# Multi-Strategy-Improvement-Based Slime Mould Algorithm
## Appendix A
**_Cont._} \\ \hline
**ID** & **Index** & **MSSMA** & **SMA** & **MSSMA-1** & **MSSMA-2** & **MSSMA-3** \\ \hline F21 & Mean & \(\mathbf{9.58\times 10^{-11}}\) & \(3.30\times 10^{-10}\) & \(3.46\times 10^{-10}\) & \(4.62\times 10^{-10}\) & \(1.04\times 10^{-10}\) \\  & Std & \(1.61\times 10^{-20}\) & \(5.55\times 10^{-19}\) & \(9.36\times 10^{-15}\) & \(5.71\times 10^{-25}\) & \(8.71\times 10^{-20}\) \\ \hline F22 & Mean & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(5.04\times 10^{-4}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) \\  & Std & \(0.00\) & \(0.00\) & \(1.87\times 10^{-16}\) & \(0.00\) & \(0.00\) \\ \hline F23 & Mean & \(\mathbf{-1.59\times 10^{5}}\) & \(-2.09\times 10^{5}\) & \(-2.09\times 10^{5}\) & \(-2.05\times 10^{5}\) & \(-1.84\times 10^{5}\) \\  & Std & \(1.28\times 10^{-2}\) & \(1.18\times 10^{2}\) & \(1.22\times 10^{-2}\) & \(3.69\times 10^{-2}\) & \(1.98\times 10^{-2}\) \\ \hline F24 & Mean & \(-1.80\) & \(-1.80\) & \(-1.80\) & \(-1.80\) & \(-1.80\) \\  & Std & \(\mathbf{2.86\times 10^{-23}}\) & \(1.67\times 10^{-17}\) & \(5.81\times 10^{-19}\) & \(5.15\times 10^{-20}\) & \(7.81\times 10^{-23}\) \\ \hline F25 & Mean & \(\mathbf{-4.58}\) & \(-4.39\) & \(-4.45\) & \(-4.45\) & \(-4.57\) \\  & Std & \(1.27\times 10^{-3}\) & \(8.90\times 10^{-2}\) & \(3.24\times 10^{-2}\) & \(1.15\times 10^{-2}\) & \(1.29\times 10^{-2}\) \\ \hline F26 & Mean & \(\mathbf{-8.57}\) & \(-8.46\) & \(-8.46\) & \(-8.49\) & \(-8.54\) \\  & Std & \(3.42\times 10^{-2}\) & \(5.28\times 10^{-1}\) & \(5.03\times 10^{-1}\) & \(5.39\times 10^{-1}\) & \(3.32\times 10^{-1}\) \\ \hline F27 & Mean & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) \\  & Std & \(0.00\) & \(0.00\) & \(0.00\) & \(0.00\) & \(0.00\) \\ \hline F28 & Mean & \(-1.03\) & \(-1.03\) & \(-1.03\) & \(-1.03\) & \(-1.03\) \\  & Std & \(\mathbf{1.27\times 10^{-25}}\) & \(9.65\times 10^{-22}\) & \(1.23\times 10^{-22}\) & \(3.48\times 10^{-24}\) & \(5.12\times 10^{-25}\) \\ \hline F29 & Mean & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) \\  & Std & \(0.00\) & \(0.00\) & \(0.00\) & \(0.00\) & \(0.00\) \\ \hline F30 & Mean & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) \\  & Std & \(0.00\) & \(0.00\) & \(0.00\) & \(0.00\) & \(0.00\) \\ \hline F31 & Mean & \(-1.87\times 10^{2}\) & \(-1.87\times 10^{2}\) & \(-1.87\times 10^{2}\) & \(-1.87\times 10^{2}\) & \(-1.87\times 10^{2}\) \\  & Std & \(4.01\times 10^{-14}\) & \(1.30\times 10^{-13}\) & \(4.03\times 10^{-13}\) & \(1.63\times 10^{-13}\) & \(\mathbf{1.22\times 10^{-14}}\) \\ \hline F32 & Mean & \(3.00\) & \(3.00\) & \(3.00\) & \(3.00\) & \(3.00\) \\  & Std & \(\mathbf{1.23\times 10^{-26}}\) & \(2.97\times 10^{-22}\) & \(1.48\times 10^{-22}\) & \(1.06\times 10^{-24}\) & \(4.34\times 10^{-25}\) \\ \hline F33 & Mean & \(\mathbf{3.08\times 10^{-4}}\) & \(4.44\times 10^{-4}\) & \(3.86\times 10^{-4}\) & \(3.10\times 10^{-4}\) & \(3.09\times 10^{-4}\) \\  & Std & \(5.99\times 10^{-14}\) & \(2.96\times 10^{-8}\) & \(7.17\times 10^{-9}\) & \(4.57\times 10^{-14}\) & \(3.94\times 10^{-12}\) \\ \hline F34 & Mean & \(-1.02\times 10^{1}\) & \(-1.02\times 10^{1}\) & \(-1.02\times 10^{1}\) & \(-1.02\times 10^{1}\) & \(-1.02\times 10^{1}\) \\  & Std & \(\mathbf{1.26\times 10^{-13}}\) & \(2.04\times 10^{-9}\) & \(1.35\times 10^{-9}\) & \(8.18\times 10^{-10}\) & \(2.28\times 10^{-12}\) \\ \hline F35 & Mean & \(-1.04\times 10^{1}\) & \(-1.04\times 10^{1}\) & \(-1.04\times 10^{1}\) & \(-1.04\times 10^{1}\) & \(-1.04\times 10^{1}\) \\  & Std & \(\mathbf{4.05\times 10^{-12}}\) & \(6.36\times 10^{-9}\) & \(2.70\times 10^{-9}\) & \(4.00\times 10^{-11}\) & \(6.44\times 10^{-12}\) \\ \hline F36 & Mean & \(-1.05\times 10^{1}\) & \(-1.05\times 10^{1}\) & \(-1.05\times 10^{1}\) & \(-1.05\times 10^{1}\) & \(-1.05\times 10^{1}\) \\  & Std & \(\mathbf{4.70\times 10^{-12}}\) & \(1.82\times 10^{-9}\) & \(3.91\times 10^{-9}\) & \(2.40\times 10^{-10}\) & \(2.67\times 10^{-12}\) \\ \hline F37 & Mean & \(\mathbf{9.26\times 10^{-2}}\) & \(1.38\times 10^{-1}\) & \(1.02\times 10^{-1}\) & \(9.58\times 10^{-2}\) & \(9.43\times 10^{-2}\) \\  & Std & \(1.91\times 10^{-2}\) & \(3.77\times 10^{-2}\) & \(1.99\times 10^{-2}\) & \(2.57\times 10^{-2}\) & \(2.50\times 10^{-2}\) \\ \hline F38 & Mean & \(\mathbf{9.57\times 10^{-4}}\) & \(7.85\times 10^{-3}\) & \(6.75\times  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**ID** & **Index** & **MSSMA** & **SMA** & **WOA** & **KO** & **BWO** & **IVY** \\ \hline \multirow{2}{*}{F1} & Mean & \(\mathbf{-5.00}\) & \(\mathbf{-5.00}\) & \(2.46\times 10^{-187}\) & \(-4.07\) & \(\mathbf{-5.00}\) & \(-8.00\times 10^{-1}\) \\  & Std & 0.00 & 0.00 & 0.00 & \(3.40\times 10^{-1}\) & 0.00 & 1.82 \\ \hline \multirow{2}{*}{F2} & Mean & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(4.35\times 10^{-104}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) \\  & Std & 0.00 & 0.00 & \(4.79\times 10^{-206}\) & 0.00 & 0.00 & 0.00 \\ \hline \multirow{2}{*}{F3} & Mean & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(2.76\times 10^{7}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) \\  & Std & 0.00 & 0.00 & \(4.76\times 10^{-13}\) & 0.00 & 0.00 & 0.00 \\ \hline \multirow{2}{*}{F4} & Mean & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(7.31\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) \\  & Std & 0.00 & 0.00 & \(6.69\) & 0.00 & 0.00 & 0.00 \\ \hline \multirow{2}{*}{F5} & Mean & \(\mathbf{5.47}\times\mathbf{10^{-8}}\) & \(3.26\times 10^{-4}\) & \(4.13\times 10^{-6}\) & \(1.26\times 10^{-4}\) & \(3.19\times 10^{-5}\) & \(1.86\times 10^{-5}\) \\  & Std & \(3.30\times 10^{-18}\) & \(5.45\times 10^{-8}\) & \(3.32\times 10^{-8}\) & \(1.82\times 10^{-8}\) & \(7.03\times 10^{-10}\) & \(3.26\times 10^{-10}\) \\ \hline \multirow{2}{*}{F6} & Mean & \(6.75\times 10^{-10}\) & \(2.85\times 10^{-8}\) & \(\mathbf{0.00}\) & \(8.46\times 10^{-7}\) & \(4.58\times 10^{-4}\) & \(6.78\times 10^{-18}\) \\  & Std & \(1.15\times 10^{-18}\) & \(2.80\times 10^{-14}\) & 0.00 & \(1.02\times 10^{-12}\) & \(4.25\times 10^{-7}\) & \(1.00\times 10^{-33}\) \\ \hline \multirow{2}{*}{F7} & Mean & \(-1.00\) & \(-9.95\times 10^{-1}\) & \(1.95\times 10^{-4}\) & \(-1.00\) & \(\mathbf{-1.00}\) & \(-2.16\times 10^{-1}\) \\  & Std & \(1.51\times 10^{-20}\) & \(5.76\times 10^{-4}\) & \(5.54\times 10^{-8}\) & \(1.96\times 10^{-13}\) & 0.00 & \(1.21\times 10^{-1}\) \\ \hline \multirow{2}{*}{F8} & Mean & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(-7.89\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) \\  & Std & 0.00 & 0.00 & \(3.19\times 10^{-17}\) & 0.00 & 0.00 & 0.00 \\ \hline \multirow{2}{*}{F9} & Mean & \(4.81\times 10^{-7}\) & \(2.37\times 10^{-4}\) & \(\mathbf{0.00}\) & \(1.39\times 10^{-1}\) & \(1.35\times 10^{-3}\) & \(1.14\) \\  & Std & \(1.50\times 10^{-12}\) & \(2.34\times 10^{-7}\) & 0.00 & \(4.16\times 10^{-2}\) & \(2.35\times 10^{-6}\) & \(3.01\) \\ \hline \multirow{2}{*}{F10} & Mean & \(\mathbf{-5.00}\times\mathbf{10^{1}}\) & \(-5.00\times 10^{1}\) & \(2.10\times 10^{-15}\) & \(-5.00\times 10^{1}\) & \(-4.98\times 10^{1}\) & \(-2.31\) \\  & Std & \(1.11\times 10^{-18}\) & \(8.08\times 10^{-9}\) & \(4.12\times 10^{-30}\) & \(1.48\times 10^{-7}\) & \(7.13\times 10^{-3}\) & \(1.65\times 10^{1}\) \\ \hline \multirow{2}{*}{F11} & Mean & \(\mathbf{-2.10}\times\mathbf{10^{2}}\) & \(-2.10\times 10^{2}\) & \(2.67\times 10^{-2}\) & \(-2.10\times 10^{2}\) & \(-1.97\times 10^{2}\) & \(-4.43\times 10^{-1}\) \\  & Std & \(1.92\times 10^{-9}\) & \(2.39\times 10^{-4}\) & \(2.86\times 10^{-3}\) & \(1.66\times 10^{-4}\) & \(2.50\times 10^{1}\) & \(4.99\) \\ \hline \multirow{2}{*}{F12} & Mean & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(2.39\times 10^{-5}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) \\  & Std & \(0.00\) & 0.00 & \(3.48\times 10^{-10}\) & 0.00 & 0.00 & 0.00 \\ \hline \multirow{2}{*}{F13} & Mean & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(1.21\times 10^{-2}\) & \(2.40\times 10^{-63}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) \\  & Std & \(0.00\) & 0.00 & \(1.79\times 10^{-4}\) & \(1.72\times 10^{-124}\) & 0.00 & 0.00 \\ \hline \multirow{2}{*}{F14} & Mean & \(\mathbf{0.00}\) & \(3.42\times 10^{-2}\) & \(1.13\times 10^{-106}\) & \(\mathbf{0.00}\) & \(2.47\times 10^{-257}\) & \(\mathbf{0.00}\) \\  & Std & \(0.00\) & \(1.06\times 10^{-2}\) & \(1.56\times 10^{-211}\) & 0.00 & 0.00 & 0.00 \\ \hline \multirow{2}{*}{F15} & Mean & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) & \(2.44\times 10^{7}\) & \(1.20\times 10^{-302}\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) \\  & Std & \(0.00\) & \(0.00\) & \(3.70\times 10^{+13}\) & 0.00 & 0.00 & 0.00 \\ \hline \multirow{2}{*}{F16} & Mean & \(\mathbf{2.28}\times\mathbf{10^{-6}}\) & \(6.85\times 10^{1}\) & \(4.95\times 10^{2}\) & \(4.95\times 10^{2}\) & \(2.68\times 10^{-3}\) & \(4.94\times 10^{2}\) \\  & Std & \(3.26\times 10^{-9}\) & \(1.20\times 10^{4}\) & \(5.42  
**Figure A1.**_Cont.