# Mobile Robot Path Planning Based on Fused Multi-Strategy White Shark Optimisation Algorithm
## 4 Experimental Simulation
### Algorithm Time Complexity Calculation
The results of 15 independent runs show high consistency and robustness, meeting the critical requirement for stable path output in engineering applications. In terms of efficiency, the runtime of 5.36 is the shortest, balancing both quality and speed. To further validate the effectiveness of the FMWSO algorithm in path planning and its adaptability in complex environments, a 40 \(\times\) 40 grid map with a relatively complex structure was used, with the starting point set at (0.5, 39.5) and the endpoint at (39.5, 0.5). The path planning simulation results and iteration count curves for the five algorithms on the 40 \(\times\) 40 grid map are shown in Figures 8a and 8b, respectively. As shown in Figure 8a, as the map complexity increases, the number of inflection points for all four algorithms significantly increases. Compared to the other four algorithms, the paths planned by  
Figure 7: (**a**) Simulation results of five algorithms path planning on 20 \(\times\) 20 raster map; (**b**) curves of the number of iterations of the five algorithms on a 20 \(\times\) 20 raster map. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & **Shortest Path** & **Average Path** & **Turning Point** & **Smoothness** & **Times** \\ \hline WSO & 30.189 & 30.585 & 9 & 2.142 & 7.51 \\ D* & 29.893 & 30.395 & 8 & 1.732 & 6.75 \\ A* & 28.419 & 29.039 & 6 & 0.689 & 7.03 \\ GWO & 28.578 & 28.947 & 8 & 0.837 & 5.87 \\ FMWSO & 27.841 & 28.404 & 5 & 0.392 & 5.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The average simulation results of 15 times for a 20 \(\times\) 20 map. FMWSO are shorter and smoother. Among them, the D* algorithm is based on incremental search. In complex path planning, due to the difficulty in precisely adapting the heuristic function to complex terrain and passage costs, and the search being easily constrained by the local environment, it is challenging to perform in-depth search under real-time requirements, often resulting in non-optimal or longer paths. As shown in Figure 8b: In a complex 40 \(\times\) 40 environment, FMWSO demonstrates superior advantages in search depth, interference resistance, and convergence efficiency. It offers superior path quality, stronger stability, and faster speed, making it well-suited for high-complexity path planning requirements, and outperforms other algorithms in all aspects. Table 6 presents the average simulation results from 15 runs on a 40 \(\times\) 40 map. The optimal path generated by the FMWSO algorithm S outperforms other algorithms. In terms of path length, its shortest path of 58.583 is the optimal, 0.95% shorter than the second-best A* and 6.48% shorter than WSO, demonstrating its robust global search capability and proficiency in identifying the true shortest path in complex environments; in terms of path quality, its smoothness of 0.884 is the lowest, with the fewest nine turning points, significantly reducing the complexity of motion commands and aligning with engineering execution requirements. In terms of stability, it is consistent with simple environments, with an average path length of 59.509, which is extremely close to the shortest path. It exhibits high consistency across 15 independent runs, demonstrating strong interference resistance and adaptability to complex scenarios with high interference levels. In terms of efficiency, it has a runtime of 13.49, which is the second shortest after the A* algorithm. While ensuring path quality, the algorithm maintains good complexity control, meeting the real-time requirements of complex scenarios.