# Behavior Composition for Marine Pollution Source Localization Using a Mobile Sensor Network
## 3 Simulation Setup  
The FPSP proposed by [PERSON] et al. [PERSON] et al. (2018) is used to test the proposed method. In FPSP, a 100 m-by-100 m square search area is simulated. Within the search area, six mobile sensor nodes are moving at a speed of 2 m/s to search for an unknown chemical plume source. From the source, a large number of chemical filaments that contain chemical material normally distributed relative to the filament center are continuously released and dispersed in the search area. Then, the released filaments are horizontally transferred by the dynamic turbulent flow. All released filaments contribute to the instantaneous concentration \(C(\mathbf{x},t)\) at \(\mathbf{x}\) as follows [PERSON] et al. (2018):  
\[ \begin{split} C(\mathbf{x},t)=\sum_{i-1}^{N}C_{i}(\mathbf{x},t),\\ C_{i}(\mathbf{x},t)=\frac{Q}{\sqrt{8\pi^{3}R_{i}^{3}(t)}}\exp\left( \frac{-d_{i}^{2}(t)}{R_{i}^{2}(t)}\right),d_{i}(t)=\|\mathbf{x}-\mathbf{p}_{i}\|,\end{split}  \tag{8}\]  
where \(N\) is the total number of filaments, \(Q\) is the amount of chemical substance units in a filament, and \(R_{i}(t)\) and \(\mathbf{p}_{i}\)are the size parameter and position of the \(i\)-th filament, respectively. Typical values of \(Q\) and \(R_{i}(t)\) can be set as \(8.3\times 10^{9}\) and \(\sqrt{0.001(1+t)}\), respectively [PERSON] et al. (2018). It can be seen that the value of \(C_{i}(\mathbf{x},t)\) is dominated by \(R_{i}(t)\) and \(\mathbf{p}_{i}\), which are influenced by the motion of the \(ith\) filament. In the FPSP, the motion speed of the filaments is governed by the surrounding flow's velocities. The degree of the flow velocity fluctuation, which can be changed by tuning the noise parameters \(a\), \(b\), and \(G\)[PERSON] et al. (2018), is positively correlated with the degree of variation in the filament's positions. To complicate the CPSL problem, large-amplitude flow fluctuations [PERSON] et al. (2018) are generated by setting the parameters \(a\), \(b\), and \(G\) to 0.04, 0.04, and 20, respectively. Moreover, as a further development of FPSP, the time-varying flow velocities are saved to a file in chronological order. Based on the same flow-velocity file, the SS method [PERSON] et al. (2018) is tested as a counterpart method for comparison with the uGA. The similarities and differences between the SS and uGA methods are summarized in Table 2. There are substantial differences between the SS and uGA methods, although both methods employ reactive upwind sprint operation to control the SN node currently in contact with the plume. First, in the plume reacquiring stage, SS and uGA steer the SNs along deterministic spiraling paths and toward the newly generated chromosome, respectively. Second, SS and uGA realize cooperation among the SNs through simple explicit \"ATTRACT\" communication and customized crossover of the genetic algorithm chromosomes, respectively. Third, as the termination condition, SS compares a predefined constant with the distance from the chemical source to the SNs, while the uGA uses the distances between successive LCPs to judge whether the SN locations converge. Because the plume source location is previously unknown in real CPSL applications, the calculation of the SN-source distance is not applicable. \begin{table}
\begin{tabular}{c c c} \hline \multicolumn{2}{c}{**GA**} & \multicolumn{1}{c}{**uGA**} \\ \hline _Initialization_ & Random initialization & Initialized around the first plume contact \\ _Population update_ & Fitness-value comparison & Moving and detecting \\ _Selection_ & Select \(m\times p_{c}\) chromosomes & Select two chromosomes \\ _Crossover_ & Probabilistic crossover & Upwind-customized probabilistic crossover \\ _Termination_ & Maximal iteration times & LCP convergence \\ _Application_ & Function optimization & Chemical plume source localization \\ \hline \end{tabular}
\end{table} 
Table 1: Differences between GA and uGA. To test the uGA and SS methods under identical conditions in all trials, three setups were created, as follows:  
1.