# Leveraging IGOOSE-XGBoost for the Early Detection of Subclinical Mastitis in Dairy Cows
## 2 Relevant Methods and Theories
### GOOSE Optimization Algorithm  
The GOOSE algorithm, an innovative intelligent optimization technique inspired by geese's activity during rest and foraging activities, was created in 2024 by [PERSON]. The algorithm draws inspiration from the unique behavioral patterns of geese, particularly their resting habits, whereby a designated guardian geose maintains vigilance by holding a stone with one leg. This natural behavior is translated into algorithmic terms through specific mathematical formulations for position updates and search strategies.  
The algorithm operates in two distinct phases determined by a random variable (rnd). When rnd \(\geq\) 0.5, the development phase activates, utilizing Equations (1) and (2) to update goose positions:  
\[X_{(it+1)}=F\_F\_S+D\_G_{it}\times T\_A^{2} \tag{1}\]  
\[X_{(it+1)}=F\_F\_S+D\_G_{it}\times T\_A^{2}\times Coe \tag{2}\]  
These equations incorporate parameters such as \(F\_F\_S\) (falling stone velocity), \(D\_G_{it}\) (guardian-individual distance), and \(T\_A\) (sound propagation time), with a specific condition for the coefficient Coe maintaining 0.17 as a threshold value. Conversely, when rnd \(<\) 0.5, Equation (3) governs the exploration phase:  
\[X_{(it+1)}=randn(1,\dim)\times(M\_T\times alpha)+Best\_pos \tag{3}\]  
To better illustrate the working mechanism of the GOOSE algorithm, a simple numerical example is presented below. Consider the optimization problem of finding the minimum of the quadratic function:  
\[f(x)\;=\;x^{2}\;-\;4x\;+\;4,\;x\in[-2,\;6] \tag{4}\]  
The implementation process begins with the initialization phase, in which a population of three geese (\(n=3\)) is randomly distributed in the search area. The initial positions are assigned as x\({}_{1}\) = \(-1\), x\({}_{2}\) = 2, and x\({}_{3}\) = 5, with corresponding fitness values of \(f(-1)\) = 9, \(f(2)\) = 0, and \(f(5)\) = 9, respectively. Given these values, the position x\({}_{2}\) = 2 represents the guardian geose position as it yields the optimal fitness value. During the iterative process, when \(rnd\)\(\geq\) 0.5, the development phase is activated. Equations (1) and (2) are applied with the following specific parameters: \(F\_F\_S\) = 0.17, \(D\_G_{it1}\) = \(12\) - \((-1)\) = 3, \(D\_G_{it3}\) = \(12\) - \(5\) = 3, and \(T\_A\) = 1. These parameters determine how the non-guardian geese update their positions relative to the guardian geose. Conversely, when \(rnd\)\(<\) 0.5,the exploring phase of the algorithm begins, utilizing Equation (3) with \(Best\_pos=2\) as the reference point, allowing geese to explore new regions of the search space.  
Through successive iterations, the geese progressively approach the optimal solution. The algorithm successfully identifies the global minimum at x = 2, where \(f(2)=0\), thereby validating the effectiveness of the GOOSE algorithm's dual-phase optimization strategy. This example clearly demonstrates how the algorithm exploitation (development phase) and exploration phase to find the best solution and effectively navigate the search area.  
While the emergence of new algorithms continually enriches the field of optimization, the \"no free lunch\" statement serves as a reminder that no one algorithm can tackle every optimization problem in an optimal manner. This understanding drives the ongoing refinement of the GOOSE algorithm to better address real-world complexities.