# Improved Brain Storm Optimization Algorithm Based on Flock Decision Mutation Strategy
## 2 Bso  
The BSO algorithm draws its inspiration from human brainstorming conferences, effectively harnessing human intelligence traits to address problems. It offers more benefits over conventional swarm intelligence algorithms, particularly addressing issues involving multiple dimensions. The algorithm is structured around four key phases: clustering, substitution, selection, and mutation.  
Initially, the population of \(n\) candidate solutions undergoing iteration is segmented into \(m\) groups using the K-means clustering technique. This approach is intended to mimic the collaborative dynamics of human group discussions, thereby enhancing the algorithm's search efficiency.  
Subsequently, a parameter \(p_{replace}\) is designated alongside the generation of a random number \(r_{1}\) within the interval \([0,1]\). Should \(r_{1}\) fall below \(p_{replace}\), a fresh individual is created to supplant the chosen cluster center. An excessively high value of \(p_{replace}\) can impede the algorithm's convergence efficacy and diminish the population's diversity. Conversely, an unduly low value might precipitate premature convergence of the algorithm.  
In the third step, three probability parameters \(p_{one}\), \(p_{one\_center}\), and \(p_{two\_center}\) are established, with the concurrent generation of random numbers \(r_{2}\), \(r_{3}\), and \(r_{4}\). If \(r_{2}\) falls below \(p_{one}\), a mutation is performed on a single individual within one cluster. If not, individuals from two clusters are merged and then mutated. During the mutation of an individual within a cluster, if \(r_{3}\) is lower than \(p_{one\_center}\), then the mutation is applied to the central individual of the cluster. If \(r_{3}\) is above the threshold, a non-central individual is randomly picked from the same cluster for mutation. Similarly, when mutating individuals from two different clusters, if \(r_{4}\) is less than \(p_{two\_center}\), the central individuals of both clusters are chosen for mutation. If \(r_{4}\) exceeds \(p_{two\_center}\), random non-central individuals from each cluster are selected and merged before applying the mutation.  
Fourth, the selected individuals undergo fusion or mutation processes, after which they are evaluated against the original individuals based on their fitness levels. Individuals who exhibit superior performance will be preserved following these operations. The process of fusion is described as follows:  
\[X_{f}=v\times X_{1}+(1-v)\times X_{2}, \tag{1}\]  
where \(X_{f}\) represents the individual post-fusion, \(v\) is a number randomly chosen from the range 0 to 1, and \(X_{1}\) and \(X_{2}\) are two random individuals selected for merging. The mutation process proceeds as follows:  
\[X_{m}=X_{s}+\xi\times n(\mu,\sigma), \tag{2}\]  
where \(X_{m}\) denotes the individual post-mutation, \(X_{s}\) identifies the chosen individual for mutation, \(n(\mu,\sigma)\) represents a Gaussian random number, and \(\xi\) serves as the mutation coefficient. The formula for this coefficient is as follows:  
\[\xi=\log sig\bigg{(}\frac{0.5\times g_{max}-g}{k}\bigg{)}\times rand(), \tag{3}\]  
where \(k\) is the adjustment factor, \(g_{max}\) denotes the upper limit of iterations, and \(g\) represents the number of the current iteration.