  Many optimization problems suffer from noise, and nonlinearity check-based
decomposition methods (e.g. Differential Grouping) will completely fail to
detect the interactions between variables in multiplicative noisy environments,
thus, it is difficult to decompose the large-scale optimization problems
(LSOPs) in noisy environments. In this paper, we propose an automatic Random
Grouping (aRG), which does not need any explicit hyperparameter specified by
users. Simulation experiments and mathematical analysis show that aRG can
detect the interactions between variables without the fitness landscape
knowledge, and the sub-problems decomposed by aRG have smaller scales, which is
easier for EAs to optimize. Based on the cooperative coevolution (CC)
framework, we introduce an advanced optimizer named Modified Differential
Evolution with Distance-based Selection (MDE-DS) to enhance the search ability
in noisy environments. Compared with canonical DE, the parameter
self-adaptation, the balance between diversification and intensification, and
the distance-based probability selection endow MDE-DS with stronger ability in
exploration and exploitation. To evaluate the performance of our proposal, we
design $500$-D and $1000$-D problems with various separability in noisy
environments based on the CEC2013 LSGO Suite. Numerical experiments show that
our proposal has broad prospects to solve LSOPs in noisy environments and can
be easily extended to higher-dimensional problems.
