## 3 Ibwo-Lssvr Online Model
### Ijwo  
This section focuses on the optimization process of IBWO, and the pseudo-code of the Algorithm 1 is shown below. The specific flow is shown in Figure 4.  
Step 1: Initiate the parameterization of the IBWO. This involves the population size \(n\), the maximum number of iterations \(T_{max}\), and the nonlinear balancing factor \(B_{f}\). Initial positions are randomly generated in the search space, and the fitness value is obtained based on the objective function.  
Step 2: Exploration phase. Based on the \(B_{f}\), it is decided that each beluga whale enters the exploration phase or the exploitation phase. If the beluga's \(B_{f}>0.5\), the update mechanism enters the exploration phase, and the beluga's position is updated by Equation (10).  
Step 3: Exploitation phase. If \(B_{f}<0.5\), the beluga position is updated using Equation (11). Then, the fitness value of the new position is calculated and ranked based on the population optimization strategy of Equation (17). Then, the results are compared with those of the previous generation to find the best result.  
Step 4: Whale fall phase. Some beluga whales die and descend into the deep sea, and the probability of whale fall is \(W_{f}\). The location is updated by the improved whale fall strategy of Equation (18).  
Step 5: Elite learning phase. The post-foraging beluga population is updated again using the elite learning strategy according to Equation (19), and elite learning is performed on the \(N\) individual beluga whales with the worst position after the update.  
Step 6: Termination condition check. If the current number of iterations is greater than the maximum number of iterations, the IBWO algorithm stops. Otherwise, repeat step 2.  
```
1:algorithm parameters (\(N_{pop}\), \(T_{max}\))
2:Optimal solution
3: Initialize the population and evaluate the adaptation values to obtain the best solution
4:While\(T\leq T_{max}\)Do
5: Calculate the whale fall probability \(W_{f}\) Equation (16) Obtain the nonlinear balancing factor \(B_{f}\) based on the Sigmoid function.
6:For\(X_{i}\)Do
7:If\(B_{f}\) (\(i\)) > 0.5
8:// Exploration phase
9: Generate \(p_{i}\) randomly from dimension (\(i\) = 1, 2,..., \(d\))
10: Randomly select a beluga whale \(X_{r}\)
11: Use Equation (10) to update the new position of the \(i\)th beluga whale
12:Else If\(B_{f}\) (\(i\)) < 0.5
13:// Exploitation phase
14: Updating the random jump strength \(C_{1}\) and computing the Levy flight function
15: Use Equation (11) to update the new position of the \(i\)th beluga whale
16:End If
17: Check the boundary, calculate and rank the fitness values, compare and select with the previous generation according to Equation (17)
18:End For
19:For\(X_{i}\)Do
20:// Whale fall phase
21:If\(B_{f}\) (\(i\)) \(\leq W_{f}\)
22: Update the new position of the \(i\)th beluga whale using Equation (18)
23: Check the boundary, calculate and rank the fitness values, compare with the previous generation according to Equation (17) and select the optimal.
24:End If
25:End For
26: Elite learning for beluga whales with the lowest fitness values according to Equation (19)
27: Check the boundary, calculate and rank the fitness values
28:Find the current optimal solution
29:\(T=T+1\)
30:End While
31:Output optimal solution
```  
**Algorithm 1**IBWO algorithm pseudocode  
Figure 4: IBWO optimization flow chart.