## 4 Experiments and Results
### Analysis of Convergence Behavior  
In the optimization process of LO, the search agents share their information and exploit the best femur to scan the search space effectively to reach the most promising regions in the search space. The search agents in the early stage of optimization allocate abruptly positions and then gradually converge. Researchers in [69] stated such behavior in other population-based algorithms can lead to achieving the desired convergence. Convergence curves of LO, ABC, SSA, BAT, FPA, and JAYA are plotted in Figure 7 based on the average best-so-far in each iteration over 30 runs for some of the unimodal and multimodal benchmark functions in this study. It can be observed that the convergence trend of LO is competitive with other stat0E-of-th0E-art meta-heuristic algorithms. Moreover, the convergence rate of LO based on best and average fitness is plotted in Figures 8 and 9. There is a descending pattern in the average fitness throughout the growth of the iterations in these figures' second and fourth columns. The successful convergence of LO in optimizing benchmark functions is owing to its search capabilities in terms of leap up (exploitation) and dance hub (exploration) that attractively improve the trajectory of lemurs toward optimality. Further, the convergence curves in Figures 8 and 9 demonstrate that the LO algorithm produces better quality solutions throughout the optimization iterations. Figure 7: LO algorithm convergence plots with the other swarm\(-\)based algorithms. Figure 8: Functions and convergence plots. Figure 9: Functions and convergence plots. Figure 10 illustrates the average rankings of the proposed algorithm and other comparative algorithms according to the average of the results. These rankings are calculated using [PERSON]'s test. It should be noted that the lower value of the rankings, the better performance. It can be seen that the LEO-MPA is placed first by getting the lowest rankings, while the proposed LO is ranked third. By following [55], the signed Wilcoxon statistical test [70] was used to determine if there is a significant improvement between the LO algorithm and the other comparative algorithms. For each algorithm, the best results of 30 runs are used in the Wilcoxon signed rank with \(p\) value equal to 0.05. The proposed LO's improvements were tested to see whether they happened by chance, or were statistically significant using this test. The \(p\) value was determined using the statistically signed Wilcoxon statistical  
Figure 11 shows the time-average rankings of the proposed lo and other comparative algorithms according to the average time of all 30 runs. This figure clearly shows that the proposed LEO-MPA takes more time to finish than other algorithms. In contrast, the proposed LO is ranked first. The results of this section revealed various characteristics of the proposed LO algorithm. The location updating mechanism of lemurs using Equation (3) case number one is responsible for LO's high exploration ability. During the initial steps of the iterations, this equation allows lemurs to move around the best nearest lemur. The rest of the iterations emphasize high exploitation and convergence, which come from Equation (3) case number two. This equation enables the lemurs to quickly reposition themselves around or step towards the current global best lemur. It is worth mentioning here that the exploration and exploitation phases are completed separately, and the LO exhibits convergence speed and high local optima avoidance at the same time. Besides, the LO is utilized one formula to manage these two phases and update the position of lemurs. The performance of LO in real engineering problems is verified in the following section.