## 2 Data and Methods
### Data-Driven Algorithms  
ROP is one of the important indicators to measure drilling efficiency. Therefore, the maximum ROP is selected as one of the optimization objectives in this study, and the ROP prediction model is taken as the optimization function in the multiobjective optimization algorithm. The traditional ROP model is based on laboratory experiments studying the relationship between parameters such as WOB, RPM, and ROP. The ROP prediction equations are established linear or nonlinear combinations of these parameters shown in Table 3[16; 17; 18; 19]. However, there are some uncertain coefficients in the traditional ROP model, which need to be adjusted according to different formations, different types of circulating media, and different drilling tool combinations. With the digital transformation of the oil field, MWD and other measurement tools are widely used. The oil field recorded and stored a large amount of drilling and logging data. Nowadays, many data-driven ROP models have been proposed. Researchers used the random forest regression method (RF) [20; 21], gradient boosting tree [22], BP neural network [23; 24; 25], Support Vector Machine Regression (SVM) [26; 27], and other algorithms to establish the ROP prediction models. These ROP prediction models have higher accuracy and timeliness than traditional ROP models. \begin{table}
\begin{tabular}{c c} \hline \hline
**Data Sources** & **Features** \\ \hline \multirow{2}{*}{Mud logging} & Depth, rate of penetration (ROP), weight on bit (WOB), handing \\  & load, revolutions per minute (RPM), torque(T), pumping flow per minute (GPM), equivalent density of drilling fluid \\ \multirow{2}{*}{Well logging} & Well deviation, azimuth, acoustic logging, density logging \\ Bit parameters & Diameter, cutting-tooth diameter, number of cutting tooth \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Oilfield multi-source data. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Work** & **Equation** & **Coefficients** \\ \hline [PERSON] [16] & \(\text{ROP}=k(\frac{W}{d})^{4}N\) & \(k,a\) \\ B and Y [17] & \(\text{ROP}=w_{f}\cdot k\cdot c\cdot W\cdot N^{\lambda}\) & \(w_{f},k,c,\lambda\) \\ [PERSON] [18] & \(\text{ROP}=w_{f}\frac{c\cdot N\cdot W^{\lambda}}{d\cdot c}\)  
In this work, we establish three drill-rate prediction models based on SVM, RF, and BP neural network algorithms and compare their prediction accuracy within the same dataset. The principles of the three algorithms are below. (1) SVM algorithm  
Support vector machine (SVM) is a machine learning method based on statistical learning theory. For regression problems, conventional regression models usually calculate the loss directly on the basis of the difference between the predicted values of the model and the true values, and the loss is 0 if and only if the predicted value of the model is exactly equal to the ground truth. The loss is 0 only if the predicted value of the model is exactly equal to the true values. However, the SVM regression model assumes that an error \(\varepsilon\) between the predicted value and the true value can be tolerated. The loss is calculated only if the absolute value of the difference between the predicted value and the true value is greater than \(2\varepsilon\), as shown in Figure 2. The training problem of the SVR model is an optimization problem under a given objective function and constraint conditions. The objective function is as follows:  
\[\min_{w,b}\frac{1}{2}||w||^{2}+C{\sum_{i=1}^{m}\xi_{i}},\ \ \ \xi_{i}\geq 0 \tag{1}\]  
The constraint is as follows:  
\[||f(x_{i})||-y_{i}=\varepsilon+\xi_{i} \tag{2}\]  
where \(w\) is weight, \(b\) is the bias, \(C\) is the penalty factor, \(\varepsilon\) is the error tolerance interval, and \(\xi_{i}\) is the slack variable. (2) Random forest algorithm  
Random forest is a classical machine learning algorithm that has been widely used in the industry since it was first proposed by [PERSON] in 2001 [28]. In this algorithm, decision trees are selected as weak learners.