# Knowledge-Based Perturbation LaF-CMA-ES for Multimodal Optimization
## 5 Conclusions  
In this paper, KbP, LaF strategies, and two variants of CMA-ES are integrated into the introduced method to solve MMOPs. These strategies are employed to balance exploration and exploitation. Simulation results on the CEC problems demonstrate that the performance of the introduced method surpasses that of five other compared algorithms. Statistical analysis indicates that the introduced method significantly differs from the other four compared algorithms. Its performance is comparable to that of EBOwithCMAR. Com  
\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 \multirow{3}{*}{1} & Mean & **0** & **0** & **0** & **0** & **0** & **0** \\  & Std. Dev. & **0** & **0** & **0** & **0** & **0** & **0** \\  & Mean & **0** & \(1.00\times 10^{-6}\) & \(2.31\times 10^{6}\) & \(4.96\times 10^{-3}\) & \(7.13\times 10^{5}\) & **0** \\  & Std. Dev. & **0** & \(2.00\times 10^{6}\) & \(8.03\times 10^{5}\) & \(1.80\times 10^{-3}\) & \(3.42\times 10^{5}\) & **0** \\  & Mean & \(1.69\times 10^{5}\) & \(8.74\times 10^{5}\) & \(1.63\times 10^{5}\) & \(6.93\times 10^{5}\) & \(5.12\times 10^{2}\) & \(\mathbf{1.35\times 10^{4}}\) \\  & Std. Dev. & \(3.07\times 10^{5}\) & \(9.47\times 10^{5}\) & \(2.39\times 10^{5}\) & \(1.10\times 10^{6}\) & \(4.91\times 10^{7}\) & \(\mathbf{2.79\times 10^{4}}\) \\  & Mean & **0** & **0** & \(4.56\times 10^{-3}\) & \(7.14\) & **0** \\  & Std. Dev. & **0** & **0** & \(9.26\times 10^{-3}\) & \(5.26\) & **0** \\  & Mean & **0** & \(1.00\times 10^{-6}\) & \(1.40\times 10^{-4}\) & **0** & **0** & **0** \\  & Std. Dev. & **0** & \(0\) & \(7.6\times 10^{-5}\) & **0** & **0** & **0** \\  & Mean & **4.13** & \(7.43\times 10^{1}\) & \(2.06\times 10^{2}\) & \(1.58\times 10^{2}\) & \(4.71\times 10^{1}\) & \(5.84\times 10^{1}\) \\  & Std. Dev. & \(\mathbf{1.73\times 10^{1}}\) & \(8.61\times 10^{1}\) & \(5.45\times 10^{1}\) & \(9.09\times 10^{1}\) & \(8.15\times 10^{1}\) & \(7.77\times 10^{1}\) \\  & Mean & \(5.73\times 10^{1}\) & \(4.70\times 10^{1}\) & \(3.06\times 10^{1}\) & **1.76** & \(1.37\times 10^{2}\) & \(3.92\times 10^{1}\) \\  & Std. Dev. & \(1.32\times 10^{1}\) & \(8.60\) & \(1.46\times 10^{1}\) & \(\mathbf{7.80\times 10^{-1}}\) & \(3.22\times 10^{1}\) & \(7.79\) \\  & Mean & \(2.14\times 10^{1}\) & \(\mathbf{2.13\times 10^{1}}\) & \(2.15\times 10^{1}\) & \(\mathbf{2.13\times 10^{1}}\) & \(\mathbf{2.13\times 10^{1}}\) & \(\mathbf{2.13\times 10^{1}}\) \\  & Std. Dev. & \(4.29\times 10^{-2}\) & \(2.74\times 10^{-2}\) & \(4.92\times 10^{-2}\) & \(3.75\times 10^{-2}\) & \(4.19\times 10^{-2}\) & \(\mathbf{2.47\times 10^{-2}}\) \\  & Mean & \(9.15\times 10^{1}\) & \(8.14\times 10^{1}\) & \(\mathbf{3.01\times 10^{1}}\) & \(1.28\times 10^{2}\) & \(1.52\times 10^{2}\) & \(7.68\times 10^{1}\) \\  & Std. Dev. & \(7.70\) & \(7.48\) & \(\mathbf{3.91}\) & \(4.21\) & \(7.51\) & \(6.43\) \\  & Mean & \(4.35\times 10^{-4}\) & \(3.14\times 10^{-3}\) & \(2.90\times 10^{-3}\) & \(1.23\times 10^{-2}\) & \(1.32\times 10^{-1}\) & \(\mathbf{2.90\times 10^{-4}}\) \\  & Std. Dev. & \(1.76\times 10^{-3}\) & \(3.82\times 10^{-3}\) & \(4.03\times 10^{-3}\) & \(8.35\times 10^{-3}\) & \(6.91\times 10^{-2}\) & \(\mathbf{1.45\times 10^{-3}}\) \\  & Mean & \(1.94\times 10^{5}\) & \(1.90\times 10^{2}\) & \(3.48\times 10^{1}\) & \(1.77\times 10^{2}\) & **0** & \(1.58\times 10^{2}\) \\  & Std. Dev. & \(1.53\times 10^{1}\) & \(2.22\times 10^{1}\) & \(5.05\) & \(7.67\) & **0** & \(2.00\times 10^{1}\) \\  & Mean & \(1.83\times 10^{2}\) & \(2.31\times 10^{2}\) & \(\mathbf{3.33\times 10^{1}}\) & \(3.13\times 10^{2}\) & \(2.69\times 10^{2}\) & \(1.99\times 10^{2}\) \\  & Std. Dev. & \(1.43\times 10^{1}\) & \(2.50\times 10^{1}\) & \(\mathbf{3.64}\) & \(5.65\) & \(3.63\times 10^{1}\) & \(2.23\times 10^{1}\) \\  & Mean & \(3.99\times 10^{2}\) & \(4.74\times 10^{2}\) & \(6.91\times 10^{1}\) & \(9.80\times 10^{2}\) & \(4.72\times 10^{2}\) & \(\mathbf{3.98\times 10^{2}}\) \\  & Std. Dev.