**3. Methods and Results**

Metaheuristics have no special data or environment requirements and have high robustness and accuracy in this studied issue, which is also the reason that they have been frequently used. Different metaheuristics were inspired by various things when they were developed. Figure 3 categorizes the metaheuristics into four genres by the type each one simulates, i.e., evolution-based methods (GA, DE, JAYA), human social activity-based methods (GSK, SDO, TLBO), animal activity-based methods (PSO, ABC, GWO, WOA, HHO), and natural phenomenon-based methods (TGA, SOS, FPOA). In this section, the widely used metaheuristics for solving this issue, namely GA, DE, PSO, ABC, GWO, JAYA, TLBO, and WOA, are selected and briefly described. They share a high degree of similarity in the optimization process. For brevity, Figure 4 gives the general flowchart of metaheuristics.

#### *3.1. GAs*

The survival of the fittest phenomenon inspires the evolutionary algorithm, i.e., genetic algorithm. A solution is encoded as binary chromosomes, and all chromosomes are updated through iteration and fitness assessment. Selection, crossover, and mutation are the iteration's three primary operations. The first operation is related to the fitness value and usually uses roulette, random traversal sampling, and ranked selection. The second operation improves exploitation by changing the subsequence of random loci between chromosomes, and the third operation improves exploration by changing genes on individual chromosomes [62].

In [63], the authors used GA in 30XLS and 34XLS PV modules. Characteristic curves were plotted to visualize the accuracy. However, the method of validating the results was relatively simple. In [64], an adaptive genetic algorithm (AGA) was designed, employing the Pearson residual reduction and minimum mean square error reduction techniques. Relevant manufacturer data at different temperatures verified the AGA's accuracy. However, it lacked the comparison under different light intensities, and the validation was too homogeneous. For intelligent algorithms, more data-based optimization often means more accurate results. Therefore, Harrag et al. [65] combined genetic algorithms with neural networks and proposed a metaheuristic based on genetic neural networks (GNN). GNN's effectiveness was verified on the SDM and DDM with the *RMSE*.

**Figure 3.** Metaheuristic methods' genres.

Table 1 lists essential information on GA variants. Among them, the squared error for GA was 5.8297 × <sup>10</sup>−<sup>8</sup> and 3.0751 × <sup>10</sup>−7, which is highly accurate, but there is a lack of comparison algorithms to judge the competitiveness of this result. AGA did not give any numerical RMSE values. The minimum *RMSE* for GNN reached the order of 1 × <sup>10</sup><sup>−</sup>3, yet almost all recent state-of-the-art algorithms reached the order of 1 × <sup>10</sup><sup>−</sup>4. The GA variants' performance is not ranked in this section, as the current GA variants did not use the same metric function.

**Figure 4.** Metaheuristics' general flowchart.


