## 4 Methodology
### SVR Optimized by the IJaya Algorithm  
SVR is an effective tool for nonlinear regression and is also suitable for grouting power forecasting. The detailed theory of SVR is presented elsewhere [45; 46]. The radial basis function kernel, which is the most applicable kernel function [47], was adopted in this study. Through it, the original data space is mapped into an infinite-dimensional space theoretically. There are three user-determined parameters: the penalty parameter \(C\), the insensitive loss function \(\varepsilon\), and the kernel function parameter \(g\); these are critical to the performance of SVR and can be determined by optimization algorithm. The new Java algorithm proposed to solve unconstrained and constrained optimization problems is a simple yet powerful optimization algorithm. Let \(O(X)\) be an objective function that needs to be optimized. Assume that the number of design variables, the statistical population size, and the maximum number of iterations are \(N_{var}\), \(N_{ppp}\), and \(N_{max}\), respectively, and that \(i\), \(j\), and \(k\) are their indices, where \(i\in(1,\,N_{var})\), \(j\in\left(1,\,N_{pop}\right)\), and \(k\in(1,\,N_{max})\). If \(X_{i,j,k}\) stands for the value of the \(i_{th}\) design variable for the \(j_{th}\) candidate during the \(k_{th}\) iteration, then this value can be updated using:  
\[X_{i,j,k}^{new}\ =\ X_{i,j,k}+r_{1}\times\left(X_{i,best,k}-\left|X_{i,j,k} \right|\right)-r_{2}\times\left(X_{i,avost,k}-\left|X_{i,j,k}\right|\right) \tag{6}\]  
where \(X_{i,j,k}^{new}\) presents the upgraded value of \(X_{i,j,k}\); \(X_{i,best,k}\) and \(X_{i,avost,k}\) denote the best solution and the worst solution of the \(i\)th variable during the \(k\)th iteration, respectively; \(r_{1}\) and \(r_{2}\) stand for two random numbers with a range of (0,1). Item \(r_{1}\times\left(X_{i,best,k}-\left|X_{i,j,k}\right|\right)\) indicates the tendency of the solution toward the best solution and item \(-r_{2}\times\left(X_{i,avost,k}-\left|X_{i,j,k}\right|\right)\) indicates the tendency to keep away from the worst solution; \(X_{i,j,k}^{new}\) is accepted if an improved objective functional value corresponding it is achieved. The following modifications are integrated into the Jaya algorithm to produce an IJaya algorithm and solve the problems of premature convergence and being trapped in local optima:  
The proposed IJaya algorithm applies tent chaotic mapping to initialize the statistical population. The initial statistical population is usually generated randomly, which makes it difficult to ensure its diversity. Chaotic maps exhibit ergodicity, certainty, and the stochastic property, which can effectively preserve statistical population diversity and prevent the algorithm from being trapped in a local optimum [48]. In this study, tent chaotic mapping is selected to generate the initial statistical population, the steps of which are as follows:  
* Generate the chaotic variable of \(X_{k}^{i}\). \[X_{k}^{i}\ =\ \frac{(X_{k}^{i}-X_{\min}^{i})}{(X_{\max}^{i}-X_{\min}^{i})}\] (7) where \(k\) is the serial number of the \(k\)-th statistical population and \(X_{\min}^{i}\) and \(X_{\max}^{i}\) stand for two extreme values of the \(i\)-th variable, which are the minimum and the maximum, respectively. * Apply tent chaotic mapping to generate the chaotic sequence: \[X_{k+1}^{i}\ =\ \left\{ \begin{array}{ll}2X_{k}^{i}&X_{k}^{i}<0.5\\ 2(1-X_{k}^{i})&X_{k}^{i}\ \geq 0.5\end{array} \right.\] (8)
* Map the chaotic sequence to the search space: \[X_{k+1}^{i}\ =\ X_{\min}^{i}+X_{k+1}^{i}(X_{\max}^{i}-X_{\min}^{i})\] (9)  
We incorporate Levy flights into the statistical population updating phase of the basic Jaya algorithm to enhance search capabilities. By employing Levy flights to update the statistical population, variables can effectively approach their best value through taking short-distance jumps together with occasional long-distance jumps [49].