# Knowledge-Based Perturbation LaF-CMA-ES for Multimodal Optimization
## 4 Experiment and Analysis
### Experimental Analysis and Result
& \(3.10\) & \(2.52\) & **2.08** & \(1.68\) & \(3.45\) & \(2.91\) \\  & Mean & \(8.70\times 10^{-4}\) & \(5.12\times 10^{-3}\) & **0** & \(1.45\times 10^{-4}\) & \(5.40\times 10^{-2}\) & \(7.25\times 10^{-4}\) \\  & Std. Dev. & \(2.41\times 10^{-3}\) & \(3.72\times 10^{-3}\) & **0** & \(1.04\times 10^{-3}\) & \(4.02\times 10^{-2}\) & \(2.22\times 10^{-3}\) \\  & Mean & \(2.92\times 10^{1}\) & \(1.98\times 10^{1}\) & 6.05 & \(1.00\times 10^{1}\) & **0** & \(8.15\) \\  & Std. Dev. & \(3.89\) & \(4.98\) & \(1.72\) & \(0\) & **0** & \(3.02\) \\  & Mean & \(2.87\times 10^{1}\) & \(2.66\times 10^{1}\) & **5.64** & \(3.37\times 10^{1}\) & \(4.27\times 10^{1}\) & \(2.65\times 10^{1}\) \\  & Std. Dev. & \(4.04\) & \(5.09\) & **2.01** & \(2.71\) & \(1.36\times 10^{1}\) & \(6.01\) \\  & Mean & \(7.14\times 10^{1}\) & \(5.90\times 10^{1}\) & **7.04** & \(6.80\times 10^{1}\) & \(7.98\times 10^{1}\) & \(5.22\times 10^{1}\) \\  & Std. Dev. & \(1.29\times 10^{1}\) & \(1.93\times 10^{1}\) & **4.68** & \(1.17\times 10^{1}\) & \(2.09\times 10^{1}\) & \(1.53\times 10^{1}\) \\  & Mean & \(3.71\times 10^{3}\) & \(1.49\times 10^{3}\) & \(2.70\times 10^{3}\) & \(6.00\times 10^{2}\) & **3.26** & \(6.16\times 10^{2}\) \\  & Std. Dev. & \(5.11\times 10^{2}\) & \(6.81\times 10^{2}\) & \(5.13\times 10^{2}\) & \(4.56\times 10^{2}\) & **6.13** & \(1.92\times 10^{2}\) \\  & Mean & \(3.71\times 10^{3}\) & \(2.99\times 10^{3}\) & \(2.65\times 10^{3}\) & \(2.58\times 10^{3}\) & \(4.42\times 10^{3}\) & \(\textbf{2.46\times 10^{3}}\) \\  & Std. Dev. & \(4.73\) & \(5.08\) & \(4.61\) & \(3.62\times 10^{2}\) & \(6.98\times 10^{2}\) & **4.38\(\times 10^{2}\)** \\  & Mean & \(3.72\times 10^{-2}\) & \(5.40\times 10^{-2}\) & \(1.50\) & \(1.04\times 10^{-1}\) & \(2.28\) & \(5.60\times 10^{-2}\) \\  & Std. Dev. & \(1.53\times 10^{-2}\) & \(2.73\times 10^{-2}\) & \(2.56\) & \(7.35\times 10^{-2}\) & \(3.74\times 10^{-1}\) & \(3.40\times 10^{-2}\) \\  & Mean & \(6.04\times 10^{1}\) & \(6.16\times 10^{1}\) & \(3.95\times 10^{1}\) & **3.04\(\times 10^{1}\)** & **3.04\(\times 10^{1}\)** & \(4.53\times 10^{1}\) \\  & Std. Dev. & \(5.20\) & \(5.97\) & \(2.82\times 10^{1}\) & \(2.44\times 10^{1}\) & **7.58\(\times 10^{-3}\)** & \(4.47\) \\  & Mean & \(6.72\times 10^{1}\) & \(6.92\times 10^{1}\) & \(1.14\times 10^{2}\) & \(7.40\times 10^{1}\) & \(8.93\times 10^{1}\) & **6.22\(\times 10^{1}\)** \\  & Std. Dev. & \(2.83\times 10^{1}\) & \(9.31\) & \(9.57\times 10^{1}\) & \(1.26\times 10^{1  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Function** & **Criterion** & **CMA-ES** & **LaF-CMA-ES** & **IPOP-CMAES** & **EBOwithCMAR** & **SPSRDEMMS** & **Kbp-LaF-CMAES** \\ \hline
**1** & Mean & **0** & **0** & **0** & **0** & **0** & **0** \\  & Std. Dev. & **0** & **0** & **0** & **0** & **0** & **0** \\  & Mean & **0** & **0** & \(3.38\times 10^{2}\) & \(2.20\times 10^{-3}\) & \(5.65\times 10^{5}\) & **0** \\
**2** & Std. Dev. & **0** & **0** & \(2.67\times 10^{2}\) & \(2.57\times 10^{-3}\) & \(2.56\times 10^{5}\) & **0** \\
**3** & Mean & \(1.45\times 10^{3}\) & \(9.80\times 10^{3}\) & \(3.11\times 10^{5}\) & \(1.16\times 10^{3}\) & \(4.44\times 10^{7}\) & **2.68** \\  & Std. Dev. & \(5.65\times 10^{3}\) & \(3.94\times 10^{4}\) & \(2.21\times 10^{6}\) & \(2.45\times 10^{3}\) & \(4.56\times 10^{7}\) & **1.54 \(\times\) 10\({}^{1}\)** \\  & Mean & **0** & **0** & \(1.97\times 10^{-4}\) & \(5.17\) & **0** \\
**4** & Std. Dev. & **0** & **0** & \(3.69\times 10^{-4}\) & \(4.72\) & **0** \\
**5** & Mean & **0** & **0** & \(1.21\) & **0** & **0** & **0** \\  & Std. Dev. & **0** & **0** & \(8.62\) & **0** & **0** & **0** \\  & Mean & \(\mathbf{3.54\times 10^{1}}\) & \(4.34\times 10^{1}\) & \(4.34\times 10^{1}\) & \(4.34\times 10^{1}\) & \(4.37\times 10^{1}\) & \(4.34\times 10^{1}\) \\  & Std. Dev. & \(1.66\times 10^{1}\) & **0** & **0** & \(4.81\times 10^{-14}\) & \(1.11\) & 0 \\  & Mean & \(3.91\times 10^{1}\) & \(1.34\times 10^{1}\) & \(6.08\) & \(\mathbf{6.57\times 10^{-2}}\) & \(3.17\times 10^{1}\) & \(9.19\) \\  & Std. Dev.