## 4 Mechanisms and Optimizations
### Preference-Based Scheduling Strategies
\begin{bmatrix}x_{11}&\cdots&x_{1m}\\ \vdots&\ddots&\vdots\\ x_{n1}&\cdots&x_{mm}\end{bmatrix}  \tag{5}\]  
Next, it is necessary to \"Benefit-Cost\" adjust the original data matrix. Among the input parameters corresponding to the preferences of RRP\({}_{1}\)-RRP\({}_{7}\) mentioned above, Available_CPU_Cores, Available_Memory, Available_Storage, and Available_Bandwidth are beneficial attributes, where larger values are better. As input parameters for the scoring algorithm, their \"Benefit-Cost\" values are the same as their original values, i.e., \(x_{ij}^{+}=x_{ij}\). On the other hand, Price, PUE, and Communication_Delay are cost attributes, where smaller values are better. If they are used as input parameters, adjustment is required using Equations (6) and (7). After adjusting the original data, the \"Benefit-Cost\" adjusted data matrix \(X_{n\times m}^{+}\) is obtained. \[max\left\{x_{j}\right\}=max\left\{x_{1j},x_{2j},x_{3j},\ldots x_{nj}\right\} \tag{6}\]  
\[x_{ij}^{+}=max\left\{x_{j}\right\}-x_{ij} \tag{7}\]  
\[X_{n\times m}^{+}= \begin{bmatrix}x_{11}^{+}&\cdots&x_{1m}^{+}\\ \vdots&\ddots&\vdots\\ x_{n1}^{+}&\cdots&x_{mm}^{+}\end{bmatrix}  \tag{8}\]  
Then, it is required to utilize Equation (9) to standardize the \(X_{n\times m}^{+}\), eliminating the influence of different dimensions and obtaining the standardized data matrix \(Z_{n\times m}\). \[z_{ij}=\frac{x_{ij}^{+}}{\sqrt{\frac{n}{i=1}^{n}\left(x_{ij}^{+}\right)^{2}}} \tag{9}\]\[Z_{n\times m}= \begin{bmatrix}z_{11}&\cdots&z_{1m}\\ \vdots&\ddots&\vdots\\ z_{n1}&\cdots&z_{nm}\end{bmatrix}  \tag{10}\]  
Finally, based on the standardized data matrix, Equations (11)-(15) are employed to calculate the comprehensive score \(s_{i}(i\in N)\) for each CRN. A higher score indicates a better overall performance of the CRN across the dimensions of input parameters corresponding to user preferences. \[max\left\{z_{j}\right\}=max\left\{z_{1j},z_{2j},z_{3j},\ldots z_{nj}\right\} \tag{11}\]  
\[min\left\{z_{j}\right\}=min\left\{z_{1j},z_{2j},z_{3j},\ldots z_{nj}\right\} \tag{12}\]  
\[d_{i}^{+}=\sqrt{\Sigma_{j=1}^{m}\omega_{j}(max\left\{z_{j}\right\}-z_{ij})^{2 }},\;i\in N \tag{13}\]  
\[d_{i}^{-}=\sqrt{\Sigma_{j=1}^{m}\omega_{j}(min\left\{z_{j}\right\}-z_{ij})^{2 }},\;i\in N \tag{14}\]  
\[s_{i}=\frac{d_{i}^{-}}{d_{i}^{-}+d_{i}^{+}}\;\times MaxNodeScore,\;i\in N \tag{15}\]  
\(\omega_{j}\) represents the weight of each input parameter, determined through the entropy weight method. Firstly, utilize Equation (16) to standardize the original data matrix. \(min\left\{x_{j}\right\}\) is the minimum values of \(\left\{x_{1j},x_{2j},x_{3j},\ldots x_{nj}\right\}\), which is opposite to \(max\left\{x_{j}\right\}\). Subsequently, for the \(j\)th (\(j\in M\)) input parameter, calculate its information entropy \(E_{j}\) using Equations (17) and (18). Finally, obtain the weight \(\omega_{j}\) using (19), with \(0\leq\omega_{j}\leq 1\), and the sum of \(m\) weights is equal to 1. \[x_{ij}^{{}^{\prime}}=\frac{x_{ij}-min\left\{x_{j}\right\}}{\max\left\{x_{j} \right\}-min\left\{x_{j}\right\}} \tag{16}\]  
\[P_{ij}=\frac{x_{ij}^{{}^{\prime}}}{\Sigma_{k=1}^{n}x_{kj}^{{}^{\prime}}} \tag{17}\]  
\[E_{j}=-\frac{1}{\ln n}\sum_{i=1}^{n}P_{ij}\times\ln P_{ij},\;j\in M \tag{18}\]  
\[\omega_{j}=\frac{1-E_{j}}{m-\sum_{k=1}^{m}E_{k}},\;j\in M \tag{19}\]  
After obtaining scores for each CRN, it is necessary to select the target CRN based on the score results. Initially, CRNs that meet the hard constraints indicated by the following condition (20) are added to the candidate CRNs set \(C\). Herein, \(A\) represents the set of all CRNs. Subsequently, within the candidate CRNs set, node selection is performed based on the score results. If a greedy algorithm is employed, always choosing the highest-scored node may exacerbate resource competition issues in distributed scheduling scenarios, leading to load imbalance and scheduling failures. On the other hand, adopting a random selection algorithm fails to meet user preferences.