  Problem decomposition plays a vital role when applying cooperative
coevolution (CC) to large scale global optimization problems. However, most
learning-based decomposition algorithms either only apply to additively
separable problems or face the issue of false separability detections.
Directing against these limitations, this study proposes a novel decomposition
algorithm called surrogate-assisted variable grouping (SVG). SVG first designs
a general-separability-oriented detection criterion according to whether the
optimum of a variable changes with other variables. This criterion is
consistent with the separability definition and thus endows SVG with broad
applicability and high accuracy. To reduce the fitness evaluation requirement,
SVG seeks the optimum of a variable with the help of a surrogate model rather
than the original expensive high-dimensional model. Moreover, it converts the
variable grouping process into a dynamic-binary-tree search one, which
facilitates reutilizing historical separability detection information and thus
reducing detection times. To evaluate the performance of SVG, a suite of
benchmark functions with up to 2000 dimensions, including additively and
non-additively separable ones, were designed. Experimental results on these
functions indicate that, compared with six state-of-the-art decomposition
algorithms, SVG possesses broader applicability and competitive efficiency.
Furthermore, it can significantly enhance the optimization performance of CC.
