# Self-adaptive Artificial Bee Colony with a Candidate Strategy Pool
## 3 The Proposed Algorithm SAABC-CS
### Candidate Strategy Pool
In this experiment, we obtained the two-dimensional individual distribution for the five strategies after 20 generations, and present the results in Figure 3. The initial population size of each strategy was 100. From Figure 3a, these individuals may be seen to disperse around local maxima, although the local maxima are still distant from the global maxima. Thus, it is obvious that the \"ABC/rand\" strategy has a strong exploration ability but weak exploitation ability. We can see clearly that all individuals converge around one local optimum in Figure 3b, but the local optimum is not the global optimum. Thus, it has a strong exploitation ability but weak exploration ability. The \"ABC/pbest-2\" strategy originates from \"ABC/pbest-1\", but with increased exploration ability. This modification causes most individuals to distribute around global optimum, with some individuals located around other local optima. The results in Figure 3c further demonstrate that the \"ABC/pbest-2\" strategy increased its exploration ability while keeping its exploitation ability. As for the results in Figure 3d, the \"ABC/current-to-pbest\" strategy uses the information of the current individual, a random different individual, and a random elite individual. Thus, it has a strong exploration ability during early generation and a strong exploitation ability during late generation. As we can see from Figure 3e, under the influence of \"ABC/pbest-to-rand\", the individuals mainly converged around the global optimum, with others also located near local optima. This was dominated by \(X_{e}\) but also uses the current individual information. Thus, it maintains a significant capacity for exploitation, while also having the opportunity to leave the local optima and go to a global or nearby one. Figure 2: Schematic diagrams of five different strategies. (Stars represent elite individuals, triangles represent common individuals,red circles represent new individual,dashed arrows represent search direction). With the exception of the \"ABC/rand\" technique, the other four search methods all utilize the information of the elite group. The following two benefits result from using an elite group instead of the elite with the best fitness:  
(1) In the first place, this allows the entire population to fully utilize the knowledge of the elite solution group during the evolution process and evolve in a better way. (2) Second, the whole population is prone to becoming locked in local optima if the population only uses the present global optimal solution as the search traction. However, the population may evolve in numerous good directions and are provided better solutions by the elite group. As a result of using an elite group, it is simple for the population to move away from the local optima and reach the global or approximated optimal region. Additionally, the original ABC search approach performs poorly for some issues with variable inseparability, since it only updates one variable at a time. Therefore, to update  
Figure 3: Five strategies’ contour graphs based on the two-dimensional Rastrigin function. (Red dots represent individuals. Subfigures (**a–e**) represent individual distribution map of the five strategies in the current generation, respectively). many dimensions at once, these techniques combine mutation and crossover, as in GA. In this approach, using various update techniques inside the adaptive mechanism enhances the algorithm's efficiency, while simultaneously strengthening its robustness. Thus, to create a trial vector \(U_{i,j}\), we apply a binomial crossover operator to \(X_{i,j}\) and \(V_{i,j}\). \[U_{i,j}=\left\{ \begin{array}{ll}V_{i,j}&\text{if rand}\leq\text{M or j}=\text{k}\\ X_{i,j}&\text{Otherwise}\end{array} \right. \tag{11}\]  
where \(i=1,2,\ldots,SN,j=1,2,\ldots,D\). A number chosen at random between [1, D] called \(k\) is utilized to make certain that at least one element is updated. \(rand\) is an arbitrary number ranging from 0 to 1 with a uniform distribution.