  It has been proposed that quantum complexity is dual to the volume of the
extremal surface, the action of the Wheeler-DeWitt patch, and the spacetime
volume of the patch. Recently, a generalized volume-complexity observable was
formulated as an equivalently good candidate for the dual holographic
complexity. This proposal is abbreviated as ``complexity=anything." This
proposal offers greater flexibility in selecting extremal surfaces and
evaluating physical quantities, e.g., volume or action, on these surfaces. In
this study, we explore the 'complexity=anything' proposal for Gauss-Bonnet
black holes in asymptotic anti-de Sitter space in various dimensions. We
demonstrate that this proposal guarantees the linear growth of the generalized
volume at late times, regardless of the coupling parameters for
four-dimensional Gauss-Bonnet gravity. However, this universality does not hold
for higher dimensions. Moreover, discontinuous deformations of the extremal
surfaces emerge when multiple peaks exist in the effective potential, which is
reminiscent of a phase transition. Additionally, we present constraints on the
coupling parameters of five-dimensional models in order for the generalized
volume to be a viable candidate for holographic complexity.
