*2.2. Objective Function*

The key deliverables in this work are the optimization of unknown specifications for both SDM and DDM models to reduce the error between the experimental and estimated data. The objective function for error used here is the same as the one that authors have used previously in [23–25]:

$$\text{RMSE} = \sqrt{\frac{1}{k} \sum\_{N=1}^{k} f\_f(V\_{l\prime}, I\_{l\prime\prime})} \tag{2}$$

, ௦ ൯ ⎠

 where *V<sup>l</sup>* and *I<sup>l</sup>* are the measured voltage and current of the PV module. The parameter *k* stands for the number of experimental data sets. The best solution found by the TSA is represented by a vector *X*.

ேୀଵ

For the PV panel module model,

$$\begin{pmatrix} \begin{pmatrix} \mathbf{f}\_{\text{single}}(\mathbf{V}\_{l\prime} \ \mathbf{I}\_{l\prime} \ \mathbf{X}) \end{pmatrix} = \begin{pmatrix} I\_p - I\_{SD} \begin{pmatrix} \frac{q\left(\frac{V\_l}{N\delta} + \frac{R\_{\text{sf}}I\_l}{Np}\right)}{a\_1 k\_B T} \end{pmatrix} - 1 \end{pmatrix} - \frac{\frac{V\_l}{N\delta} + \frac{R\_{\text{sf}}I\_l}{Np}}{R\_{\text{sl}}} - \frac{I\_l}{N\_p} \\\ \begin{pmatrix} \mathbf{X} = \ I\_{p\prime} \ I\_{SD\prime} \ a\_\prime \ R\_{\text{sf}} \ R\_{\text{sl}} \end{pmatrix} \end{pmatrix} \tag{3}$$

### ⎝ **3. Tunicate Swarm Algorithm**

In [6], authors have proposed a new metaheuristic algorithm known as the Tunicate swarm algorithm. These are visible from a few meters' distance and create a pale blue– green bioluminescent light which is intense in nature. These are cylindrically shaped and must open at one end only when they grow to the size of a few millimeters. Each tunic consists of growing a gelatinous tunic which helps to join all individuals. These tunicates are opened at one end only, and they grow up to a few millimeters in size. In every tunicate, a gelatinous tunic grows, which helps all the individuals to join. Each tunicate, through atrial syphons, generates jet propulsion from its opening by receiving water from the adjacent sea. To understand the actions of jet propulsion using the mathematical model, the tunicate should fulfill three conditions: prevent collisions between candidate solutions, step more toward the location of the best solution, and stick close to the best solution. Figure 2 depicts the process flow chart of TSA for parameter extraction.

൫ = , ௌ, , <sup>௦</sup>

**Figure 2.** Process flow diagram of the Tunicate swarm algorithm (TSA).
