## 4 Analysis of Experimental Results
### Cognitive Radio Application  
#### 4.2.1 IGEO Problem Solving Model  
In the proposed model for solving the spectrum allocation problem, each golden eagle's binary-coded position represents a feasible spectrum allocation strategy. To determine the optimal spectrum allocation scheme, it is necessary to solve the interference-free allocation problem. Figure 6: IGEO and various single\(-\)strategy algorithms’ convergence curves on the benchmark functions. tion matrix \(\mathbf{A}\) to maximize the total system benefit. Based on the status of the secondary user (SU) utilizing the channel in the idle matrix \(l_{n,m}=0\), SU \(n\) cannot utilize channel \(m\). Consequently, matrix \(a_{n,m}\) in the corresponding position must be zero. Conversely, if \(l_{n,m}=1\), then \(a_{n,m}\) can be either 0 or 1. The processing strategy proposed in the literature [45] for the idle matrix \(\mathbf{L}\) involves exclusively numbering those elements for which the array is 1. Furthermore, the number of elements in matrix \(\mathbf{L}\) that equal 1, representing the coding length D of the golden eagle individuals, is recorded. The formula for calculating this is as follows:  
\[D=\sum_{n=1}^{\text{N}}\sum_{m=1}^{\text{M}}l_{n,m}, \tag{18}\]  
Figure 7 illustrates the mapping relationship between the location encoding and the assignment matrix. In the current cognitive wireless network environment, assuming N = 6 cognitive users and M = 4 channels, the idle matrix \(\mathbf{L}\) is calculated based on the network topology. The locations of 1 in matrix \(\mathbf{L}\) are identified, and the location x of an individual golden eagle's binary encoding is mapped to the allocation matrix \(\mathbf{A}\) in increasing order. The pseudo-code of the proposed IGEO solving CR when applying IGEO to the cognitive radio model is shown in Algorithm 2. ```
1 Initialize the idle matrix \(\mathbf{L}\), the benefit matrix \(\mathbf{B}\), the non-interference distribution matrix \(\mathbf{C}\)
2 Calculate the number of values in \(\mathbf{L}\), and then enter the appropriate values of n and m at the position of 1 in the idle matrix \(\mathbf{L}\). Find the dimensions D of the optimization problem, which corresponds to the number of unique golden eagle codes, by listing the position elements in an increasing order of n and m
3 Set algorithm parameters \(\mathbf{N}\), t = 0, T = 1000
4 Initialize Arnold chaotic map
5 According to the problem dimension D, the number N, and Arnold map, the individual position is initialized, and the golden eagles' position is mapped to the allocation matrix \(\mathbf{A}\). 6 If all n and k in the coherence matrix satisfy the condition \(c_{n,k,m}=1\), the values of \(a_{n,m}\) and \(a_{n,m}\) in the assignment matrix \(\mathbf{A}\) are both 1. 7 Set one of them to 0 and keep the other unchanged
8 End If
9 The binary coding corresponding to the golden eagle individual after processing the non-interference constraint matrix
10 According to the distribution matrix \(\mathbf{A}\) and the benefit matrix \(\mathbf{B}\), the individual fitness value is calculated. 11 Initialize other parameters: \(P_{x}\), \(P_{a}\) and golden eagle's memory
12 While \(\mathbf{t}<1\)
13 Update \(P_{a}\) and \(P_{x}\) based on Equation (9)
14 For i = 1:N
15 Calculate \(A\)(attack vector) based on Equation (1)
16 If the length of A is not equal to zero
17 Calculate C based on Equations (5) and (6)
18 Calculate \(\omega(\mathbf{t})\) based on Equation (12)
19 Calculate A based on Equation (7)
20 Calculate the population fitness and selected fitness optimal individual \(\mathbf{\tau}_{\text{best}}\)
21 Update new position \(\omega^{\lambda^{\lambda^{\lambda^{\lambda^{\lambda^{\lambda^{\lambda^{ \lambda^{\lambda^{\lambda^{\lambda^{\lambda^{\lambda^{\lambda^{\lambda^ \lambda}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}\)\)\)\)\)\

#### 4.2.2 The Solution Results of the Problem Model

In this experiment, the number of populations is set to 50, the number of iterations is set to 1000, and the number of primary users (number of spectrums) is set to M and N, respectively.