# Performance Comparisons of Bio-Micro Genetic Algorithms on Robot Locomotion
## 7 Discussion and Results  
Experiments on the four algorithms were carried out to identify the best performing algorithm in terms of the shortest time and the lowest number of generations in which the trotting CPG for robot's locomotion was found (Figures 16-19 show these performances). The GA showed the worst performance of around 7.188 s, with 911 generations needed to obtain the trotting CPG for robot's locomotion. In these conditions, learning to trot was slow; it was not continuous, and 7.188 s was a long time for the generation of continuous locomotion (see the information in Figure 16). The \(\mu\)GA and \(\mu\)AIS schemes have better performance than the GA algorithm and find the trotting CPG for robot's locomotion in less than one second since each the trotting CPG for robot's locomotion was found in 73 generations (Figure 17). Figure 16: Performance of Genetic Algorithm (GA) standard with a reference of 30-bit length. (a) fitness and (b) absolute error. The \(\mu\)AIS scheme found the trotting CPG for robot's locomotion in 0.327s and 55 generations (Figure 18). Our proposed \(\mu\)sGA scheme found the trotting CPG for robot's locomotion in the shortest time of 0.131 s and 21 generations. The \(\mu\)sGA had several advantages; for example, it had the characteristics of the \(\mu\)GA approach. The nominal convergence accelerated finding process and the general convergence reset the algorithm and explored a new space of values. The second and main advantage was that the  
Figure 17: Performance of \(\mu\)GA with a reference of 30-bit length. (**a**) fitness and (**b**) absolute error. Figure 18: Performance of \(\mu\)AIS with a reference of 30-bit length. (**a**) fitness and (**b**) absolute error. individual chains were segmented into bytes to find the reference values in a shorter time, rather than one individual of 32 bits. The time to find the CPG trot gait was reduced with the \(\mu\)GA from 0.7687 s to 0.131 s, as can be seen in Figure 19.  
In the design of the GA, the time required to generate individuals was lower for the 32-bit individual divided by four 8-bit string than for a 32-bit string. If an individual was a large string, the computing time needed to generate the population was longer; this concept allowed us to segmented the individuals, and required less time (0.131 s) to generate the population, as can be seen in the last experiments with the \(\mu\)sGA. Another concept is the application of genetic operators. Computing time can be reduced by eliminating cyclic structures without neglecting the use of the operator to each individual. For example, when applying the mutation, individuals with 32 bits must be accessed 32 times by every other individual, as shown in Figures 3 and 4. The goal was to learn to walk as soon as possible. Table 2 summarizes the results of the experiments and describes the performance of the algorithms in terms of finding the solution, based on the time and numbers of generations. In the paper of Stability Criterion for Dynamic Gaits of Quadruped Robot [25], the trot-gait parameters are shown; in particular, the duration of a gait cycle reported is 1 second. If it is compared with the results of Table 2, we can explain that computing time for GA is not suitable, \(\mu\)GA uses 76% of a cycle, \(\mu\)AIS the 32% and the best time is for \(\mu\)sGA with 13%. Two micro genetic algorithms were evaluated for robot locomotion: a \(\mu\)GA with 30-bit strings and the \(\mu\)sGA (four 8-bit strings). In each experiment, the algorithm was executed 10 times, and the best individual \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **GA** & \(\mu\)**GA** & \(\mu\)**AIS** & \(\mu\)**sGA** \\ \hline Generations & 911 & 73 & 55 & 21 \\ Time (s) & 7.188 & 0.765 & 0.327 & 0.131 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of experimental results. Figure 19: Performance of \(\mu\)sGA with a reference of 30-bit segmented in 4 bytes. (**a**) fitness and (**b**) absolute error. was selected based on its fitness.