# Inversion of Chlorophyll-a Concentration in Wuliangsu Lake Based on OGolden-DBO-XGBoost
## 3 Methods
### Dung Beetle Optimization Algorithm  
The dung beetle optimization (DBO) algorithm ([PERSON] and [PERSON], 2018) is a swarm intelligence algorithm proposed by [PERSON] in 2023 to find the optimal solution by simulating the dung beetle's ball-rolling, breeding, foraging, and stealing behaviors for position updating. The following only provides a quick description of the rolling dung beetle's position update method, because the main focus of this work is on improving the strategy in DBO.  
Dung beetles rolling dung balls need to navigate with the help of celestial cues (sun, light source intensity, and wind direction, etc.) in order to keep the dung balls rolling along a straight line. The position update strategy is shown in Equation (1).  
\[X_{i}^{n}(t+1)=X_{i}^{n}(t)+\alpha\times k\times X_{i}^{n}(t-1)+b\times\Delta x \tag{1}\]  
\[\Delta x=|X_{i}^{n}(t)-W^{n}(t)| \tag{2}\]  
where, \(t\) denotes the current iteration number, n denotes the dung beetle's position in n-dimensional space, \(X_{i}^{n}(t)\) denotes the position of the \(i\)th dung beetle at the \(t\) iteration, \(k\in(0,0.2]\) denotes the deflection coefficient, \(b\) is a constant value in the range (0,1), and \(\alpha\) denotes a natural coefficient with the value of 1 or \(-1\). When \(\alpha=-1\), it means that the dung beetle has deviated from the original direction due to the natural factors, while \(\alpha=1\) means that there is no deviation. \(W^{n}(t)\) denotes the worst position of the global position at the \(t\) iteration, and \(\Delta x\) is used to simulate the change in the light intensity.  
When the dung beetle encounters an obstacle and is unable to move forward, it simulates dance behavior by using the tangent function to obtain a new rolling direction. The position update strategy is shown in Equation (3).  
\[X_{i}^{n}(t+1)=X_{i}^{n}(t)+\tan\theta|X_{i}^{n}(t)-X_{i}^{n}(t-1)| \tag{3}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Number** & **June** & **July** & **August** & **September** & **B01** & **B02** & \(\ldots\) & **B12** &
\begin{tabular}{c} **Measured Chl-a** \\ **Concentration (\#g/L)** \\ \end{tabular} \\ \hline Data1 & 0 & 0 & 0 & 1 & 61 & 152 & \(\ldots\) & 40 & 12.018 \\ Data2 & 1 & 0 & 0 & 0 & 176 & 165 & \(\ldots\) & 60 & 10.095 \\ Data3 & 0 & 0 & 1 & 0 & 158 & 254 & \(\ldots\) & 197 & 20.012 \\ Data4 & 0 & 1 & 0 & 0 & 120 & 213 & \(\ldots\) & 53 & 3.6673 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Data feature structure.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Meaning** \\ \hline n\_estimators & Number of iterations \\ max\_depth & Maximum depth \\ learning\_rate & Learning rate \\ gamma & Coefficient of the number of leaf nodes \\ reg\_alpha & L1 regular term coefficient \\ reg\_lambda & L2 regular term coefficient \\ min\_child\_weight & Sum of sample weights of minimum leaf nodes \\ \hline \hline \end{tabular}
\end{table}
Table 5: Parameters of XGBoost and meaning.  
where \(\theta\) is a random number uniformly distributed in the range [0,\(\pi\)], and the dung beetle position is not updated when \(\theta=0\), \(\pi/2\), \(\pi\).