  We present an analytical scheme to achieve optimal synchronization in
multiplex networks of frustrated and non-frustrated phase oscillators. We
derive a multiplex synchrony alignment function (MSAF) for that purpose, the
expression of which consists of structural as well as dynamical information of
the layers of the multiplex network. Analyzing the MSAF, a set of frequencies
(optimal frequencies) is determined to achieve optimal synchronization in the
network. Further, using the scheme, we show that perfect synchronization can be
achieved in a layer of the multiplex network for given coupling strength and
phase frustration parameters. The analytical scheme presented here has been
tested for heterogeneous multiplex networks of frustrated and non-frustrated
Kuramoto dynamics.
