## 5 Verification Experiments and Analysis
### Verification of Planning Mechanism and GA Operators  
To verify this planning mechanism, we firstly construct a scenario as shown in Figure 3, where seven robots cooperate to fight a fire. This mission is parsed into five atomic tasks \(t_{1}\)-\(t_{5}\) for 5 different target places with 4 type of services, as exhibited in Table 2. Each robot carries a different number and type of fire-fighting resources: water (\(\varepsilon.typ=1\)), carbon dioxide fire extinguisher (\(\varepsilon.typ=2\)), dry powder fire extinguisher (\(\varepsilon.typ=3\)), foam fire extinguisher (\(\varepsilon.typ=4\)), fan fire extinguisher (\(\varepsilon.typ=5\)), sand fire extinguisher (\(\varepsilon.typ=6\)), rock powder extinguishing (\(\varepsilon.typ=7\)). The properties of each task, the distribution of all resources, and the parameters of robots are detailed in Tables 2, 3, and 4, separately. Based on these settings, the performance of planning mechanism is verified from different aspects, especially, the chromosome coding, population size, and three proposed operators. Because all these tasks are related, both directly and indirectly, to each other, only one task cluster is established. Figure 4 presents the chromosome code of 41 bits in length for this scene, which means that the size of solution space is equal to \(2^{41}\). Furthermore, we design a more complex scene with 9 tasks and 7 services. The result of task cluster-based chromosome coding for this scene is shown in Figure 5, where there are 3 segments of 47 bits, 14 bits, and 1 bit in length, respectively. These segments corresponds to three solution spaces, the size of which are \(2^{47}\), \(2^{14}\), and 2, separately. Obviously, the total size of these three space is \((2^{47}+2^{14}+2)\), rather than the original larger one \(2^{62}\). It is the main advantage of such cluster-based mechanism that the solution time cost can be reduced significantly, especially when parallel solving is possible. It should be noted that in both Figures 4 and 5, the values of all bits of both coded chromosomes are fixed, indicating in fact two feasible solutions by our planning algorithm. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**ID** & \(t_{s}\) & \(t_{e}\) & **X** & **Y** & **Service Requirements** & **Risk** & **Value** \\ \hline
1 & 2 & 5 & 200 & 400 & \textless{}1,2\textgreater{}\textless{}2,2\textgreater{} & 0.1 & 1000 \\
2 & 3 & 5 & 300 & 400 & \textless{}2,2\textgreater{} & 0.1 & 700 \\
3 & 5 & 9 & 500 & 700 & \textless{}3,4\textgreater{} & 0.1 & 900 \\
4 & 6 & 10 & 600 & 600 & \textless{}3,2\textgreater{}\textless{}4,2\textgreater{} & 0.1 & 800 \\
5 & 9 & 13 & 600 & 900 & \textless{}4,2\textgreater{} & 0.1 & 900 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Descriptions of 5 Atomic Tasks. Figure 3: A Simulated Scene for Cooperative Fire Fighting by Swarm Robots. As we know, the size of population is the first important factor for GA, which affects the quality of solutions and the convergence speed. After experimenting this parameter 100 times on such scene, we found that when the population size was about 50, the fitness values of optimal solutions and the convergence speed would be well balanced, as shown in Figure 6 and in Figure 7. This conclusion is worthy of reference to determine a proper population scale before solving a special problem. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**ID** & **Mode** & **X** & **Y** & **Value** & **Speed** & **Voyage Range** \\ \hline
1 & 1 & 600 & 300 & 100 & 100 & 2000 \\
2 & 1 & 600 & 300 & 123 & 120 & 2100 \\
3 & 1 & 600 & 300 & 116 & 110 & 1900 \\
4 & 1 & 200 & 800 & 95 & 105 & 1800 \\
5 & 1 & 200 & 800 & 90 & 113 & 2200 \\
6 & 1 & 200 & 800 & 89 & 95 & 2000 \\
7 & 1 & 800 & 800 & 114 & 90 & 1890 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of Robots. Figure 4: A single Chromosome Coded for 5 Tasks and 4 Services. Figure 5: Three Chromosome Segments Coded for 9 Tasks and 7 Services.