# Mobile Robot Path Planning Based on Fused Multi-Strategy White Shark Optimisation Algorithm
## 3 Improved White Shark Optimisation Algorithm
### Simulation of Annealing Operations  
Since the traditional white shark algorithm will also fall into the problem of local optimum, this paper uses the improved simulated annealing algorithm and white shark algorithm to combine optimisation to strengthen the optimisation ability of the white shark algorithm, the introduction of the Metropolis criterion [21] allows the white shark algorithm to avoid falling into the local optimum in the algorithmic search process, and the use of tempering method to maintain the ability of white shark algorithm to jump out of the local optimum in the search process. Since frequent tempering will reduce the search efficiency of the white shark algorithm, considering the possibility of a longer search process, the white shark algorithm carries out tempering and warming once in the early and middle stages of the search, so that the white shark algorithm can still jump out of the local optimum in the first and middle stages of the search process, and to avoid the premature failure of the Metropolis criterion. And set the memory to record the historical optimal position of each great white shark, so that part of the great white sharks can return to the search. Considering the optimisation efficiency of the white shark algorithm, the temperature decay function of the very fast annealing method is introduced, so that the white shark algorithm can jump out of the local optimum while having a better convergence speed.  
Combining the simulated annealing algorithm with memory, the tempered annealing method, the very fast simulated annealing method and the traditional simulated annealing algorithm, the tempered fast annealing method with return search can be obtained. Taking the search for the minimum value as an example, the search steps of the method are shown below:  
1. Set the initial temperature \(T_{0}\), temperature decay coefficient \(\alpha\), Markov chain length \(\mathrm{L_{k}}\) and total number of iterations K. Generate an initial solution \(\mathrm{x_{0}}\) randomly within the set range and compute its fitness value \(f(x_{0})\), and set the optimal solution \(best_{x}\) with the optimal value \(G_{best}\) as the initial solution \(x_{0}\) and fitness value \(f(x_{0})\).
2. Perform a Cauchy-like distribution perturbation in the vicinity of \(x_{0}\) to generate a new solution \(x_{1}\) with transgression and compute its fitness value \(f(x_{1})\).
3. If \(f(x_{1})\) is less than \(f(x_{0})\), then accept the new solution \(\mathrm{x_{1}}\) and replace \(\mathrm{x_{0}}\); if \(f(x_{1})\) is greater than \(f(x_{0})\), it is not immediately discarded, and calculate the difference \(\Delta f\) between \(f(x_{1})\) and \(f(x_{0})\), and calculate the probability of accepting the new solution \(x_{1}\) by the Metropolis criterion, comparing it with a random number uniformly distributed at \([0,1]\); if the probability is greater than the random number, then the new solution \(x_{1}\) is accepted and replaced with \(x_{0}\), and vice versa, it is discarded.
4. Determine whether the algorithm reaches the loop termination condition within that temperature, if not, the algorithm returns to (2) to continue the loop.
5. If the termination conditions of the inner loop are met, the temperature T is reduced by rapid annealing to determine whether tempering and warming is required, otherwise return to step (2) to continue the cycle, and if the optimal value has not been updated to reach the number of times, then return to the search.  
If the algorithm reaches the termination condition, output the global optimum value \(G_{best}\).