## 5 Results and Discussion
### Performance Analysis of FedLO  
This subsection examines the performance of the LO algorithm in the FL scenario. The focus is on comparing LO's behavior with other optimization algorithms across various datasets. Figure 5(a) presents the accuracy results of the proposed algorithm and other algorithms in the context of FL, specifically across 30 rounds, using the CIFAR-10 dataset, examining the accuracy trends across various regularization parameter values (C) in the context of FedAVG (Fed Aggregating) [47], where C represents the proportion of clients participating in the FedAVG process. A value of C = 1 indicates the involvement of all clients, C = 0.10 implies 10% participation, C = 0.20 implies 20% participation, and C = 0.50 implies 50% participation. This analysis shows that the LO algorithm consistently exhibits competitive or superior accuracy compared to other optimization algorithms under different C values in the FedAVG framework. For FedAVG, increasing C from C = 0.10 to C = 1.0 results in a steady improvement in accuracy. Specifically, at C = 1.0, FedAVG exhibits a notable increase in accuracy, reaching 0.602195028, making it a robust contender in the FL context. Similarly, at C = 0.20, FedAVG maintains a competitive edge, achieving an accuracy of 0.59187885 over the 30 rounds. Although FedAVG's accuracy improves with higher C values, the focus remains on evaluating LO's performance. Compared to optimization algorithms like PSO, SCA, and GWO, LO is consistently accurate or superior in all 30 rounds; while PSO displays gradual improvement and SCA maintains consistent accuracy, LO delivers impressive results, making it an ideal choice for FL tasks. In Figure 5(b), the performances of various algorithms in FL using the MNIST dataset over 30 rounds are compared. The proposed FedLO algorithm and other algorithms like PSO, SCA, and GWO are evaluated. The presented results highlight the superior performance of the proposed LO algorithm, FedLO, compared to other algorithms, particularly regarding accuracy. For instance, at C = 0.5, FedAVG achieves an accuracy of 96.2%, surpassing the accuracies achieved at C = 0.2 and C = 0.1. Similarly, at C = 1.0, FedAVG attains an accuracy of 98.1%, outperforming the accuracy obtained at C = 0.5. Notably, the PSO method consistently enhances its accuracy, peaking at 0.9757, indicating its adaptability and effectiveness in optimizing  
Figure 6: Model accuracy over 100 epochs for different datasets. model parameters within the FL framework. The SCA method exhibits a steady accuracy increase, reaching a maximum of 0.9778. This consistent improvement throughout rounds underscores SCA's reliability and adaptability in FL scenarios. The GWO method demonstrates a noteworthy accuracy of 0.9863, showcasing its effectiveness in optimizing model parameters. The competitive performance of GWO suggests its suitability for FL tasks. The key strength of the LO algorithm lies in its ability to exploit local areas within the search space. This strategic approach leverages the inherent capability of the algorithm as a metaheuristic, allowing it to navigate and exploit the search space efficiently. This proficiency in exploring the solution space at a more localized level enhances its adaptability, enabling the algorithm to optimize model parameters based on the nuanced characteristics of each client's data. In contrast, global algorithms like PSO and SCA may struggle to capture and exploit these localized features, contributing to the observed superior performance of the LO algorithm in the context of metaheuristic optimization. Figure 6(a) shows the performance of various algorithms in FL using the rice leaf disease dataset over 30 rounds. C = 0.1 exhibits consistent improvement, reaching a peak accuracy of 0.8043. Similarly, C = 0.2 demonstrates a positive trend, achieving a maximum accuracy of 0.8112. C = 0.5 showcases substantial improvement, reaching an accuracy of 0.8377, while C = 1.0 achieves a remarkable 0.8597 accuracy.