# Improved Brain Storm Optimization Algorithm Based on Flock Decision Mutation Strategy
## 4 Results
### Simulation Results and Analysis
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**BFs** & \multicolumn{2}{c}{**BSO**} & **ADMBSO** & **GDBSO** & **DDCBSO** & **FDIBSO** \\ \hline \multirow{2}{*}{C1} & Mean & \(7.48\times 10^{9}\) & \(3.22\times 10^{3}\) & \(8.49\times 10^{3}\) & \(2.75\times 10^{3}\) & \(\mathbf{1.06\times 10^{3}}\) \\  & Min & \(4.83\times 10^{9}\) & \(3.78\times 10^{2}\) & \(2.65\times 10^{3}\) & \(2.68\times 10^{3}\) & \(2.83\times 10^{2}\) \\ \hline \multirow{2}{*}{C3} & Mean & \(1.97\times 10^{5}\) & \(1.23\times 10^{5}\) & \(2.16\times 10^{5}\) & \(1.58\times 10^{5}\) & \(\mathbf{3.73\times 10^{4}}\) \\  & Min & \(1.58\times 10^{5}\) & \(9.89\times 10^{4}\) & \(1.73\times 10^{5}\) & \(1.02\times 10^{5}\) & \(1.74\times 10^{4}\) \\ \hline \multirow{2}{*}{C4} & Mean & \(1.75\times 10^{3}\) & \(5.26\times 10^{2}\) & \(5.31\times 10^{2}\) & \(\mathbf{2.45\times 10^{2}}\) & \(6.18\times 10^{2}\) \\  & Min & \(1.13\times 10^{3}\) & \(4.33\times 10^{2}\) & \(4.63\times 10^{2}\) & \(1.71\times 10^{2}\) & \(5.61\times 10^{2}\) \\ \hline \multirow{2}{*}{C5} & Mean & \(8.16\times 10^{2}\) & \(\mathbf{6.09\times 10^{2}}\) & \(9.33\times 10^{2}\) & \(1.10\times 10^{3}\) & \(8.41\times 10^{2}\) \\  & Min & \(7.78\times 10^{2}\) & \(5.83\times 10^{2}\) & \(9.16\times 10^{2}\) & \(1.06\times 10^{3}\) & \(8.22\times 10^{2}\) \\ \hline \multirow{2}{*}{C6} & Mean & \(6.60\times 10^{2}\) & \(\mathbf{6.01\times 10^{2}}\) & \(6.05\times 10^{2}\) & \(6.83\times 10^{2}\) & \(6.55\times 10^{2}\) \\  & Min & \(6.55\times 10^{2}\) & \(6.01\times 10^{2}\) & \(6.03\times 10^{2}\) & \(6.73\times 10^{2}\) & \(6.51\times 10^{2}\) \\ \hline \multirow{2}{*}{C7} & Mean & \(1.68\times 10^{3}\) & \(\mathbf{9.08\times 10^{2}}\) & \(1.23\times 10^{3}\) & \(1.95\times 10^{3}\) & \(1.54\times 10^{3}\) \\  & Min & \(1.53\times 10^{3}\) & \(8.85\times 10^{2}\) & \(1.19\times 10^{3}\) & \(1.84\times 10^{3}\) & \(1.33\times 10^{3}\) \\ \hline \multirow{2}{*}{C8} & Mean & \(1.12\times 10^{3}\) & \(\mathbf{9.27\times 10^{2}}\) & \(1.23\times 10^{3}\) & \(1.43\times 10^{3}\) & \(1.10\times 10^{3}\) \\  & Min & \(1.04\times 10^{3}\) & \(9.91\times 10^{2}\) & \(1.19\times 10^{3}\) & \(1.37\times 10^{3}\) & \(1.07\times 10^{3}\) \\ \hline \multirow{2}{*}{C9} & Mean & \(1.15\times 10^{4}\) & \(\mathbf{1.18\times 10^{3}}\) & \(1.99\times 10^{3}\) & \(3.00\times 10^{4}\) & \(9.31\times 10^{3}\) \\  & Min & \(8.24\times 10^{3}\) & \(9.13\times 10^{2}\) & \(1.10\times 10^{3}\) & \(2.31\times 10^{4}\) & \(6.43\times 10^{3}\) \\ \hline \multirow{2}{*}{C10} & Mean & \(8.28\times 10^{3}\) & \(\mathbf{7.94\times 10^{3}}\) & \(1.48\times 10^{4}\) & \(1.43\times 10^{4}\) & \(8.23\times 10^{3}\) \\  & Min & \(7.01\times 10^{3}\) & \(6.48\times 10^{3}\) & \(1.37\times 10^{4}\) & \(1.26\times 10^{4}\) & \(6.83\times 10^{3}\) \\ \hline \multirow{2}{*}{C11} & Mean & \(4.98\times 10^{3}\) & \(\mathbf{1.32\times 10^{3}}\) & \(1.49\times 10^{3}\) & \(2.29\times 10^{4}\) & \(1.44\times 10^{3}\) \\  & Min & \(2.40\times 10^{3}\) & \(1.21\times 10^{3}\) & \(1.42\times 10^{3}\) & \(1.23\times 10^{4}\) & \(1.29\times 10^{3}\) \\ \hline \multirow{2}{*}{C12} & Mean & \(3.51\times 10^{6}\) & \(2.19\times 10^{6}\) & \(\mathbf{1.62\times 10^{6}}\) & \(4.74\times 10^{6}\) & \(2.28\times 10^{5}\) \\  & Min & \(2.01\times 10^{7}\) & \(2.57\times 10^{5}\) & \(4.93\times 10^{5}\) & \(2.55\times 10^{5}\) & \(1.03\times 10^{5}\) \\ \hline \multirow{2}{*}{C13} & Mean & \(7.28\times 10^{4}\) & \(\mathbf{5.69\times 10^{3}}\) & \(6.07\times 10^{3}\) & \(1.79\times 10^{4}\) & \(9.74\times 10^{4}\) \\  & Min & \(2.67\times 10^{4}\) & \(2.23\times 10^{3}\) & \(1.73\times 10^{3}\) & \(7.89\times 10^{3}\) & \(2.47\times 10^{4}\) \\ \hline \multirow{2}{*}{C14} & Mean & \(7.82\times 10^{5}\) & \(1.39\times 10^{5}\) & \(2.15\times 10^{5}\) & \(2.12\times 10^{5}\) & \(\mathbf{1.62\times 10^{5}}\) \\  & Min & \(3.69\times 10^{4}\) & \(4.34\times 10^{4}\) & \(4.42\times 10^{4}\) & \(5.88\times 10^{6}\) & \(1.56\times 10^{3}\) \\ \hline \multirow{2}{*}{C15} & Mean & \(2.57\times 10^{4}\) & \(7.29\times 10^{3}\) & \(9.65\times 10^{3}\) & \(4.03\times 10^{3}\) & \(\mathbf{2.46\times 10^{3}}\) \\  & Min & \(1.80\times 10^{4}\) & \(1.73\times 10^{3}\) & \(2.00\times 10^{3}\) & \(1.59\times 10^{9}\) & \(1.73\times 10^{3}\) \\ \hline \multirow{2}{*}{C16} & Mean & \(3.86\times 10^{3}\) & \(3.63\times 10^{3}\) & \(4.96\times 10^{3}\) & \(6.87\times 10^{3}\) & \(\mathbf{3.58\times 10^{3}}\) \\  & Min & \(3.24\times 10^{3}\) & \(3.32\times 10^{3}\) & \(4.38\times 10^{3}\) & \(5.93\times 10^{3}\) & \(3.04\times 10^{3}\) \\ \hline \multirow{2}{*}{C17} & Mean & \  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**BEs** & & **MSWQA** & **HOA** & **WMFO** & **MFO-SFR** & **FDIBSO** \\ \hline \multirow{2}{*}{C1} & Mean & \(9.50\times 10^{3}\) & \(3.03\times 10^{9}\) & \(3.82\times 10^{3}\) & \(1.79\times 10^{3}\) & \(\mathbf{1.36\times 10^{3}}\) \\  & Min & \(3.90\times 10^{3}\) & \(2.20\times 10^{9}\) & \(2.10\times 10^{4}\) & \(1.01\times 10^{2}\) & \(1.02\times 10^{2}\) \\ \hline \multirow{2}{*}{C3} & Mean & \(9.10\times 10^{3}\) & \(3.08\times 10^{4}\) & \(\mathbf{3.91\times 10^{2}}\) & \(1.31\times 10^{4}\) & \(1.70\times 10^{3}\) \\  & Min & \(6.65\times 10^{3}\) & \(2.03\times 10^{4}\) & \(3.01\times 10^{2}\) & \(7.51\times 10^{3}\) & \(7.02\times 10^{3}\) \\ \hline \multirow{2}{*}{C4} & Mean & \(4.84\times 10^{2}\) & \(1.05\times 10^{3}\) & \(\mathbf{4.81\times 10^{2}}\) & \(4.91\times 10^{2}\) & \(4.88\times 10^{2}\) \\  & Min & \(4.81\times 10^{2}\) & \(7.60\times 10^{2}\) & \(4.25\times 10^{2}\) & \(4.70\times 10^{2}\) & \(4.69\times 10^{2}\) \\ \hline \multirow{2}{*}{C5} & Mean & \(6.08\times 10^{2}\) & \(7.94\times 10^{2}\) & \(6.74\times 10^{2}\) & \(\mathbf{5.23\times 10^{2}}\) & \(6.98\times 10^{2}\) \\  & Min & \(5.93\times 10^{2}\) & \(7.61\times 10^{2}\) & \(6.23\times 10^{2}\) & \(5.11\times 10^{2}\) & \(6.54\times 10^{2}\) \\ \hline \multirow{2}{*}{C6} & Mean & \(6.01\times 10^{2}\) & \(6.61\times 10^{2}\) & \(6.37\times 10^{2}\) & \(\mathbf{6.00\times 10^{2}}\) & \(6.46\times 10^{2}\) \\  & Min & \(6.01\times 10^{2}\) & \(6.50\times 10^{2}\) & \(6.14\times 10^{2}\) & \(6.00\times 10^{2}\) & \(6.34\times 10^{2}\) \\ \hline \multirow{2}{*}{C7} & Mean & \(8.08\times 10^{2}\) & \(\mathbf{1.03\times 10^{2}}\) & \(1.06\times 10^{3}\) & \(7.67\times 10^{2}\) & \(1.01\times 10^{3}\) \\  & Min & \(7.82\times 10^{2}\) & \(9.98\times 10^{2}\) & \(6.25\times 10^{2}\) & \(7.46\times 10^{2}\) & \(9.19\times 10^{2}\) \\ \hline \multirow{2}{*}{C8} & Mean & \(1.10\times 10^{3}\) & \(1.06\times 10^{3}\) & \(9.54\times 10^{2}\) & \(\mathbf{8.21\times 10^{2}}\) & \(9.36\times 10^{2}\) \\  & Min & \(9.59\times 10^{2}\) & \(1.04\times 10^{3}\) & \(8.55\times 10^{2}\) & \(8.09\times 10^{2}\) & \(9.09\times 10^{2}\) \\ \hline \multirow{2}{*}{C9} & Mean & \(9.93\times 10^{2}\) & \(4.29\times 10^{3}\) & \(4.54\times 10^{3}\) & \(\mathbf{9.04\times 10^{2}}\) & \(3.21\times 10^{3}\) \\  & Min & \(8.38\times 10^{2}\) & \(2.67\times 10^{3}\) & \(1.68\times 10^{3}\) & \(9.01\times 10^{2}\) & \(2.39\times 10^{3}\) \\ \hline \multirow{2}{*}{C10} & Mean & \(7.76\times 10^{3}\) & \(8.34\times 10^{3}\) & \(5.19\times 10^{3}\) & \(\mathbf{4.06\times 10^{3}}\) & \(5.44\times 10^{3}\) \\  & Min & \(5.03\times 10^{3}\) & \(7.55\times 10^{3}\) & \(3.76\times 10^{2}\) & \(2.46\times 10^{3}\) & \(4.83\times 10^{3}\) \\ \hline \multirow{2}{*}{C11} & Mean & \(\mathbf{1.08\times 10^{3}}\) & \(1.80\times 10^{3}\) & \(1.25\times 10^{3}\) & \(1.14\times 10^{3}\) & \(1.26\times 10^{3}\) \\  & Min & \(1.05\times 10^{3}\) & \(1.70\times 10^{3}\) & \(1.17\times 10^{3}\) & \(1.11\times 10^{3}\) & \(1.13\times 10^{3}\) \\ \hline \multirow{2}{*}{C12} & Mean & \(5.15\times 10^{4}\) & \(3.76\times 10^{8}\) & \(1.01\times 10^{5}\) & \(1.51\times 10^{5}\) & \(\mathbf{2.75\times 10^{4}}\) \\  & Min & \(3.32\times 10^{4}\) & \(2.82\times 10^{8}\) & \(6.93\times 10^{3}\) & \(2.04\times 10^{4}\) & \(1.12\times 10^{4}\) \\ \hline \multirow{2}{*}{C13} & Mean & \(1.98\times 10^{4}\) & \(1.05\times 10^{8}\) & \(6.66\times 10^{3}\) & \(6.41\times 10^{3}\) & \(\mathbf{3.72\times 10^{3}}\) \\  & Min & \(1.52\times 10^{4}\) & \(3.30\times 10^{7}\) & \(1.40\times 10^{3}\) & \(1.69\times 10^{3}\) & \(2.53\times 10^{3}\) \\ \hline \multirow{2}{*}{C14} & Mean & \(2.39\times 10^{4}\) & \(1.34\times 10^{5}\) & \(1.41\times 10^{4}\) & \(8.20\times 10^{3}\) & \(\mathbf{1.46\times 10^{3}}\) \\  & Min & \(9.40\times 10^{3}\) & \(5.22\times 10^{4}\) & \(3.03\times 10^{3}\) & \(2.02\times 10^{3}\) & \(1.45\times 10^{3}\) \\ \hline \multirow{2}{*}{C15} & Mean & \(5.18\times 10^{3}\) & \(3.14\times 10^{7}\) & \(1.16\times 10^{4}\) & \(5.61\times 10^{3}\) & \(\mathbf{1.71\times 10^{3}}\) \\  & Min & \(4.54\times 10^{3}\) & \(8.14\times 10^{6}\) & \(1.61\times 10^{3}\) & \(1.52\times 10^{3}\) & \(1.61\times 10^{3}\) \\ \hline \multirow{2}{*}{C16} & Mean & \(3.78\times 10^{3}\) & \(3.79\times 10^{3}\) & \(2.62\times 10^{3}\) & \(\mathbf{1.86\times 10^{3}}\) & \(2.61\times 10^{3}\) \\  & Min & \(2.82\times 10^{3}\) & \(3.42\times 10^{3}\) & \(2.07\times 10^{3}\) & \(1.62\times 10^{3}\) & \(2.09\times 10^{3}\) \\ \hline \multirow{2}{*}{C17} & Mean & \(2.89\times 10^  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**BFs** & & **MSWOA** & **HOA** & **WMFO** & **MFO-SFR** & **FDIBSO** \\ \hline \multirow{2}{*}{C1} & Mean & \(1.46\times 10^{8}\) & \(1.15\times 10^{10}\) & \(4.26\times 10^{3}\) & \(3.46\times 10^{4}\) & \(\mathbf{1.06\times 10^{3}}\) \\  & Min & \(6.34\times 10^{7}\) & \(8.35\times 10^{9}\) & \(1.05\times 10^{2}\) & \(9.39\times 10^{3}\) & \(2.83\times 10^{2}\) \\ \hline \multirow{2}{*}{C3} & Mean & \(2.03\times 10^{5}\) & \(8.23\times 10^{4}\) & \(\mathbf{9.95\times 10^{2}}\) & \(5.50\times 10^{4}\) & \(3.37\times 10^{4}\) \\  & Min & \(9.34\times 10^{4}\) & \(6.99\times 10^{4}\) & \(3.22\times 10^{2}\) & \(4.22\times 10^{4}\) & \(1.74\times 10^{4}\) \\ \hline \multirow{2}{*}{C4} & Mean & \(\mathbf{5.06\times 10^{2}}\) & \(2.59\times 10^{3}\) & \(5.39\times 10^{2}\) & \(5.87\times 10^{2}\) & \(6.18\times 10^{2}\) \\  & Min & \(4.28\times 10^{2}\) & \(2.06\times 10^{3}\) & \(4.96\times 10^{2}\) & \(5.20\times 10^{2}\) & \(5.61\times 10^{2}\) \\ \hline \multirow{2}{*}{C5} & Mean & \(\mathbf{5.47\times 10^{2}}\) & \(1.05\times 10^{3}\) & \(8.61\times 10^{2}\) & \(5.62\times 10^{2}\) & \(8.41\times 10^{2}\) \\  & Min & \(5.18\times 10^{2}\) & \(1.01\times 10^{3}\) & \(7.21\times 10^{2}\) & \(5.32\times 10^{2}\) & \(8.22\times 10^{2}\) \\ \hline \multirow{2}{*}{C6} & Mean & \(6.29\times 10^{2}\) & \(6.75\times 10^{2}\) & \(6.51\times 10^{2}\) & \(\mathbf{6.00\times 10^{2}}\) & \(6.55\times 10^{3}\) \\  & Min & \(6.21\times 10^{2}\) & \(6.65\times 10^{2}\) & \(6.29\times 10^{2}\) & \(6.00\times 10^{2}\) & \(6.51\times 10^{2}\) \\ \hline \multirow{2}{*}{C7} & Mean & \(\mathbf{7.81\times 10^{2}}\) & \(1.34\times 10^{3}\) & \(1.46\times 10^{3}\) & \(8.68\times 10^{2}\) & \(1.54\times 10^{3}\) \\  & Min & \(7.54\times 10^{2}\) & \(1.29\times 10^{3}\) & \(1.20\times 10^{3}\) & \(8.10\times 10^{2}\) & \(1.33\times 10^{3}\) \\ \hline \multirow{2}{*}{C8} & Mean & \(1.41\times 10^{3}\) & \(1.35\times 10^{3}\) & \(1.13\times 10^{3}\) & \(\mathbf{8.61\times 10^{2}}\) & \(1.10\times 10^{3}\) \\  & Min & \(8.10\times 10^{2}\) & \(1.28\times 10^{3}\) & \(1.02\times 10^{3}\) & \(8.32\times 10^{3}\) & \(1.07\times 10^{3}\) \\ \hline \multirow{2}{*}{C9} & Mean & \(1.46\times 10^{3}\) & \(2.15\times 10^{4}\) & \(1.19\times 10^{4}\) & \(\mathbf{9.24\times 10^{2}}\) & \(9.31\times 10^{3}\) \\  & Min & \(1.11\times 10^{3}\) & \(1.42\times 10^{4}\) & \(5.50\times 10^{3}\) & \(9.07\times 10^{2}\) & \(6.43\times 10^{3}\) \\ \hline \multirow{2}{*}{C10} & Mean & \(2.21\times 10^{3}\) & \(1.47\times 10^{4}\) & \(7.76\times 10^{3}\) & \(\mathbf{6.53\times 10^{3}}\) & \(8.23\times 10^{3}\) \\  & Min & \(2.03\times 10^{3}\) & \(1.32\times 10^{4}\) & \(6.40\times 10^{3}\) & \(5.14\times 10^{3}\) & \(6.83\times 10^{3}\) \\ \hline \multirow{2}{*}{C11} & Mean & \(1.26\times 10^{3}\) & \(3.78\times 10^{3}\) & \(1.30\times 10^{3}\) & \(\mathbf{1.26\times 10^{3}}\) & \(1.44\times 10^{3}\) \\  & Min & \(1.16\times 10^{3}\) & \(3.24\times 10^{3}\) & \(1.20\times 10^{3}\) & \(1.15\times 10^{3}\) & \(1.29\times 10^{3}\) \\ \hline \multirow{2}{*}{C12} & Mean & \(1.27\times 10^{7}\) & \(2.42\times 10^{9}\) & \(5.72\times 10^{5}\) & \(1.87\times 10^{6}\) & \(\mathbf{2.28\times 10^{5}}\) \\  & Min & \(8.56\times 10^{6}\) & \(1.71\times 10^{9}\) & \(1.34\times 10^{5}\) & \(1.08\times 10^{6}\) & \(1.03\times 10^{5}\) \\ \hline \multirow{2}{*}{C13} & Mean & \(7.87\times 10^{4}\) & \(5.70\times 10^{8}\) & \(8.90\times 10^{3}\) & \(\mathbf{5.36\times 10^{3}}\) & \(9.74\times 10^{4}\) \\  & Min & \(4.86\times 10^{4}\) & \(4.31\times 10^{8}\) & \(2.61\times 10^{3}\) & \(1.75\times 10^{3}\) & \(2.47\times 10^{4}\) \\ \hline \multirow{2}{*}{C14} & Mean & \(2.59\times 10^{3}\) & \(8.32\times 10^{5}\) & \(3.67\times 10^{4}\) & \(4.02\times 10^{4}\) & \(\mathbf{1.62\times 10^{3}}\) \\  & Min & \(2.54\times 10^{3}\) & \(2.22\times 10^{5}\) & \(1.15\times 10^{4}\) & \(1.20\times 10^{4}\) & \(1.56\times 10^{3}\) \\ \hline \multirow{2}{*}{C15} & Mean & \(3.21\times 10^{3}\) & \(2.30\times 10^{8}\) & \(7.07\times 10^{3}\) & \(2.96\times 10^{3}\) & \(\mathbf{2.46\times 10^{3}}\) \\  & Min & \(2.81\times 10^{3}\) & \(9.91\times 10^{7}\) & \(1.94\times 10^{3}\) & \(1.53\times 10^{3}\) & \(1.73\times 10^{3}\) \\ \hline \multirow{2}{*}{C16} & Mean & \(3.71\times 10^{3}\) & \(5.18\times 10^{3}\) & \(3.58\times 10^{3}\) & \(\mathbf{2.61\times 10^{3}}\) & \(3.58\times 10^{3}\) \\  & Min & \(2.57\times 10^{3}\) & \(4.75\times 10^{3}\) & \(2.51\times 10^{3}\) & \(2.15\times 10^{3}\) & \(3.04\times 10^{3}\) \\ \hline \multirow{2}{*}{C17} & Mean & \(3.81\times 10 Drawing on the optimization accuracy outcomes for each algorithm, this study underscores the FDIBSO algorithm's efficacy with additional proof from the Friedman test.