## 1 Introduction  
Traditional evolutionary algorithms are successfully used for solving black-box optimization problems [1]. Cooperative coevolution (CC) was proposed by [PERSON] and [PERSON], in [2], to increase the performance of the standard genetic algorithm (GA) [1] when solving continuous optimization problems. The authors proposed two versions of CC-based algorithms, CCGA-1 and CCGA-2. The main idea behind CC is to decompose a problem into parts (subcomponents) and optimize them independently. The authors noted that any evolutionary algorithm (EA) can be used to evolve subcomponents. The first algorithm merges the current solution with subcomponents from the best solutions. The second algorithm merges the current solution with randomly selected individuals from other subcomponents. As has been shown in numerical experiments, CCGA-1 and CCGA-2 outperform the standard GA. This study marked the beginning of a new branch of methods for solving large-scale global optimization problems [3]. The pseudo-code of a CC-based EA is presented in Algorithm 1. The termination criterion is the predefined number of function evaluations (FEs). It should be clarified that CC has two main control parameters: the population size and the number of subcomponents. ```
Set the number of individuals (pop_size), the number of subcomponents (\(m\))
1: Generate an initial population randomly;
2: Decompose an optimization vector into \(m\) independent subcomponents;
3:while (FES \(>0\)) do
4:for\(i=1\) to \(m\)
5: Evaluate the \(i\)-th subcomponent using _pop_size_ individuals;
6: Construct a solution by merging the best-found solutions from all subcomponents;
7:endfor
8:endwhile
9:return the best-found solution;
```  
**Algorithm 1** The classic CC-based EA  
In general, an LSGO problem can be stated as a continuous optimization problem (1):  
\[f(\overline{x})\rightarrow\min_{\overline{x}\in D\subset\mathbb{R}^{n}}f^{*}=f (x^{*})\leq f(\overline{x}),\;x\in D\subset R^{n}, \tag{1}\]  
where \(f(\overline{x})\) is a fitness function to be minimized, \(f:R^{n}\to R^{1},\overline{x}\) is an n-dimensional vector of continuous variables, \(D\) is the search space defined by box constraints \(x_{i}^{l}\leq x_{i}\leq x_{i}^{u}\), \(i=\overline{1,n}\), \(x_{i}^{l}\) and \(x_{i}^{u}\) are the lower and upper borders of the \(i\)-th variable, respectively, and \(x^{*}\) is a global optimum. It is assumed that the fitness function is continuous. The satisfaction of the Lipschitz condition is not assumed; therefore, no operations are performed to estimate the Lipschitz constant. In this case, the convergence of an algorithm to the global optimum cannot be guaranteed. In the case of a huge number of decision variables, it is not possible to adequately explore the high-dimensional search space using a limited fitness budget. Additionally, we can clarify the goal of the stated problem as proposed in [4]: \"the goal of global optimization methods is often to obtain a better estimate of \(f^{*}\) and \(x^{*}\) given a fixed limited budget of evaluations of \(f(\overline{x})\)\". In the last two decades, many researchers and applied specialists have successfully applied CC-based approaches to the increase of performance of metaheuristics when solving real-world LSGO problems [5; 6; 7; 8; 9; 10]. According to the generally accepted classification [11; 12], CC-based approaches can be divided into three groups: static, random, and learning-based variable groupings. In case of static grouping (decomposition), one needs to set a fixed number of subcomponents and how the variables will be assigned to these subcomponents during the optimization process. It is appropriate to apply the static decomposition provided that the relationship between an optimized variables is known. However, many hard LSGO problems are represented by a black-box or gray-box model. The relationship between optimized variables is unknown, and it is risky to choose the number of subcomponents randomly.