# K-RBBSO Algorithm: A Result-Based Stochastic Search Algorithm in Big Data
## 2 Methods: K-Means-Initiated Rapid Biogeography-Based Silhouette Optimization  
According to [PERSON] and [PERSON] [19], the habitat, which signifies solution expression, searches for better solutions via migration and mutation, and changes or adapts solutions with poor evaluation values into those with good evaluation values. Habitats with good evaluation values preserve their existing states by reducing the immigration rate \(\lambda\) relative to other habitats and increasing the emigration rate \(\mu\) relative to habitats with different solutions, thereby adjusting the solution values corresponding to other habitats and improving their evaluation values. BBO changes and adapts the solutions by adjusting the immigration and emigration rates of habitats of solutions with good and poor evaluation values. This gives it an advantage over conventional algorithms, which search for new solutions completely randomly. In this study, the algorithm was modified to enable the application of the silhouette coefficient to the immigration, emigration, and mutation rates introduced by [PERSON] & [PERSON] [19] and [PERSON] [20]. The procedure of the algorithm devised in this study is as follows. * Step 1. Configure parameters such as the initial solution and the termination condition. The parameters required to operate the algorithm are configured. These include the number of data points to be analyzed (row); the number of attributes (col); the number of clusters K; the number of habitats to be used in the K-RBBSO algorithm execution stage H; the initial solution for each habitat; and the termination condition. Any desired condition can be selected as the termination condition. The initial solution is selected randomly. As described above, if K = 3, the solution expression matrix for row x K is denoted by (1, 2, 3,..., n) or (010, 100, 001). * Step 2. Execute k-means to determine the initial solution. K-means is executed for \(H_{1}\ \sim\ H_{n}\) for the habitat set H defined in Step 1. Here, the termination condition of k-means is taken to be \"A = B if B > A\" when the current evaluation value A is compared with the new evaluation value B. Moreover, if A does not depend on the row number, K-means is terminated, and the final solution is selected as the initial solution for the habitat. After the initial solution for each habitat is selected, the silhouette coefficient for the selected initial solution is calculated using Equations (1) and (2). * Step 3. Select the emigration habitat. Once the initial solution for the initially established habitat H has been established, the emigration habitat is selected. First, the silhouette coefficients of \(H_{1}\ \sim\ H_{n}\) are determined for the habitat H for which the initial solution has been established using Equations (1) and (2). The silhouette coefficient for each habitat H is taken to be \(S_{H_{n}}=Silhouette(H_{n})+1\). This is because the habitat search process does not function properly if the silhouette coefficient becomes negative. First, the emigration habitat selection probability is determined using the following equation:  
\[E_{H_{n}}=\frac{S_{H_{n}}}{\sum_{j=1}^{n}S_{H_{n}}} \tag{5}\]  
The probabilities of \(\,\mathrm{E_{H_{1}}}\,\sim\,\mathrm{E_{H_{n}}}\) are determined using Equation (5), and one migration habitat is selected by comparing the probabilities with that of a random function in (0, 1). * Step 4. Select the immigration habitat. The silhouette coefficients of initial habitats \(\,\mathrm{H_{1}}\,\sim\,\mathrm{H_{n}}\) are selected before selecting the emigration habitat using Equations (1) and (2).