## 3 Research Methodology
### Proposed OGBDTs Cyber-Attack Detection
GBTs chose features with maximum information gain, such as the tree's root node, where root nodes then distribute additional characteristics into child nodes with the next best information gain. Iterations of the division and addition processes resulted in new sets of grandchild nodes. The input space (\(I\)) was divided into \(km\) joint regions \(I_{1m},I_{2m},I_{jm}\), with estimated constant values of \(c_{1m},c_{2m},c_{jm}\), correspondingly. The base learner \(base_{m}(x)\) constitutes the total of these predicted values. In the next step, \(a_{m}base_{m}(x_{i})\) was chosen to minimize the loss function. At the end, the new model \(f_{m}(x)\) was updated with the sum of \(f(m-1)\) and \(a_{m}base_{m}(x_{i})\). However, the highest number of rounds leads to badly generalized models. To deal with this problem, [PERSON]'s algorithm uses a shrinkage variable \(\mathcal{S}\) on the computed technique \(a_{m}base_{m}(x_{i})\), so that the learning rate of the training process is reduced. Further, the EABOs is used to optimize the hyperparameters of GBDT. \(\gamma\)_and_\(\lambda\) are hyper-parameters, \(T_{loss}\) refers to the number of leaves, and \(w\) indicates the leaf weight. Enhanced African Buffalo Optimization (EABOs)  
The EABOs can be developed using the integration of the Discrete Crossover operators (DCOs) and African Buffalo Optimization (ABO) algorithms, with the special swap sequence operator SS principle, as shown in Algorithm 1. Figure 3 shows an illustration of the tree structure-based framework in conjunction with penetrating OGDTs, utilizing a depth of 3 or d = 3 to highlight the part of trees used for IDS that is determined by features. For instance, the branches of the tree were further expanded after the feature was still chosen as the root node based on the Gini indices. The decision nodes show the class names, the feature names, the Gini index, samples, and recorded values. The class name denotes whether a specific behavior is expected or hostile. Figure 3: The tree structure-based framework (OGBDTs). Step 1: The population size (Pop size), the learning parameters L1 and L2, the maximum iterations count tmax, and the GBDT's parameters, such as \(\gamma,\ \ \lambda,\ T_{loss}\), and \(w\), are set. EABOs evaluate the movements (arbitrary exploitation and exploration of buffalo, i.e., \(\alpha_{k}\) and \(\beta_{k}\)), where the buffalo represent random parameter value vectors, and the characteristics can be chosen. Exploitations are substitutions made up of random sequences produced by the swap operator (\(\widehat{\mathbb{SO}}\)). Step 2: Buffalo's evaluations, wherein buffalo are assessed in terms of their objective function values, computed based on (Equation (3)). Step 3: DCOs (discrete crossover operators): to ensure that the entire population moves towards global optimal solutions, DCOs [26] are incorporated to create a child from two parents using random real numbers. The offspring can be created by randomly selecting genes from both parents and distributing them evenly, depending on the random real number \(r\in\left\langle\ 0,1\ \right\rangle\). To produce new solutions, DCOs are applied between the global herd's best solution \(b_{g}\) and the present solutions \(a_{k}^{t}\) (i.e., child), resulting in \(a_{k-cross}^{t}\) as the solution. Step 4: Updating exploitations: the initial buffalo's exploitations \(\beta_{k}^{t}\) consists of random swap operator sets \(\widehat{\mathbb{SO}}\), which can be modified based on Equation (5). \[\beta_{k}^{t+1}=\beta_{k}^{t}\oplus L_{1}\otimes\left(a_{k-cross}^{t}-\beta_{k }^{t}\right)\oplus L_{2}\otimes\left(b_{g}^{t}-a_{k}^{t}\right) \tag{5}\]  
When referring to an integrating sequence operator that consists of two swap operators, the terms \(L_{1}\) and \(L_{2}\) specify the learning parameters with random values ranging between [0, 1], respectively.