Tecniques used in this work

Least squares method

The least squares method is typically used to estimate regression parameters by minimization of the sum of squared errors (SSE). Let theexperimental region , R , be the ith-dimensional hyper-space made up of all possible values that each input variable can take;
\begin{equation} \mathbf{R}:\left\{\text{\ f}\left(x_{i}\right)\ \right|\ x_{i}\in\left[\ x_{i}^{\min}\ {,\ x}_{i}^{\max}\ \right]\ \}\ \nonumber \\ \end{equation}
In this work, the SSE is given by:
\begin{equation} \begin{matrix}SSE=\ \sum_{j=1}^{n}{\ \left(Y\left(\mathbf{R}\right)-Z\left(\mathbf{R}\right)\right)}^{2}\ \#\left(1\right)\\ \end{matrix}\nonumber \\ \end{equation}
Where , \(\mathbf{Y\ =\ f}\left(\mathbf{R}\right)\), is the response of the function to approximate that needs to be optimally addressed and\(\mathbf{Z\ =\ f}\left(\mathbf{R}\right)\), is the response of the model or function to superimpose, which has desired and well-established optimality properties, i.e. it is convex and has a global optimum.

Experimental region discretization

To generate the grid of experimental points used in the proposed method, a discretization size, or step size, ∆x can be chosen when the input variable initialization values are selected not to be integers. This step size can be user-defined, and its use is presented later on in the evaluation of the method using global optimization test functions.

Multiple starting points

The multiple starting points technique, a heuristic method, is frequently used in order to increase the chance of finding an attractive solution close to the global optimum. When a local optimization method is used, this method is executed many times using different starting points to increase the chance of convergence to a competitive solution [7].