# Self-adaptive Artificial Bee Colony with a Candidate Strategy Pool
## 3 The Proposed Algorithm SAABC-CS  
### Candidate Strategy Pool  
In most cases, different problems have different characteristics, and they are hard to describe clearly in advance. Thus, problems are usually black boxes. Moreover, different update strategies for ABC have unique characteristics. It is unrealistic to rely on only one strategy to solve all problems. These observations make us reconsider how to select strategies or construct novel strategies to improve the robustness when facing different problems. Based on the motivations above, we selected five search strategies with different characteristics from the relevant literature [18; 31] to construct our candidate strategy pool. In addition, we employed the binomial crossover method to enable the algorithm to find optimal solutions more effectively. Considering both exploration and exploitation during the entire evolution process, five strategies were selected and are described in detail, as follows:  
(i) \"rand\":  
\[V_{i,j}=X_{r1,j}+\phi_{i,j}\cdot(X_{r1,j}-X_{r2,j}) \tag{5}\]  
(ii) \"pbest-1\":  
\[V_{i,j}=X_{e,j}+\phi_{i,j}\cdot(X_{r1,j}-X_{r2,j}) \tag{6}\]  
(iii) \"pbest-2\":  
\[V_{i,j}=X_{e,j}+\phi_{i,j}\cdot(X_{r1,j}-X_{r2,j})+\phi_{i,j}\cdot(X_{r3,j}-X_ {r4,j}) \tag{7}\]  
(iv) \"current-to-pbest\":  
\[V_{i,j}=X_{i,j}+\phi_{i,j}\cdot(X_{i,j}-X_{r1,j})+\phi_{i,j}\cdot(X_{e,j}-X_{ i,j}) \tag{8}\]  
(v) \"pbest-to-rand\":  
\[V_{i,j}=X_{e,j}+\phi_{i,j}\cdot(X_{e,j}-X_{i,j}) \tag{9}\]  
where \(X_{r1}\), \(X_{r2}\), \(X_{r3}\), and \(X_{r4}\) are the different individuals selected randomly in the population, and they are all distinctive from \(X_{i}\). A homogeneous random number between [\(-1\),\(1\)] is \(\phi_{i,j}\). A solution from an elite group is represented by \(X_{e}\). The top q-SN solutions are chosen to form the elite group, after all the individuals are sorted according to their fitness values. The size of the elite group is controlled by \(q\), which is set at 0.1. \(\varphi_{i,j}\) is a homogeneous random number between [0,1.5]. Figure 2 roughly depicts the behavior of each strategy, the individuals in ellipse are the elite individuals, and the remaining triangle icons represent other common individuals. The red circle in Figure 2 represents the new individual generated by the corresponding strategy. With the \"rand\" strategy, the position of the new individual in Figure 2a is between two different individuals, and it is close to the first random individual. Actually, its position falls within a circle with \(X_{r1}\) as the center and \(|X_{r1}-X_{r2}|\) as the radius. The behavior of the \"rand\" strategy makes the algorithm focus more attention on a global search. Similarly, the position of the new individual in Figure 2b is between an elite individual and two different common individuals with the \"pbest-1\" strategy. This strategy leads the algorithm to learn the elite's information, while focusing on a global search. With the \"pbest-2\" strategy, the position of the new individual in Figure 2c is also in the center of the selected individuals, this makes our algorithm utilize more individual sampling information. As shown in Figure 2d, the position of the new individual is affected by the current individual, an elite individual, and a randomly selected individual in the \"current-to-pbest\" strategy. The position of the new individual in Figure 2e is based on the elite  
individual and current individual, which comprehensively takes the current individual and elite individual into consideration. In order to further reflect the different characteristics of the five strategies in seeking optimal solutions, we performed an experiment on the Rastrgin function [32] under the same conditions. The formula of Rastrgin is as follows, and its dimension was set to 2:  
\[f(X)=10\cdot D+\sum_{i=1}^{D}[X_{i}^{2}-10\cdot\cos(2\cdot\pi\cdot X_{i})] \tag{10}\]  
where X is a 2-dimensional individual.