# Multiprocessor Fair Scheduling Based on an Improved Slime Mold Algorithm
## 5 Performance Testing and Analysis of the Improved Slime Mold Algorithm  
To test the performance of the improved slime mold algorithm, simulation experiments were conducted. The experimental environment utilized an 11 th Gen Intel(r) CoreTM i5-11400H CPU with a clock speed of 2.70 GHz (Intel Corporation, Santa Clara, CA, USA), 16 GB of RAM, and a 64-bit Windows 11 operating system. The programming language used was Python, version 3.6. Four test functions, namely F1 to F4, were selected for the experiments. F1 and F2 are unimodal functions, while F3 and F4 are multimodal functions from the CEC2019 benchmark test functions. Detailed information about these four benchmark test functions is provided in Table 2.  
The algorithm's performance was assessed using the four chosen test functions, and a comparison was made among the WOA, BOA, SSA, SMA, and the IMSMA proposed in this paper. To ensure fairness in the experiments, the testing environment and algorithm parameters were set to the same values. The swarm size was fixed at 30 for all intelligent algorithms, with a dimension of 30 and a maximum iteration of 500. The convergence curved lines of the five algorithms are displayed in Figure 3 after each benchmark function was executed 30 times. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Function** & **Function Expressions** & **Number of Peaks** & **Variable Range** \\ \hline F1 & \(f_{1}(x)=\sum_{i=1}^{x}|x_{i}+\prod_{i=1}^{x}|x_{i}|\) & Unimodal & \([-10,10]\) \\ F2 & \(f_{2}(x)=\sum_{i=1}^{x}\left(\sum_{i=1}^{x}x_{i}\right)^{2}\) & Unimodal & \([-100,100]\) \\ F3 & \(f_{3}(x)=\frac{1}{100}\sum_{i=1}^{x}x_{i}^{2}-\prod_{i=1}^{x}\left(\frac{x_{i} }{\sqrt{4}}\right)+1\) & Multimodal & \([-600,600]\) \\ F4 & \(f_{4}=\sum_{i=1}^{x}\left(x_{i}^{2}-10\cos(2\pi x_{i})+10\right)\) & Multimodal & \([-5.12,5.12]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Benchmark test functions details. Figure 3: Curves of the test functions’ convergence. Analyzing the experimental results and the convergence curves of algorithms, for function F1, from its convergence curve, it can be observed that the IMSMA starts to converge around 260 iterations, while SMA starts to converge around 280 iterations. The IMSMA exhibits a slightly faster convergence speed. From the final results of 30 experiments, the IMSMA achieves an average fitness value of 1.1214 \(\times\)\(10^{-295}\), as can be observed, which is even closer to the theoretical optimum value of 0. For function F2, the IMSMA starts to converge around 300 iterations, and it exhibits the fastest convergence speed. From Table 3, it is evident that the IMSMA obtains a fitness value of zero on average, indicating that it can find the optimal result. For function F3, the convergence curve plot shows that the SSA and BOA have better convergence performance than the IMSMA in the first 300 iterations. However, after 300 iterations, the SSA gets trapped in local optima and struggles to escape, while BOA's convergence curve becomes flatter, resulting in a slower convergence speed. On the other hand, the IMSMA and SMA quickly converge and find the optimal value around 300 iterations. Comparing the IMSMA and SMA individually, it can be observed that the IMSMA rapidly converges at around 270 iterations and finds the optimal value of zero, while SMA converges faster at around 330 iterations. Table 3 also shows that the IMSMA has an average fitness value, best value, and worst value of zero, indicating that the IMSMA outperforms the SMA. For function F4, the early versions of the SSA provide the best convergence performance, as can be seen from the graphic of the convergence curves. However, in subsequent iterations, its convergence speed becomes significantly slower. On the other hand, the IMSMA shows a good ability to escape local optima between the 200 th and 300 th iterations, and it reaches the ideal value after only 300 iterations. The SMA converges to the optimal value at around 410 iterations.