# Mobile Robot Path Planning Based on Fused Multi-Strategy White Shark Optimisation Algorithm
## 4 Experimental Simulation
### Algorithm Testing and Analysis
For the multi-peak oscillating Rastrigin function, it efficiently escapes oscillation traps with adaptive weights, demonstrating far superior ability to escape local optima compared to PSO, which easily gets completely trapped; SA, which has poor oscillation resistance; WSO, which has low efficiency in escaping traps; HWSO, which lacks search stability; and IWSO, which struggles to sustain optimization after escaping. In the multi-peak, noise-containing Ackley function, it leverages simulated annealing enhancement mechanisms and Metropolis criteria to exhibit strong interference resistance and precisely lock onto the global optimum; Its robustness and convergence accuracy outperform PSO, which is prone to being trapped locally by noise; SA, which is highly susceptible to noise and exhibits strong fluctuations; WSO, which struggles to penetrate noise and lock onto the global optimum; HWSO, which converges slowly and exhibits late-stage fluctuations; and IWSO, which has low search efficiency in noisy environments. FMWSO leverages the dynamic flexibility of multi-strategy fusion to achieve rapid convergence in single-peak scenarios, sustained exploration in multi-peak scenarios, efficient escape from oscillations, and precise locking onto the global optimum in noisy environments. \begin{table}
\begin{tabular}{c c c} \hline
**Function Name** & **Function Expression** & **Search Space** \\ \hline Search space & \(f_{1}(x)=\sum\limits_{i=1}^{n}x_{i}^{2}\) & [\(-\)100, 100] \\ Schwefel & \(f_{2}(x)=\sum\limits_{i=1}^{n}|x_{i}|+\prod\limits_{i=1}^{n}|x_{i}|\) & [\(-\)100, 100] \\ Rastrigin & \(f_{3}(x)=\sum\limits_{i=1}^{n}\big{[}x_{i}^{2}-10\cos(2\pi x_{i})+10\big{]}\) & [\(-\)5.12, 5.12] \\ [PERSON] & \(f_{4}(x)=-20\exp(-0.2\sqrt{\frac{1}{n}\sum\limits_{i=1}^{n}x_{i}^{2}})\) & [\(-\)32, 32] \\  & \(-\exp[\frac{1}{n}\sum\limits_{i=1}^{n}\cos(2\pi x_{i})]+20+e\) & \\ \hline \end{tabular}
\end{table} 
Table 2: International standard test functions. Figure 5: _Cont._  
Table 3 shows the optimization results for each test function:  
1. Search capability: Strategic synergy breaks through search bottlenecks, achieving optimal global and local performance. FMWSO significantly enhances search capabilities through its core strategies of the Chaos Elite Pool and Rapid Annealing: The Chaos Elite Pool leverages chaotic traversal and convex lens reverse learning to generate initial solutions, addressing the issues of PSO particles lacking guidance and early convergence, as well as SA's low efficiency in single-temperature control. This approach expands the global exploration range and enables the discovery of more optimal solutions; Annealing rapid annealing combines adaptive weights to dynamically balance exploration and exploitation, avoiding the defect of the original WSO mechanism of easily falling into local optima in complex scenarios, while overcoming the parameter coordination difficulties caused by HWSO mixing two algorithms and the limitations of IWSO's dependence on data. Even under extreme operating conditions, the local search lower limit is still much higher than other algorithms, achieving a breakthrough in search capabilities across all scenarios. 2. Search stability: Multi-strategy collaboration ensures iteration consistency, with the mean closely following the optimal solution. FMWSO demonstrates exceptional search stability through multi-strategy collaboration: the chaotic elite pool ensures high-quality initial solutions with uniform distribution, reducing random fluctuations; adaptive weights dynamically adjust the search rhythm, balancing global exploration and local development; annealing continuously optimizes solution quality, ensuring that the mean remains close to the algorithm's optimal value across multiple independent runs.