**2. Mathematical formulation**

Generally, all the optimization design having the following steps:


The design of optimization will be expressed in a standard form as follows:

$$\text{Objective Function} = f(\mathbf{X}) = \text{maximizing or minimizing} \ (\text{cost}) \tag{1}$$

Subjected to

$$In equality \text{ constraints for}$$

$$\text{minimizing objective function } (pnumber) \ a\_x(\mathbf{X}) \le \mathbf{0}, \text{ where } \mathbf{z} = \mathbf{1}, \mathbf{2}, \mathbf{3}, \dots, p$$

$$\begin{aligned} \text{Inequality constraints for} \\ \text{maximizing objective function} &(p \text{ number}) \ a\_x(\mathbf{X}) \ge 0, \text{ where } \mathbf{z} = \mathbf{1}, \mathbf{2}, \mathbf{3}, \dots, p \end{aligned} \tag{3}$$

$$\text{Equality constraints } (q \text{ number}) \, b\_z(X) = 0, \text{ where } z = 1, 2, 3, \dots, q \tag{4}$$

$$\text{Input or design variables defined as } \text{x}\_i \text{, where } i = 1, 2, 3, \dots, n \tag{5}$$

$$\begin{aligned} \text{Input or design variable expressed as } X = \begin{Bmatrix} \mathbf{x}\_1 \\ \mathbf{x}\_2 \\ \mathbf{x}\_3 \\ \vdots \\ \mathbf{\cdot} \\ \vdots \\ \mathbf{\cdot} \end{Bmatrix} \end{aligned} \tag{6}$$

The design variables can also be expressed as *x<sup>l</sup> <sup>i</sup>* <sup>¼</sup> *xi* <sup>¼</sup> *xu <sup>i</sup>* . Here *xl <sup>i</sup>* is the lower limit and *xu <sup>i</sup>* is the upper limit.
