## 4 Results
### Comparison with Other Algorithms under Different Agent Numbers  
Figure 6 shows the number of iterations based on the proposed HRL algorithm. Two lines are shown in the figure: the orange one shows the second layer's optimization and the blue line shows the first layer's optimization. It is evident that the first layer of the algorithm converges around 100 iterations and the second layer converges around 220 iterations. Eventually, the fitness function stabilizes around 1.0.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Item** & **Type** & \multicolumn{4}{c}{**Number**} \\ \hline \multirow{2}{*}{Astronaut} & Astronauts in the Capsule & 3 & 4 & 5 & 6 & 7 \\  & Astronauts outside the Capsule & 3 & 4 & 5 & 6 & 7 \\ \hline \multirow{4}{*}{Robot} & Small Exploration Robot & 3 & 4 & 5 & 6 & 7 \\  & Large Rescue Robot & 3 & 4 & 5 & 6 & 7 \\  & Material transport Robot & 3 & 4 & 5 & 6 & 7 \\  & Lunar Rover & 3 & 4 & 5 & 6 & 7 \\ \hline \multirow{4}{*}{Task} & Ground Exploration & 1 & 1 & 1 & 1 \\  & Robot Rescue & 1 & 1 & 1 & 1 & 1 \\ \cline{1-1}  & Material transport & 1 & 1 & 1 & 1 & 1 \\ \cline{1-1}  & Lunar surface samples & 1 & 1 & 1 & 1 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Experimental setting of experiment 2.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Item** & **Type** & **Number** \\ \hline \multirow{2}{*}{Astronaut} & Astronauts in the Capsule & 4 \\  & Astronauts outside the Capsule & 4 \\ \hline \multirow{4}{*}{Robot} & Small Exploration Robot & 4 \\  & Large Rescue Robot & 4 \\  & Material transport Robot & 4 \\  & Lunar Rover & 4 \\ \hline \multirow{4}{*}{Task} & Ground Exploration & 1 \\  & Robot Rescue & 1 \\ \cline{1-1}  & Material transport & 1 \\ \cline{1-1}  & Lunar surface samples & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Experimental setting of multi-agent human–robot function allocation.  
In Figure 7, one can observe the iteration curves of RL and DRL for the same computational case. Remarkably, the reward function of RL converges to approximately 1.0 after around 12,500 iterations, while the reward function of DRL converges to approximately 1.0 after around 18,000 iterations. Both algorithms have the same final stationary value of the fitness function as HRL. Nonetheless, their ergodic counts are significantly higher than those of HRL.  
In Figure 8, there are two iteration curves representing the HDRL algorithm for the same computational situation. In particular, the blue one represents the optimisation curve for the first layer and the orange one for the second layer. Of interest is that the reward functions of the two layers of HDRL converge to approximately 1.0 after 580 and 780 iterations, respectively. Although the fitness function converges to the same value, the number of iterations is still higher for this algorithm than for HRL.  
Figure 6: The result of the human–robot function allocation based on the HRL algorithm.  
Figure 7: The calculation results based on the RL and DRL algorithm.  
To sum up, the proposed HRL improves the efficiency of human-robot function allocation by no less than 98.24%, 98.78% and 71.79%, respectively, compared to the RL, DRL and HDRL algorithms for the same number of agents. It can be demonstrated that the proposed approach could effectively improve the efficiency of task allocation compared to traditional algorithms.