# A Fusion Multi-Strategy Marine Predator Algorithm for Mobile Robot Path Planning
## 4 Analysis of Simulation Experiment Results
### Comparison with Different Strategies  
To verify the effectiveness and superiority of FMMPA, we compare the basic MPA and MPA1 which incorporates the Golden-SA, MPA2, which incorporates the nonlinear convex decreasing weight strategy, and MPA3, which incorporates [PERSON] spiral search strategy on 16 benchmark test functions. The conditions were set to be the same, with the population size \(N=30\), the dimension \(dim=30\), and the maximum number of iterations \(Max\_Iter=1000\). The experimental results are evaluated through four performance metrics \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Fun No.**} & \multirow{2}{*}{**Name**} & \multicolumn{2}{c}{**30\(dim\)**} & \multicolumn{2}{c}{**50\(dim\)**} & \multicolumn{2}{c}{**100\(dim\)**} \\  & & **Mean** & **Std** & **Mean** & **Std** & **Mean** & **Std** \\ \hline \multirow{6}{*}{F14} & MPA & \(3.98\times 10^{-1}\) & \(7.67\times 10^{-15}\) & \(3.98\times 10^{-1}\) & \(1.68\times 10^{-14}\) & \(3.98\times 10^{-1}\) & \(3.03\times 10^{-15}\) \\  & SCA & \(3.99\times 10^{-1}\) & \(1.92\times 10^{-3}\) & \(4.00\times 10^{-1}\) & \(2.09\times 10^{-3}\) & \(4.00\times 10^{-1}\) & \(3.45\times 10^{-3}\) \\  & WOA & \(3.98\times 10^{-1}\) & \(3.78\times 10^{-5}\) & \(3.98\times 10^{-1}\) & \(4.77\times 10^{-5}\) & \(3.98\times 10^{-1}\) & \(8.86\times 10^{-6}\) \\  & EO & \(3.98\times 10^{-1}\) & \(0\) & \(3.98\times 10^{-1}\) & \(0\) & \(3.98\times 10^{-1}\) & \(0\) \\  & AOA & \(4.14\times 10^{-1}\) & \(1.68\times 10^{-2}\) & \(4.13\times 10^{-1}\) & \(1.26\times 10^{-2}\) & \(4.11\times 10^{-1}\) & \(9.39\times 10^{-3}\) \\  & GWO & \(3.98\times 10^{-1}\) & \(3.87\times 10^{-4}\) & \(3.98\times 10^{-1}\) & \(9.55\times 10^{-7}\) & \(3.98\times 10^{-1}\) & \(1.58\times 10^{-6}\) \\  & FMMPA & **3.98\(\times 10^{-1}\)** & **8.83\(\times 10^{-15}\)** & **3.98\(\times 10^{-1}\)** & **4.16\(\times 10^{-15}\)** & **3.98\(\times 10^{-1}\)** & **1.26\(\times 10^{-15}\)** \\ \hline \multirow{6}{*}{F15} & MPA & \(0\) & \(0\) & \(0\) & \(0\) & \(0\) & \(0\) \\  & SCA & \(0\) & \(0\) & \(0\) & \(0\) & \(0\) & \(0\) \\  & WOA & \(1.82\times 10^{-4}\) & \(6.96\times 10^{-4}\) & \(1.07\times 10^{-4}\) & \(5.00\times 10^{-4}\) & \(1.10\times 10^{-6}\) & \(6.03\times 10^{-6}\) \\  & EO & \(0\) & \(0\) & \(0\) & \(0\) & \(0\) & \(0\) \\  & AOA & \(0\) & \(0\) & \(0\) & \(0\) & \(0\) & \(0\) \\  & GWO & \(0\) & \(0\) & \(0\) & \(0\) & \(0\) & \(0\) \\  & FMMPA & **0** & **0** & **0** & **0** & **0** & **0** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._that is optimal, worst, mean and standard deviation. The results of the experiment are shown in Table 4.  
In Table 4, the experimental data of all algorithms can reach the theoretical optimal value in F7, F9, F11 and F15, indicating that the Original MPA algorithm has a better performance. There are a large number of local optimal values in F5, and the algorithm search easily falls into the local extreme value space, so none of them find the theoretical value. However, the four evaluation indexes of FMMPA, MPA1, MPA2 and MPA3 are all improved compared with the original MPA algorithm, which indicates that different strategies have improved the optimal performance of the algorithm to different degrees. From the optimal values, the accuracy of the MPA1 optimization is significantly higher than that of the other strategies algorithms when solving F1 to F4 and F10, which verifies the significant improvement of the Golden-SA position update strategy on the algorithm convergence accuracy and local perturbation ability. The standard deviation of all four improved algorithms at solution F8 is 0, which indicates the effective improvement of the stability and robustness of the three strategies. FMMPA has the best data for all four evaluation metrics on all remaining test functions, showing a significant improvement in all-around performance and demonstrating the synergistic complementarity between different improvement strategies.