# Learning Behavior Trees for Autonomous Agents with Hybrid Constraints Evolution
## 4 Experimental Section
### Results and Analysis
Figure 9 shows the results distribution of mean best fitness with variable crossover probability 0.6, 0.7, 0.8 and 0.9 respectively, Figure 10 shows the results distribution of mean best fitness with variable new chromosomes 0.1, 0.2 and 0.3 respectively, and Figure 11 shows the results distribution of mean best fitness with variable mutation probability 0.01 and 0.1 respectively..  
From Table 2 we can see that, when crossover probabilities are 0.7, 0.8 and 0.9, the EBT-HC can achieve bigger means of 7371.0, 7419.5 and 7406.5 than the EBT-SC with 7174.5, 7169.6 and 7173.5 respectively, and lower standard deviation of 224.0, 218 and 258.2 than the EBT-SC with 454.0, 353.1 and 402.2 respectively. In the boxplot Figure 9 we also can see that, the whole distribution of all the individuals in EBT-HC is above the distribution in EBT-SC. All three lower adjacent values in EBT-HC are higher than the lower whiskers in EBT-SC, which indicates the lowest individual in EBT-HC is  
Figure 8: Learning curves of different approaches with variable mutation probability 0.01 and 0.1.  
better than more than 25% of individuals in EBT-SC. When the crossover probability is 0.6, the EBT-HC gets slightly smaller values of mean and standard deviation than EBT-SC. In terms of EBT-DC and EBT, we can see when the crossover probability is 0.6, the EBT-DC gets a lower 5734.6 than EBT with 6011.8. When the value grows to 0.7, the EBT-DC achieves similar mean with EBT, and when the value is 0.8 and 0.9, the EBT-DC achieves higher mean than EBT. In most cases, the standard deviation of EBT-DC is bigger than EBT. Those results indicate that the dynamic constraint can help EBT-DC and EBT-HC achieve better final solutions than EBT and EBT-SC respectively under bigger crossover probability like 0.8 and 0.9. The EBT-DC can achieve comparable final solution under crossover probability 0.8 and 0.9, but result in unstable solution. While for EBT-HC, it achieves higher and more stable final solution than EBT-SC. In Table 2 and Figure 10, when the new chromosomes is 0.1, the EBT-HC and EBT-DC get similar results with EBT-SC and EBT respectively. When the new chromosomes are 0.2 and 0.3, the EBT-HC and EBT-DC get higher mean and median than EBT-SC and EBT respectively. The EBT-DC gets bigger standard deviation than EBT, while EBT-HC gets smaller standard deviation than EBT-SC. That may be because when new chromosome proportion is lower as 0.1, the population diversity is declined,  
Figure 10: Boxplot results for the best generated BTs with variable new chromosomes 0.1, 0.2 and 0.3. Figure 9: Boxplot results for the best generated BTs with variable crossover probability 0.6, 0.7, 0.8 and 0.9.  
which may increase the risk of dynamic constraint trapped local minimum. Thus, we should use slight bigger new chromosome proportion like 0.2 and 0.3. In Table 2 and Figure 11, when the mutation probability is 0.01, the EBT-DC gets higher mean and median but larger distribution. Comparing with EBT-SC, EBT-HC gets higher median, similar mean and smaller standard deviation. When the mutation probability is 0.1, EBT-DC gets obviously lower mean and median than EBT, EBT-HC gets higher median and mean than EBT-SC. It should be noted that the values of EBT-SC and EBT-DC under mutation probability 0.01 are obviously lower than those values under mutation probability 0.1. That is because the static constraint on crossover will decline the diversity of swapped behavior blocks, we should set a big mutation probability for the EBT-SC and EBT-HC. Those results show that the EBT-HC can achieve higher and more stable solution than EBT-SC in most tested parameter values. While for EBT-DC, the dynamic constraint can help it to achieve higher mean but bigger standard deviation when the population diversity is declined. From above statistical experimental results of learning curves and final best individuals, we can draw conclusions that the EBT-DC with dynamic constraint can get faster learning speed and comparable final solution than EBT. However the results are more unstable.