# An Enhanced Lightning Attachment Procedure Optimization Algorithm
## 3 The Enhanced Lightning Attachment Procedure Optimization Algorithm
### The Improved Enhancement Performance
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Function** & **Statistic** & **ADN-RSN-PSO** & **ABCADE** & **DSTLBO** & **IMSaDE** & **LAPO** & **ELAPO** \\ \hline \multirow{7}{*}{f16} & Min & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) \\  & Mean & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) \\  & Max & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) \\  & Std & \(1.3596\times 10^{-5}\) & \(1.3074\times 10^{-4}\) & \(2.5463\times 10^{-12}\) & \(4.5168\times 10^{-16}\) & \(1.4600\times 10^{-7}\) & \(4.5168\times 10^{-16}\) \\  & Robustness & 100 & 100 & 100 & 100 & 100 & 100 \\  & Rank & 5 & 6 & 3 & 2 & 4 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._To further compare the performance of the six algorithms, assuming that the convergence performance of ELAPO is better than the other five methods. Comparing \(p_{i}\) and \(\alpha/(k-i)\), if \(p_{i}<\alpha/(k-i)\) at the 5% significant level, then reject the original hypothesis, that is, the ELAPO have significant differences to the algorithm i. By observing the data in the table, we found that only \(p_{5}<\alpha/(k-5)\), Holm Test rejects the other four hypotheses and accepts the fifth hypothesis, which means that the performance of the ELAPO algorithm in this paper was equivalent to that of DSTLBO in the above test functions, while the other four \(p\) values were less than \(\alpha/(k-i)\), which means that the performance of ELAPO was obviously better than ADN-RSN-PSO, ABCADE, IMSaDE, and LAPO. Although the accuracy of the ELAPO algorithm was not significantly higher than that of DSTLBO, it had a smaller average rank. Comprehensive analysis of the experimental results of ELAPO in single-peak function and multi-peak function shows that ELAPO was relatively balanced in the search calculation of two kinds of functions, and for all functions, the improved ELAPO algorithm was superior to the LAPO algorithm in solving accuracy. From the perspective of robustness, the ELAPO algorithm proposed in this paper had a low success rate only on f9 and f14, while the solution of other functions was relatively stable. DSTLBO had a low success rate on f4, f11, and f14 functions and belongs to sub-stability, while ADN-RSN-PSO, ABCADE, IMSaDE, and LAPO had a relatively low success rate in achieving the specified accuracy of the solution function. Through comparative analysis, the proposed ELAPO algorithm had better robustness. In addition, in order to intuitively see the convergence of each algorithm, experiments were carried out with the number of evaluations of 30,000 times, and the following experimental comparison figures were obtained, in which the abscissa represents the number of evaluation times of the function and the ordinate represents the logarithmic value of the fitness values obtained. It can be seen from Figure 4 that the convergence speed of ELAPO proposed in this paper was relatively fast when solving single-peak functions f2, f3, f4, and f5, while the convergence speed of f8 and DSTLBO was similar, f1, f6, and f7 were worse than DSTLBO, but the convergence speed of ELAPO was faster than ADN-RSN-PSO, ABCADE, IMSaDE, and LAPO when solving the above functions. When solving multimodal functions f9-f13, f15, and f16, the ELAPO algorithm in this paper had a faster convergence speed, while in function f14, the convergence speed in the early stage of evolution had no obvious advantage, but in the middle stage of evolution, there was a clear tendency to jump out of the local optimum.