## 4 Methodology
### Data Filtering
#### 4.3.1 ABC, or Artificial Bee Colony (ABC)  
The Artificial Bee Colony (ABC) algorithm takes cues from honey bee activities. Finding the best answers to various issues is made possible by a swarm intelligence system known as colonies [42]. This represents a potential food supply by each point in the search space of the ABC algorithm, which depicts the surroundings of a colony of honey bees. Each food source has a different amount of nectar, and those indicate the fitness value of the food supply. Researchers use three different types of bees in the ABC algorithm: scout, employed, and observation bees [42; 43]. The algorithm only plans to provide a working bee with food. Worker bees figure out how much nectar there is. There are the same number of workers in the colony and observers of artificial bees. The task of collecting high-quality data and forwarding it to observer bees falls to employed bees. Consequently, nectar-rich food sources will be directed toward observers among the bee population. We continued these steps until we obtained the limit value. Researchers have developed numerous ABC algorithms in the literature [44] for various purposes. Researchers have created numerous enhanced ABC variations to address global optimization issues [45]. To create test cases, for example, two novel combinatorial ABC algorithms with many requirements have been devised [46]. These algorithms improve both intensification and variety in the bee population by optimizing coverage criteria. There are five primary phases to the ABC algorithm:  
**First Step:** Based on the amount of food sources indicated by \(SN\), the initialization randomly creates the initial food sources. Two times \(SN\) (\(SN\) employed bees + \(SN\) onlooker bees) is the colony size \(NP\). We generate food sources between the variables' top and lower boundaries. Equation (8) generates the food source positions during the startup stage:  
\[X_{ij}=X_{minij}+\text{rand(0,1)(X_{maxj}-X_{minj})} \tag{8}\]  
In dimension \(j\), where \(j=1,2,3\ldots,D\), \(Xminij\), and \(Xmaxj\) represent the lower and upper bounds. \(SN\) defines the number of worker or observer bees. For every solution, we construct a \(D\)-dimensional vector \(xi\) (\(i=1,2,\ldots,\)\(SN\)), where \(D\) is the quantity of optimization factors. Following the initialization stage, we repeat cycles with the populations of the scout, employed, and onlooker bees \(C=1,2\ldots,\)\(MCN\) used in the solution search strategies. \(MCN\) is the maximum count of iterations. **Second step:** Evaluate the food sources' fitness value (i.e., nectar amount). We use Equation (9) to compute the attributes of every food source individually:  
\[fit_{i}= \begin{cases}\frac{1}{1+f_{i}},\text{ }if(f_{i}\geq 0)\\ 1+abS(f_{i}),\text{ }otherwise\end{cases}  \tag{9}\]  
where \(fit_{i}\) is the value of the specific objective function and \(fi\) is the fitness of the \(i\)th food source. **Third Step:** After initialization and fitness calculations, the employed bees, following the bee method, explore new food sources with better nectar. Every worker bee updates the locations of their relevant food sources. This way, we create a new food source position \(vij\):  
\[v_{ij}=X_{ij}+\phi_{ij}\left(X_{ij}-X_{kj}\right) \tag{10}\]  
The letters \(j\in\{1,2,\ldots,\)\(d\}\) and \(k\in\{1,2,\ldots,\)\(SN\}\) represent the randomly selected index values. The uniform random number \(Jij\), in this instance, is located in the interval \([-1,\)\(1]\). In dimension \(j\), the reference and randomly chosen food sources are at \(Xij\) and \(Xkj\), respectively. Equation (9), once we have established \(vij\), is used to calculate its fitness value. An employed bee stores the position of the new food source when its fitness exceeds that of the previous one. **Fourth step: The onlooker bee method:** Each chooses a food source based on the fitness values determined in Step 3. High-fitness food sources are more likely to be chosen than others in this selection mechanism [42].