# Improved Brain Storm Optimization Algorithm Based on Flock Decision Mutation Strategy
## 3 Fdibso
### Flock Decision Mutation Strategy  
During the initial stages of intelligent algorithm search iterations, it is crucial to enhance global search to increase population diversity and accelerate convergence. In the later stages, bolstering the local search becomes essential to refine optimization precision. To achieve the above objectives, methods such as the difference step strategy [28], global-best strategy [29; 30], and elite mutation strategy [31; 32] have been sequentially introduced to enhance the precision of the BSO algorithm's optimization. However, the improved BSO algorithms using these strategies are still ineffective for addressing multi-model problems in multiple dimensions, which is mainly due to insufficient exploration of the search domain, i.e., the issue of insufficient population diversity, which causes the algorithms to quickly converge to a local optimum during the final phases of the iteration process, ultimately impacting the optimization precision of the algorithm. Therefore, this paper designed a flock decision mutation strategy, drawing on the concept of flock evolution, which sufficiently improves the population diversity during initial iterations and introduces a globally optimal individual to strengthen the local search towards the end of the iterations, significantly improving the performance of the algorithm. The basic principle of the flock decision mutation strategy is shown as follows:  
First, the scope of an individual and the flock to which it belongs can be defined using Equation (7):  
\[Dis_{i}(t)=\|X_{i}(t-1)-X_{i}(t)\|, \tag{7}\]  
where \(Dis_{i}(t)\) is the Euclidean distance between the current generation of individuals and the preceding cohort of individuals, \(X_{i}(t-1)\) is the previous generation of individuals, and \(X_{i}(t)\) is the current generation of individuals to be mutated. Second, an individual is considered to belong to the flock of \(X_{i}(t)\) if that individual satisfies the following conditions. Then, the flock of \(X_{i}(t)\) is shown in Equation (8). \[PF_{i}(t)=\big{\{}X_{j}(t)\mid D_{i}\big{(}X_{i}(t),X_{j}(t)\big{)}\leq Dis_{i} (t)\big{\}}, \tag{8}\]  
where \(PF_{i}(t)\) is the flock of \(X_{i}(t)\), \(X_{j}(t)\) is the individual from the whole population, and \(D_{i}\big{(}X_{i}(t),X_{j}(t)\big{)}\) represents the Euclidean separation between \(X_{i}(t)\) and \(X_{j}(t)\). Third, mutation on \(X_{i}(t)\) is realized through the flock of individual \(X_{i}(t)\), any member within the population, along with the globally optimal individual, as demonstrated in (9). \[\left\{ \begin{array}{l}X_{iF}(t)=X_{i}(t)+rand\times(X_{F1,i}(t)-X_{1}(t))+rand \times(X_{F2,i}(t)-X_{2}(t)),t<0.7g_{max}\\ X_{iF}(t)=X_{i}(t)+rand\times(X_{best}-X_{1}(t)),t\geq 0.7g_{max},\end{array} \right. \tag{9}\]  
where \(X_{iF}(t)\) is the new individual after the flock decision mutation strategy, \(X_{1}(t)\) and \(X_{2}(t)\) are two randomly selected members from the entire population, \(X_{F1,i}(t)\) and \(X_{F2,i}(t)\)  
Figure 2: The comparison effect of the spectral clustering. are two random individuals from the flock of individual \(X_{i}(t)\), \(X_{best}\) represents the optimal member of the preceding population, and \(g_{max}\) denotes the upper limit of iterations. The core idea of the flock decision mutation strategy is to make each individual in the population carry out a better mutation centered on itself during the initial phase of the algorithm's iteration, enhancing the caliber of the individuals and ensuring the population's diversity. During the advanced phases of the algorithm's iteration, its capacity to conduct local searches is enhanced by guiding the individuals to emulate the behavior of the the globally optimal individual. The pseudocode for this algorithm is presented in Algorithm 1 below.