  One of the main limitations of variational quantum algorithms is the
classical optimization of the highly dimensional non-convex variational
parameter landscape. To simplify this optimization, we can reduce the search
space using problem symmetries and typical optimal parameters as initial points
if they concentrate. In this article, we consider typical values of optimal
parameters of the Quantum Approximate Optimization Algorithm for the MaxCut
problem with $d$-regular tree subgraphs and reuse them in different graph
instances. We prove symmetries in the optimization landscape of several kinds
of weighted and unweighted graphs, which explains the existence of multiple
sets of optimal parameters. However, we observe that not all optimal sets can
be successfully transferred between problem instances. We find specific
transferable domains in the search space and show how to translate an arbitrary
set of optimal parameters into the adequate domain using the studied
symmetries.
