## 8 Conclusions  
Particle Swarm Optimization is an excellent bio-inspired optimization algorithm, capable of handling complex problems and obtaining very good results; in this case, the optimization of membership functions from a fuzzy controller. From the results in the comparison of different variants of PSO, the PSO + IT2 FS variant, which uses an interval type-2 fuzzy system for dynamic parameter adaptation, can obtain better results than all other variants of PSO and also better results than BA and BCO.  
The Bee Colony Optimization algorithm is used to optimize membership functions of a fuzzy logic controller applied to track the trajectory of an autonomous mobile robot, with the objective of minimizing an error. After observing and analyzing the obtained results, we can conclude that BCO is efficient in optimization problems. In this case, it can achieve acceptable results; however, the algorithm presents stability problems, and does not always finds acceptable results, i.e., some experiments are good and some are bad.  
The integration of Type-1 and Interval Type-2 fuzzy systems into the bat algorithm represents a high level of difficulty for the solution of optimization problems and, analyzing the results that the fuzzy bat algorithm obtained, the MSE is acceptable in following an established trajectory, but the results can be improved by optimizing other parameters in the original bat algorithm method or by optimizing the rules in the fuzzy systems.  
The motivation for the development of this paper was to verify the improvement with our methodology for parameter adaptation through fuzzy logic, applied to different bio-inspired methods. The main contribution of this paper is a comparative study based on three bio-inspired algorithms for the design and implementation of fuzzy controllers. In addition, a comparative study of traditional methods, proposed methods with parameter adaptation using type-1 and interval type-2 fuzzy logic systems as tools for modeling complex problems in control.  
For future work, we want to extend the proposed methodology for parameter adaptation to other bio-inspired methods as well as use other applications, such as the optimization of neural networks, fuzzy systems applied to other problems, or even a hybridization between two or more of the proposed modified bio-inspired methods.  
**Author Contributions:** [PERSON] prepared the part of the paper related to particle swarm optimization. [PERSON] prepared the methods and implementation of bee colony optimization. [PERSON] prepared the part of the paper related to the bat algorithm. [PERSON] performed the experiments of bee colony optimization and made comparative tables. [PERSON] prepared the comparisons for bat algorithm and particle swarm optimization. [PERSON] coordinated the whole team and prepared the organization and writing of the paper.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Griewank Function**} \\ \hline
**Population Size** & **Dimensions** & **Iterations** & **[PERSON] et al. (2019)** & **Our Approach** \\ \hline  & 10 & 1000 & 0.091623 & **0.0654** \\
20 & 20 & 1500 & 0.027275 & **0.0192** \\  & 30 & 2000 & 0.02156 & **0.0114** \\ \hline  & 10 & 1000 & 0.075674 & **0.0568** \\
40 & 20 & 1500 & 0.031232 & **0.0149** \\  & 30 & 2000 & 0.012198 & **0.0097** \\ \hline  & 10 & 1000 & 0.068323 & **0.0628** \\
80 & 20 & 1500 & 0.025956 & **0.0181** \\  & 30 & 2000 & 0.014945 & **0.0110** \\ \hline \hline \end{tabular}
\end{table}
Table 18: Comparison against [PERSON] et al. [PERSON] et al. (2019).