# Investigation of Improved Cooperative Coevolution for Large-Scale Global Optimization Problems +
## 2 Related Work
### Subcomponent Optimizers in Cooperative Coevolution  
CC-based metaheuristics use different EAs as the subcomponent optimizer. For example, CCGA-1 and CCGA-2 use the standard genetic algorithm [18]. SaNSDE [42] (Self-adaptive differential evolution with neighborhood search) has been applied in many CC-based metaheuristics [25; 33; 43]. An improved version of PSO [44] has been used in [28].  
In this study, the SHADE [45] (Success-History Based Parameter Adaptation for Differential Evolution) algorithm has been used as a subcomponent optimizer. SHADE is high performed differential evolution (DE) which is based on the previous modifications of DE: JADE [46], CoDE [47], EPSDE [48], and dynNP-DE [49].  
SHADE uses the following features: an external archive and a historical memory. At the selection stage, replaced individuals are moved to the external archive. These individuals save information about the previous good solutions. SHADE uses them at the mutation stage for generating new individuals: \(u_{i}=x_{i}+F_{i}\cdot\left(x_{pbest}-x_{i}\right)+F_{i}\cdot\left(x_{r1}-x_{ r2}\right)\), where \(x_{i}\) is the current individual, \(x_{pbest}\) is a randomly selected solution from the best \((pop\_size\cdotp)\) individuals, \(pop\_size\) is the population size, \(p\) is the piece of the best individuals, \(p\in[0;1]\), \(F_{i}\) is a scale factor for the \(i\)-th individual. \(r_{1}\) and \(r_{2}\) are randomly se  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Author** & **Year** & **Algorithm** & **Ref.** &
\begin{tabular}{c} **Decomposition** \\ **Strategy** \\ \end{tabular} \\ \hline [PERSON] et al. & 1994 & CCGA-1(2) & [18] & Static \\ [PERSON] et al. & 2004 & CPSO & [28] & Static \\ [PERSON]. & 2010 & CABC & [29] & Static \\ [PERSON] et al. & 2005 & CCDE & [30] & Static \\ [PERSON] et al. & 2008 & CBFO & [31] & Static \\ [PERSON] et al. & 2008 & MLCC & [32] & Random \\ [PERSON] et al. & 2008 & DECC-G & [33] & Random \\ [PERSON] et al. & 2012 & CCPSO2 & [34] & Random \\ [PERSON] et al. & 2009 & CCEA-AVP & [35] & Learning \\ [PERSON] et al. & 2014 & DECC-DG & [26] & Learning \\ [PERSON] et al. & 2011 & CBCC-DG & [36] & Learning \\ [PERSON] et al. & 2013 & CC-CMA-ES & [37] & Learning \\ [PERSON] et al. & 2020 & TSPDG & [38] & Learning \\ [PERSON] et al. & 2021 & DGSC2 & [39] & Learning \\ [PERSON] et al. & 2019 & mSaDS-COA & [40] & Learning \\ [PERSON] et al. & 2020 & BHCC & [41] & Learning \\ \hline \hline \end{tabular}
\end{table}
Table 1: LSGO grouping techniques.  
lected individuals from the current population and the external archive, \(r_{1}\in[1;pop\_size]\), \(r_{2}\in[1;pop_{size}+|A|]\), here \(|A|\) is the number of individuals in the external archive. The historical memory is used for recording successful values of \(F\) and \(CR\) parameters. In this study, the fine-tuned parameter values of the subcomponent optimizer (SHADE) are obtained using the grid search. According to the numerical experiments, the size of the historical memory \(H\) is set to 6, the size of the external archive _arch_size_ is set to \((2\cdot pop_{size})\), and the piece of the best individuals \(p\) is set to 0.1.