## 4 Evaluation of the Task Assignment Algorithm
### Performance Evaluation
The result of (3) indicates that the rescuer may not be perfectly suited to save a victim, though the rescuer has been allocated [27]. Because the rescuers may not know the inside situations in uncertain environments, they may be exposed to highly hazardous areas for a long time, since they move into the disasters and may be obstructed by the congestion. Therefore, more rescuers in a \"without algorithm\" system not only aggravate congestion, but also may not increase the number of rescued people, due to problems (1) to (3). In this case, the performance of the system with more rescuers may be worse. However, with the RNN-based algorithm, the percentage of rescued civilians has a tendency to increase with more rescuers in the system (Figure 3). Although the rescuers still increase the congestion in the building, the RNN-based algorithm makes the rescuers save victims effectively, which dominates the overall performance of the rescue system. This is because the RNN-based algorithm can alleviate the three problems mentioned above by modelling a network of N fully connected neurons with a cost objective function. The algorithm treats each rescuer-victim pair as a neuron, such as neuron \(i\) means that rescuer \(r\) is allocated to victim \(v\), and it can minimize the total cost by solving the objective function. The objective function takes into account the cost of allocating rescuer \(r\) to victim \(v\), the probability that rescuer \(r\) is unable to save victim \(v\) (say, the failed rescue probability of neuron \(i\)), and the penalty of not rescuing victim \(v\). Therefore, a rescuer-victim pair will be selected if the allocation can minimize the cost of the objective function. For example, if the failed rescue probability of neuron \(i\) is high, the neuron may not be selected, since it might increase the overall cost. Although the fail rescue probability, \(L(r,v)\), is initialized randomly in the simulations, we notice that the RNN-based approach can avoid the selection of a neuron with high \(L\). Thus, problem (3) can be solved if we generate the fail rescue probability relying on the situations of the rescuers and victims, which will be discussed in future work. Moreover, the algorithm considers the rate of excitatory and inhibitory signals from firing neuron \(i\) to neuron \(j\). If neuron \(i\) has been selected, the inhibitory signals from neuron \(i\) to other neurons, \(j\), where \(j\
eq i\), will be updated to discourage the allocations of different rescuers to the same victim and different victims to the same rescuer. Then, problems (1) and (2) can be avoided to some degree. Therefore, more rescuers are able to save more people with the RNN-based algorithm, and the percentage of rescued civilians can be increased. In Table 3, given a set of victims, the increase of the number of rescuers cannot significantly improve the performance on the number of rescu  
Figure 3: Percentage of evacuees saved by rescuers under diverse population densities. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No. of rescuers \(|R|\)**} & \multirow{2}{*}{**No. of victims \(|V|\)**} & \multirow{2}{*}{**Without algorithm**} & \multicolumn{2}{c}{**With the**} & \multirow{2}{*}{**Optimal solutions**} \\  & & & & **RNN-based algorithm** & \\ \hline
3 & 4 & 3.00 & 3.80 & 4 \\
5 & 4 & 3.43 & 4.00 & 4 \\
7 & 4 & 4.00 & 4.00 & 4 \\
3 & 8 & 4.71 & 5.75 & 6 \\
5 & 8 & 6.00 & 7.50 & 8 \\
7 & 8 & 5.89 & 8.00 & 8 \\
3 & 16 & 4.88 & 6.00 & 6 \\
5 & 16 & 7.40 & 9.75 & 10 \\
7 & 16 & 6.67 & 13.25 & 14 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Number of evacuees saved by rescuers.