## 3 Adaptive Bandwidth Allocation Algorithm for Improved Bald Eagle Optimization
### Adaptive Bandwidth Allocation Algorithm Based on Improved Bald Eagle Optimization  
The original bald eagle search algorithm does not involve the processing constraints, but the objective function of this paper is proposed under the constraints of Formula (5). In order to deal with constraints, a penalty function is introduced to transform the constrained objective function into an unconstrained penalty function. This paper designs the following penalty function:  
\[\begin{array}{c}z=\max\sum\limits_{i\in R}\mathrm{u}(x_{i})-\eta_{1}\sum \limits_{i\in R}{[\max(0,x_{\min_{i}}-x_{i})]^{2}}\\ -\eta_{2}\sum\limits_{i\in R}{[\max(0,x_{i}-x_{\max_{i}})]^{2}-\eta_{3}[\max( 0,\sum\limits_{i\in R}{x_{i}-x_{all}})]^{2}}\end{array} \tag{9}\]  
Among them, \(\eta_{1}\), \(\eta_{2}\), and \(\eta_{3}\) represent penalty factors, indicating the penalty weight for violating the corresponding constraints. Generally, in order to highlight the impact of infeasible solutions, the penalty factors are set to larger values. In \(\eta_{1}\) penalty item, if the number of time slots allocated to user \(i\) is not lower than the minimum guaranteed number of time slots, no penalty will be given, otherwise, punishment will be imposed. In \(\eta_{2}\) penalty item, the condition for not giving penalty is that the number of time slots allocated to user \(i\) is not greater than the number of time slots requested. \(\eta_{3}\) corresponds to the second constraint in (5).  
The specific steps of the improved bald eagle search for adaptive bandwidth allocation algorithm (IBES-ABA) are as follows:  
1. User business arrives and receives business parameters, including business priority, number of user requested time slots, minimum guaranteed time slot, modulation order, coding efficiency, and transmission rate.
2. Calculate the dynamic priority of the user and perform user scheduling.
3. Allocate the minimum guaranteed time slot for the user to ensure the basic communication of the user.
4. Calculate the number of remaining time slots \(X^{\prime}\), the number of scheduled users who have not yet met the time slot request \(R^{\prime}\), and the number of unscheduled users who have not yet met the time slot request \(S^{\prime}\). If \(X^{\prime}=0\), it means that there is no unallocated time slot under the system, and the bandwidth allocation process ends; if \(R^{\prime}=0\) and \(X^{\prime}\
eq 0\), then assign the number of time slots to the users in the set S = N - R in sequence according to the priority and continue to perform step (5) until \(X^{\prime}=0\) or \(S^{\prime}=0\).
5. Generate an initial solution according to the number of remaining time slots and the value range of the number of time slots that can be allocated to each user.
6. Using Formula (9) as the fitness function, calculate the fitness function value of the above initial solution, and sort from large to small.
7. According to the improved bald eagle search algorithm, the position update strategy is implemented. If the fitness function value of the new position is greater than the value of the original position, the position is updated.
8. Return to step (4).
9. Output the result.  
The flowchart is shown in Figure 2: