# Adaptive Mutation Dynamic Search Fireworks Algorithm
## 4 Simulation Results and Analysis
### Simulation Results and Analysis
#### 4.2.2 Comparison of AMdynFWA with FWA-Based Algorithms
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Functions**} & **EFWA** & **AFWA** & **dynFWA** & **AMdynFWA** \\ \cline{2-5}  & **Mean Error** & **Mean Error** & **Mean Error** & **Mean Error** \\ \hline f1 & \(7.82\times 10^{-2}\) & \(\mathbf{0}\) & \(\mathbf{0}\) & \(\mathbf{0}\) \\ f2 & \(5.43\times 10^{5}\) & \(8.93\times 10^{5}\) & \(7.87\times 10^{5}\) & \(\mathbf{3.84\times 10^{5}}\) \\ f3 & \(1.26\times 10^{8}\) & \(1.26\times 10^{8}\) & \(1.57\times 10^{8}\) & \(\mathbf{8.32\times 10^{7}}\) \\ f4 & \(1.09\) & \(11.5\) & \(12.8\) & \(\mathbf{2.02\times 10^{-2}}\) \\ f5 & \(7.9\times 10^{-2}\) & \(6.04\times 10^{-4}\) & \(5.42\times 10^{-4}\) & \(\mathbf{1.86\times 10^{-4}}\) \\ f6 & \(34.9\) & \(29.9\) & \(31.5\) & \(\mathbf{23.9}\) \\ f7 & \(1.33\times 10^{2}\) & \(9.19\times 10^{1}\) & \(1.03\times 10^{2}\) & \(\mathbf{8.85\times 10^{1}}\) \\ f8 & \(2.10\times 10^{1}\) & \(\mathbf{2.09\times 10^{1}}\) & \(\mathbf{2.09\times 10^{1}}\) & \(\mathbf{2.09\times 10^{1}}\) \\ f9 & \(3.19\times 10^{1}\) & \(2.48\times 10^{1}\) & \(2.56\times 10^{1}\) & \(\mathbf{2.28\times 10^{1}}\) \\ f10 & \(8.29\times 10^{-1}\) & \(4.73\times 10^{-2}\) & \(4.20\times 10^{-2}\) & \(\mathbf{3.18\times 10^{-2}}\) \\ f11 & \(4.22\times 10^{2}\) & \(1.05\times 10^{2}\) & \(1.07\times 10^{2}\) & \(\mathbf{9.75\times 10^{1}}\) \\ f12 & \(6.33\times 10^{2}\) & \(1.52\times 10^{2}\) & \(1.56\times 10^{2}\) & \(\mathbf{1.25\times 10^{2}}\) \\ f13 & \(4.51\times 10^{2}\) & \(2.36\times 10^{2}\) & \(2.44\times 10^{2}\) & \(\mathbf{1.63\times 10^{2}}\) \\ f14 & \(4.16\times 10^{3}\) & \(2.97\times 10^{3}\) & \(2.95\times 10^{3}\) & \(\mathbf{2.64\times 10^{3}}\) \\ f15 & \(4.13\times 10^{3}\) & \(3.81\times 10^{3}\) & \(\mathbf{3.71\times 10^{3}}\) & \(3.87\times 10^{3}\) \\ f16 & \(5.92\times 10^{-1}\) & \(4.97\times 10^{-1}\) & \(4.77\times 10^{-1}\) & \(\mathbf{3.4\times 10^{-1}}\) \\ f17 & \(3.10\times 10^{2}\) & \(1.45\times 10^{2}\) & \(1.48\times 10^{2}\) & \(\mathbf{1.25\times 10^{2}}\) \\ f18 & \(\mathbf{1.75\times 10^{2}}\) & \(\mathbf{1.75\times 10^{2}}\) & \(1.89\times 10^{2}\) & \(1.77\times 10^{2}\) \\ f19 & \(12.3\) & \(6.92\) & \(6.87\) & \(\mathbf{6.55}\) \\ f20 & \(14.6\) & \(\mathbf{13}\) & \(\mathbf{13}\) & \(\mathbf{13}\) \\ f21 & \(3.24\times 10^{2}\) & \(3.16\times 10^{2}\) & \(\mathbf{2.92\times 10^{2}}\) & \(3.51\times 10^{2}\) \\ f22 & \(5.75\times 10^{3}\) & \(3.45\times 10^{3}\) & \(3.41\times 10^{3}\) & \(\mathbf{3.12\times 10^{3}}\) \\ f23 & \(5.74\times 10^{3}\) & \(4.70\times 10^{3}\) & \(\mathbf{4.55\times 10^{3}}\) & \(4.67\times 10^{3}\) \\ f24 & \(3.37\times 10^{2}\) & \(2.70\times 10^{2}\) & \(2.72\times 10^{2}\) & \(\mathbf{2.65\times 10^{2}}\) \\ f25 & \(3.56\times 10^{2}\) & \(2.99\times 10^{2}\) & \(2.97\times 10^{2}\) & \(\mathbf{2.87\times 10^{2}}\) \\ f26 & \(3.21\times 10^{2}\) & \(2.73\times 10^{2}\) & \(2.62\times 10^{2}\) & \(\mathbf{2.12\times 10^{2}}\) \\ f27 & \(1.28\times 10^{3}\) & \(9.72\times 10^{2}\) & \(9.92\times 10^{2}\) & \(\mathbf{8.87\times 10^{2}}\) \\ f28 & \(4.34\times 10^{2}\) & \(4.37\times 10^{2}\) & \(\mathbf{3.40\times 10^{2}}\) & \(3.62\times 10^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean errors and total number of rank 1 achieved by EFWA, AFWA, dynFWA, and AMdynFWA. Figure 3: The EFWA, AFWA, dynFWA, and AMdynFWA run-time cost. The results from Figure 3 indicate that the average run-time cost of EFWA is the most expensive among the four algorithms. The time cost of AFWA is the least, but the run-time cost of AMdynFWA is almost the same compared with AFWA. The run-time cost of AMdynFWA is less than that of dynFWA. Taking into account the results from Table 3, AMdynFWA performs significantly better than the other three algorithms. To evaluate whether the AMdynFWA results were significantly different from those of the EFWA, AFWA, and dynFWA, the AMdynFWA mean results during the iteration for each test function were compared with those of the EFWA, AFWA, and dynFWA.