*3.2. DEs*

DE is fast in converging, simple in structure, and easy to implement [66,67]. As a population-based metaheuristic, DE has the same three operations with GA. DE individuals achieve mutation by adding different weight coefficients to the product of the difference between two individuals. The crossover is used to produce a trial vector from the target individual and the mutant vector. The selection usually chooses a greedy selection scheme to retain fitter individuals.

In [68], an improved adaptive DE (IADE) with exponential scaling factor (*F*) and crossover rate (*CR*) based on automatic performance updates was presented. The results' accuracy was verified using PV data with different temperatures and light intensities in

terms of mean RMSE and fitted plots. Biswas et al. [61] designed a novel successful historybased DE (L-SHADE) with a linear reduced population size (NP) technique. Its parameter estimation was implemented using three particular points. The results showed that the error was almost zero. In [23], Chin et al. designed a differential evolution based on three points to improve the speed and accuracy of L-SHADE. In [69], an enhanced adaptive differential evolution (EJADE) was implemented by cross-ranking and dynamic population reduction techniques, and the algorithm's reliability was verified well. Xiong et al. [70] designed a new method (QILDE) for developing optimal value fields by adding quadratic interpolation to the crossover step. Applications of QILDE to six different PV models showed its strong competitiveness in different cases. In [71], a new method (EBLSHADE) based on SHADE with the linear population size reduction technique and greedy variation technique was designed. Its practical application in PV models demonstrated its importance in optimizing PV model parameters. In [72], dynamic control factors, including mutation and crossover, were designed and introduced into DE to form the new method called DEDCF. In [73], the authors designed a directed permutation differential evolution (DPDE) using the information on the direction of movement of populations and individuals, and applied it to a solar cell model. Hu et al. [41] designed a novel DE (RLDE) with reinforcement learning that adjusts the value of *F* by the Q-learning to achieve automatic parameter tuning, and compared RLDE with other methods, showing its superior robustness and accuracy. A heterogeneous differential evolution (HDE) was built in [74] with two improved mutation methods, a heterogeneous technique and an information exchange technique. It was demonstrated that the performance of HDE was representative in multiple dimensions through its application to the problems covered in this study. Kharchouf et al. [75] introduced Lambert's W function and metaheuristic techniques to DE for preferential *F* and *CR*, and named the method MSDE. It demonstrated high success through application. In [76], a novel DE (FADE) capable of optimizing *F* and *CR* was designed by employing fuzzy selection techniques and adaptive parameter tuning techniques. SIAE and RMSE demonstrated its excellent accuracy and robustness.

Tables 2 and 3 show the essential information and numerical metrics for each DE's variant, respectively. It is noticeable that there are many recent studies on DE, and most of them have obtained excellent performance. Regarding resource consumption, DE3P has the least, at 2500, followed by EBLSHADE, DEDCF, MSDE, EJADE, QILDE, RLDE, L-SHADE, DPDE, HDE, FADE, and IADE, respectively. Since ERRs were rarely used, data for WRT, WST, FT, and IAE were unavailable for statistics, and SIAE and MIAE are similar, we tabulate specific data for SIAE and various types of RMSE in Table 3 for comparison. To achieve a comprehensive accuracy comparison across multiple cases, the SDM, DDM, and Photowatt-PWP201 with the minimum RMSE values are used for the combined ranking. According to the FT results, MSDE (1.333) ranks first, followed by DEDCF (1.667), EJADE (4.333), QILDE (4.333), RLDE (4.333), HDE (4.667), DPDE (5.333), and EBLSHADE (5.833). However, EBLSHADE achieves excellent accuracy even though it is in last place, so future research in DE could further focus on reducing resource consumption and achieving improved performance in multiple accuracy evaluation metrics.
