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Recent metaheuristics on control parameter determination
Table 8. Statistical results of the methods

No Methods Min Mean Max. Std
1 CO 3.8723 75.7473 341.1709 148.4326
2 PO 3.5314 4.1219 5.0070 0.7211
3 AO 3.5161 4.6367 6.6439 1.3972
4 GOA 3.4950 3.5158 3.5716 0.0317
5 POA 3.4790 3.8902 4.9990 0.6589
6 GJO 3.4839 3.5038 3.5383 0.0222
7 FDA 3.4913 3.5625 3.6115 0.0518
8 EO 3.4775 3.5065 3.5461 0.0319
9 ARO 3.5161 4.6367 6.6439 1.3972
10 CSA 3.9982 73.3512 339.1747 148.6448
11 WOA 3.5171 6.8791e+218 3.4395e+219 Inf
12 GWO 3.4833 4.4826 6.8118 1.4526
13 FPA 3.6329 71.7655 338.1445 148.9295
14 CMAES 63.4304 317.4418 383.8003 142.0176

CSA. Computational times for all methods are been used in this field, and an effective con-
presented in Figure 7. In terms of the computa- trol design for a two-wheeled self-balancing vehi-
tional times, CO method converged to the optimal cle. The optimal controller designed with con-
solution in the shortest time. EO, GWO, FPA, sidered metaheuristics, which are Flow Direc-
ARO, and CMA-ES also converge to the optimal tional, Cheetah Algorithm and Politican, Equi-
point shorter time than other algorithms. The librium, Aquila, Artificial Rabbit, Golden Jackal,
GWO method is found the optimal point in the Gazelle, and Pelican Optimizers, are implemented
longest time. to the two-wheeled vehicle. The balance and
The statistical results of all algorithms are pre- speed controller of the vehicle are performed with
sented in Table 8. The minimum, maximum, PI controllers. For this purpose, the cascade PI
mean, and standard deviations are included in controller parameters are tuned with the meta-
this table. The results for all algorithms are ob- heuristic methods. Since conventional PID tun-
tained with 5-runs. ing methods need more flexibility and robustness,
In Table 8, PO, AO, GOA, POA, GJO, FDA, EO, metaheuristic methods-based tuning approaches
ARO, CSA, GWO, and FPA methods produce are seen as crucial importance in solving com-
16, 38-40
similar results in terms of mean values, whereas plex engineering problems. The efficiencies
the CO, WOA, and CMA-ES methods have the of the optimization-based tuning algorithms are
worst values. The GJO method is seen as the assessed, comparatively. The statistical results,
best algorithm, and EO, GOA, and FDA follow convergence curves, dynamic system character-
the GJO method in terms of the mean values. Ac- istics, and computation times are evaluated by
cording to the minimum values of the algorithms, performing all methods under equal conditions.
the EO, POA, GWO, and GJO algorithms pro- In the qualitative and quantitative analysis, it is
duced the best results, respectively. Since the observed that 11 out of 14 compared algorithms,
methods take a long time to run in such systems, namely PO, AO, GOA, POA, GJO, FDA, EO,
ARO, CSA, GWO, and FPA methods, produced
it is important to reach the most optimal solution
similar optimal results in the speed and balance
in a short time when solving such problems.
control of the two-wheeled vehicle. However, it
When examining the theoretical aspects of algo-
is observed that CMA-ES, WOA, and CO meth-
rithms, it is clear that while the applications and
ods do not give satisfactory results for tuning the
common control parameters of metaheuristic al-
optimal control parameters.
gorithms are similar, the convergence behaviors
in finding the optimal solution change due to the The control parameter determination with meta-
differences in the strategies used in the movement heuristics approaches is one of the best ways be-
updates of the agents. This provides an overview
cause they offer more efficient solution with their
of the effectiveness of the strategies employed in
simple structures compared with the traditional
the methods.
methods. In addition, this problem is quite ap-
propriate for demonstrating the success of the
5. Conclusion
metaheuristic algorithms. This study will pro-
This study presents a comprehensive analysis of vide insights for researchers using metaheuristic
current metaheuristics, most of which have never methods in this field for where to start and which
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