360 s in the MO and ISE criterion, respectively. For the DSA algorithm,
these are about 296 and 310 s, respectively. For example and in the case of GSA
metaheuristic, we obtain about 540 and 521 s for the above criterion respectively.
For the ISE criterion case, all optimization results are close to each other in terms
of solutions quality, except those obtained by the ABC-based method. The relative
numerical simulation shows the sensitivity of this algorithm under the

“

Limit for

abandonment ” parameter variation. The best optimization result, with fitness value

equal to 0 : 1928, is obtained with L ¼ 60.