## 1 Introduction
For example, two interacting variables can be placed in different groups and as a result the performance of this approach will be worse on average than the performance in a case in which the variables are placed in the same group. Nevertheless, the static decomposition performs well on fully separable optimization problems. Random grouping is a kind of static grouping, but variables can be placed in different subcomponents in different steps of the optimization process. The size of the subcomponents can be fixed or dynamically changed. The main purpose of applying random grouping is to increase the probability of placing interacted variables in the same subcomponents. Furthermore, after a random mixing of variables and the creation of new groups, an optimizer solves a slightly or totally different problem in terms of task features. As a result, the regrouping of variables acts as a reorganization for an optimizer. Learning grouping is based on experiments that aim to find the original interaction between decision variables. In most cases, these approaches are based on permutations, statistical models, and distribution models. Permutation techniques perturb variables and measure the change in the fitness function. Based on the changes, variables are grouped into subcomponents. In general, permutation-based techniques require a huge number of fitness evaluations. For example, the DGCC [13] algorithm requires \(2\left[\frac{n}{2m}\left(n+m-1\right)+\frac{n}{m}\right]\)fitness evaluations (FEs) to detect variable interactions. A modification of DGCC, titled DG2 [14], requires \(n(n+1)/2\) FEs. In the first iteration, a statistical analysis is performed. In the second iteration, a grouping of decision variables is performed using a statistical metric, for example, a correlation between variables based on fitness function values or a distribution of variable values. In distribution models, the first iteration is based on the estimation of variable distributions and an interaction between variables in the set of the best solutions. After that, new candidate solutions are generated on the basis of the learned variable distributions and variable interactions. In practice, the determination of the appropriate group size is a hard task, because of unknown optimization problem properties. In static and random grouping, setting an arbitrary group size can lead to low performance. On the other hand, learning grouping needs a large amount of FEs to determine true connections between variables, and there is no guarantee that an EA will perform better using the discovered true connection between variables. Usually, the small group size performs better in the beginning of the optimization process, and the large group size performs better in the last stages [15]. Thereby, there is the need to develop a self-adaptive mechanism for the automatic selection of the number of subcomponents and the population size. The paper is organized as follows. Section 2 outlines the proposed approach. In Section 3, we discuss our experimental results. We considered how the population size and the number of subcomponents affect the performance of static CC-based approaches. We evaluated the performance of the proposed self-adaptive CC-based algorithm and have compared it with the performance of CC-based approaches with a static number of subcomponents and a static population size. Additionally, we investigated a selective pressure parameter when choosing the number of subcomponents and the population size. All numerical experiments were confirmed by the Wilcoxon rank-sum test. Section 4 concludes the paper and outlines possible future work.