# Artificial Flora (AF) Optimization Algorithm
## 2 Artificial Flora Algorithm
### The Proposed Algorithm Flow and Complexity Analysis
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Functions** & **Algorithm** & **Best** & **Mean** & **Worst** & **SD** & **Runtime** \\ \hline Sphere & PSO & \(0.022229639\) & \(10.36862151\) & \(110.8350423\) & \(21.05011998\) & \(0.407360\) \\  & ABC & \(2.22518\times 10^{-16}\) & \(3.03501\times 10^{-16}\) & \(4.3713\times 10^{-16}\) & \(5.35969\times 10^{-17}\) & \(2.988014\) \\  & AF & \(0\) & \(0\) & \(0\) & \(2.536061\) \\ Rosenbrock & PSO & \(86.00167369\) & \(19,283.23676\) & \(222,601.751\) & \(43,960.73321\) & \(0.578351\) \\  & ABC & \(0.004636871\) & \(0.071185731\) & \(0.245132434\) & \(0.065746751\) & \(3.825228\) \\  & AF & \(17.93243086\) & \(18.449849189\) & \(18.77273791\) & \(0.238206854\) & \(4.87639\) \\ Rastrigin & PSO & \(60.69641471\) & \(124.3755019\) & \(261.6735015\) & \(43,5945194\) & \(0.588299\) \\  & ABC & \(0\) & \(1.7053\times 10^{-14}\) & \(5.68434\times 10^{-14}\) & \(1.90442\times 10^{-14}\) & \(3.388325\) \\  & AF & \(0\) & \(0\) & \(0\) & \(2.730699\) \\ Schwefel & PSO & \(-1.082\times 10^{105}\) & \(-2.0346\times 10^{149}\) & \(-1.0156\times 10^{15}\) & \(4.1362\times 10^{15}\) & \(1.44870875\) \\  & ABC & \(-8379.657745\) & \(-8379.656033\) & \(-8379.618707\) & \(0.007030823\) & \(3.462507\) \\  & AF & \(-7510.128926\) & \(-11,279.67966\) & \(-177,281.186\) & \(25,371.33579\) & \(3.144982\) \\ Griewank & PSO & \(0.127645871\) & \(0.639982775\) & \(1.252113282\) & \(0.31200235\) & \(1.097885\) \\  & ABC & \(0\) & \(0\) & \(0\) & \(0\) \\ Ackley & PSO & \(0\) & \(0\) & \(0\) & \(0\) & \(2.927380\) \\  & AF & \(0\) & \(0\) & \(0\) & \(0\) & \(0\) \\ Ackley & PSO & \(19.999906463\) & \(20.04706409\) & \(20.46501638\) & \(0.103726728\) & \(0.949812\) \\  & ABC & \(2.0338\times 10^{-10}\) & \(4.5334\times 10^{-10}\) & \(1.02975\times 10^{-  
As shown in Figure 10, for Rosenbrock function, the PSO algorithm and ABC algorithm both converge at about 100 iterations, and the AF algorithm converges at about the 55 th iteration. Figure 11 illustrates that the convergence rate of the AF algorithm is still better than the other two algorithms for Rastrig in function. The AF algorithm is convergent to a good numerical solution at the 15 th iteration. The PSO algorithm converges fast, but it is easily trapped into the local optimal solution. The convergence rate of ABC is slow. Figure 10: The convergence curve of the three algorithms for Rosenbrock function in 50-dimensional space. Schwefel is a typical deceptive function, as shown in Figure 12. The convergence rate of the AF algorithm is similar to that of ABC for Schwefel function. Figure 13 shows that the AF algorithm converges at about the 23 rd iteration, and the PSO and ABC algorithms converge at about the 50 th iteration and 200 th iteration, respectively. Figure 12: The convergence curve of the three algorithms for Schwefel function in 50-dimensional space. Figure 13: The convergence curve of the three algorithms for Griewank function in 50-dimensional space. As Figure 14 shows, for Ackley function, the PSO algorithm is easily trapped into a local optimization. The convergence speed of the ABC algorithm is slow. The ABC algorithm converges at about the 900 th iteration. However, the AF algorithm can get a convergence solution at only the 40 th iteration. Figure 14: The convergence curve of the three algorithms for Ackley function in 50-dimensional space. Figure 15: The convergence curve of the three algorithms for Sphere function in 100-dimensional space. Figure 16: The convergence curve of the three algorithms for Rosenbrock function in 100-dimensional space. Figure 17: The convergence curve of the three algorithms for Rastrigin function in 100-dimensional space. Figure 19: The convergence curve of the three algorithms for Griewank function in 100-dimensional space. Figure 10:0 The convergence curve of the three algorithms for Schwefel function in 100-dimensional space. It can be seen from Figures 15-20 that the trend of convergence curves in 100-dimensional space is similar to that in 50-dimensional space.