# Self-adaptive Artificial Bee Colony with a Candidate Strategy Pool
## 2 Related Work  
### ABC Algorithm  
The initialization period, employed bee period, onlooker bee period, and scout bee period make up the primary foundation of the ABC. All bees have different responsibilities at different stages. It should be noted that each bee has its own food resources in each period, and the number of bees in each period is consistent. The food resource in this statement often represents a candidate solution to the optimization problem. The evolution framework of the ABC is seen in Figure 1.  
Like all SAs, the ABC needs to go through an initialization stage before performing the other three stages of work cyclically. The following are the relevant contents of each phase:  
1. Initialization phase
2. In this phase, the entire population is randomly initialized, each individual represents a food resource and this is generated using Equation (1). \[X_{i,j}=Lower+rand\cdot(Upper-Lower)\] (1) where \(i=1,2,\cdots,SN\) and \(j=1,2,\cdots,D\). \(D\) stands for the dimension of the optimization problems, while \(SN\) is the number of solutions in a swarm. \(rand\) is a random number belonging to (0,1), \(X_{i,j}\) represents the element of \(j\)th dimension of the \(i\)th individual. _Lower_ and _Upper_ denote the minimum value and maximum value in all dimensions of each individual, respectively. 2. Employed bee phase  
The evolution reaches the employed bee phase after startup. According to Equation (2), each employed bee searches the full search area for new food sources during this phase. \[V_{i,j}=X_{i,j}+\phi_{i,j}\cdot(X_{i,j}-X_{k,j}) \tag{2}\]  
The random number \(\phi_{i,j}\) has the value (\(-1\),1). Unlike \(X_{i}\), which belongs to the whole population, \(X_{k}\) is a randomly chosen solution. The value of \(V_{i,j}\) is reinitialized using Equation (1) if it oversteps either the lower or higher barrier. \(V_{i}\) takes the place of \(X_{i}\) if its object function value is superior to that of \(X_{i}\). In addition, there are a number of updated individuals (NUI) for each solution. Thus, NUI is recorded using a \(1\cdot\)SN matrix. At the beginning, every element of NUI is initialized to zero. After that, once the \(X_{i}\) has successfully been replaced by \(V_{i}\), the \(i\)th value of NUI is reset to zero. Otherwise, the \(i\)th value of NUI is increased by one. The NUI matrix has an effect on the subsequent scout bee phase. Onlooker bee phase  
Figure 1: The ABC framework. The bee continues to search for new food sources during the onlooker bee phase. In contrast to the employed bee phase, the onlooker bee only has to seek in the vicinity of the chosen food resource, which is equivalent to expanding the utilization of the food resource. At this stage, not every food resource can be selected to search in its vicinity, but a probability search is carried out according to its fitness value. The calculation equation for the fitness value is as shown in Equation (3). \[Fit_{i}=\left\{ \begin{array}{ll}\dfrac{1}{1+f(X_{i})}&\text{if }f(X_{i})\geq 0\\ 1+abs(f(X_{i}))&\text{otherwise}\end{array} \right. \tag{3}\]  
where \(Fit_{i}\) and \(f(X_{i})\) are the fitness values of \(X_{i}\) and objective function result, correspondingly. \(f(X_{i})\) is calculated in the employed bee phase. Equation (4) determines the selection probability of each food resource. \[p_{i}=\dfrac{Fit_{i}}{\sum_{j=1}^{\mathcal{S}N}Fit_{j}} \tag{4}\]  
After that, the onlooker bees use the classic roulette wheel selection strategy to select a food resource. Obviously, the larger the fitness value obtained, the greater the chance the food resource is selected. Equation (2) is also used as an update equation for the onlooker bees. In addition, the same process is used as for the employed bees after generating a candidate solution. * Scout bee phase  
At scout bee phase, the element value NUI associated with each individual is checked. Once an individual's NUI exceeds a predefined value, it is believed that this food resource has been exhausted, which implies that the individual may be trapped at a local optima.