# Learning Behavior Trees for Autonomous Agents with Hybrid Constraints Evolution
## 4 Experimental Section
### Results and Analysis
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**EBT**} & \multicolumn{2}{c}{**EBT-DC**} & \multicolumn{2}{c}{**EBT-SC**} & \multicolumn{2}{c}{**EBT-HC**} \\ \hline \multirow{4}{*}{Crossover probability} & 0.6 & 6011.8 \(\pm\) 320.2 & 5734.6 \(\pm\) 347.3 & 7344.8 \(\pm\) 428.4 & 7324.5 \(\pm\) 221.8 \\  & 0.7 & 5768.0 \(\pm\) 341.6 & 5930.9 \(\pm\) 572.2 & 7174.5 \(\pm\) 454.0 & 7371.0 \(\pm\) 224.0 \\  & 0.8 & 5781.7 \(\pm\) 267.9 & 6274.8 \(\pm\) 728.5 & 7169.6 \(\pm\) 353.1 & 7419.5 \(\pm\) 218.5 \\  & 0.9 & 5978.8 \(\pm\) 361.1 & 6168.4 \(\pm\) 609.4 & 7173.5 \(\pm\) 402.2 & 7406.5 \(\pm\) 258.2 \\ \hline \multirow{4}{*}{new chromosomes} & 0.1 & 5886.4 \(\pm\) 282.9 & 5962.3 \(\pm\) 311.3 & 7353.6 \(\pm\) 274.9 & 7350.0 \(\pm\) 221.4 \\  & 0.2 & 5471.7 \(\pm\) 769.9 & 6105.8 \(\pm\) 592.1 & 7197.0 \(\pm\) 369.3 & 7300.5 \(\pm\) 344.9 \\  & 0.3 & 5978.8 \(\pm\) 361.1 & 6168.4 \(\pm\) 609.4 & 7173.5 \(\pm\) 402.2 & 7406.5 \(\pm\) 258.2 \\ \hline \multirow{2}{*}{Mutation probability} & 0.01 & 5978.8 \(\pm\) 361.1 & 6168.4 \(\pm\) 609.4 & 6720.7 \(\pm\) 606.6 & 6737.2 \(\pm\) 262.6 \\  & 0.1 & 6456.9 \(\pm\) 523.0 & 6087.7 \(\pm\) 473.0 & 7173.5 \(\pm\) 402.2 & 7406.5 \(\pm\) 258.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean and standard deviation of the best individual of four evolving approaches under different parameters settings. The mean and standard deviation of the baseline handcrafted BT are 5351.3 and 47.6 (with 95% confidence interval), evolving BTs approach (EBT), existing ‘static’ structural constraint (EBT-SC). Figure 6: Learning curves of different approaches with variable crossover probability 0.6, 0.7, 0.8 and 0.9. Figure 7: Learning curves of different approaches with variable new chromosomes 0.1, 0.2 and 0.3. In Figure 8 we can see that, when the mutation probability is 0.01, the EBT-DC learns faster than EBT and converges to a higher mean best fitness in the end of evolution. For the EBT-HC, it climbs faster than EBT-SC within generation 10 and gets a comparable mean best fitness. When the mutation probability is 0.1, the EBT-DC is faster than EBT at early stage but converges to a lower value than EBT in the end of evolution. The EBT-HC learns faster than EBT-SC at early stage and both two converge to a similar mean best fitness in the end. It should be noted that, the final mean best fitness of EBT-SC and EBT-HC under mutation probability 0.01 are obviously lower than those under mutation probability of 0.1. In both the approaches EBT-SC and EBT-HC, the adjacent terminal child nodes are regarded as a sequential behavior block and the crossover is carried out only between nodes/blocks with the same type, thus the possible behavior blocks will remain unchanged and the population diversity declines to a great extent. The results indicate that under both mutation probabilities, the dynamic constraint can help EBT and EBT-SC to accelerate learning, but the approaches EBT-SC and EBT-HC need a bigger mutation probability to maintain higher diversity in generated blocks. On the whole, in most tested GA parameters, the dynamic constraint can help standard evolving BT and evolving approach with static constraint to accelerate learning speed and achieve better individuals with higher final fitness. For agent behavior modeling, another important concern is whether we can get an expected behavior model satisfying the evaluation criterions of domain expert. In evolving BTs for behavior modeling specifically, the goal is to produce the best BT individual with higher fitness than other existing approaches in simulation tests. Thus, we will check the average fitness of the best individual generated by different approaches. Table 2 shows all the average fitness results of mean and standard deviation under different GA parameters.