*4.2. Results*

The number of iterations is set to 4000, and Figure 6 exhibits the convergence of fitness values during iterations. When the iteration reaches 2000, the fitness value does not descend. Accordingly, the result returned at the end of the iteration is considered the optimal solution. Figure 7 presents the tree structure of optimal results. The tree structure can be simplified to Equation (4). Equation (4) is the final equation developed by GP to estimate the *UC*.

$$\begin{array}{l} \text{UC} = IC + 2T + \left(IC + Su(\sin(\sqrt{(LOP + Su)}) \\ \quad + \sin(LOP + Su)) + 3T - 2\sin(PD - T) + \sin(\sin(LOP) \\ \quad + \cos(\sin(\tan(D - T))) \end{array} \right) \tag{4}$$

**Figure 6.** The value of fitness function during iterations.

**Figure 7.** Tree structure representation of optimal results (X0 = LOP; X1 = PD; X2 = IC; X3 = Su; X4 = T).

For evaluating the performance of the developed equation, *R*2, RMSE, mean absolute error (MAE), variance account for (VAF), and A-20 index were introduced to evaluate the performance of Equation (4) in training and testing sets [46–49]. Equations (5)–(7) display the calculation equations for MAE, VAF, and A-20 index, respectively. When the MAE gets closer to 0, the model has better accuracy. When the VAF reaches 100, the predicted UC is perfectly equated to the actual. When the predicted UC is equal to the actual UC, the A-20 index is 1.

$$MAE = \frac{1}{M} \sum\_{i=1}^{M} | \mathbf{U} \mathbf{C} - \mathbf{U} \mathbf{C}' | \tag{5}$$

$$VAF = [1 - \frac{var(\mathbf{UC} - \mathbf{UC'})}{var(\mathbf{UC})}] \mathbf{U} \times 100\tag{6}$$

$$A - 20 = \frac{m20}{M} \tag{7}$$

where *var*(·) means the variance, and *m*20 is the number of samples with a ratio of the predicted value to the actual value in the range (0.8–1.2).

Figure 8 shows the predicted results and five regression indicators in training and testing tests. When the predicted UC equals the true UC, the corresponding point falls on the red line in the figure. The points falling between the two purple dotted lines indicate that the ratio of the predicted UC to the real UC is between 0.8 and 1.2. The A-20 index indicates that some of the predicted values are different from the actual values.

**Figure 8.** The performance of equation developed by GP in training and testing sets.
