**4. Results and Discussion**

In this section, a benchmark test research approach was used to evaluate the proposed algorithm in the case of parameter identification for PEMFC. Table 1 displays the ten benchmark test functions, one to seven of which are unimodal and the remaining functions are multimodal. Some well-known meta-heuristic algorithms, such as ant lion optimizer (ALO) [51], dragonfly algorithm (DA) [52], grasshopper optimization algorithm (GOA) [53], and multiverse optimization (MVO) [54] are especially compared to assess the precision and efficiency of the suggested algorithm. The statistical outcomes of benchmark test functions are shown in Table 2. In this research paper, the benchmark functions are denoted by the letter "F" accompanied by a number (e.g., F1).

According to Table 2, the proposed algorithm has the least mean and standard deviation (SD) values except for the F6. In the case of F6, ALO generates the best optimized value. Based on the benchmark test function, it is asserted that the proposed algorithm outperforms and outperforms the other compared algorithms in terms of effectiveness and precision.


