  Can synchronization properties of a network of identical oscillators in the
presence of noise be improved through appropriate rewiring of its connections?
What are the optimal network architectures for a given total number of
connections? We address these questions by running the optimization process,
using the stochastic Markov Chain Monte Carlo method with replica exchange, to
design the networks of phase oscillators with the increased tolerance against
noise. As we find, the synchronization of a network, characterized by the
Kuramoto order parameter, can be increased up to 40 %, as compared to that of
the randomly generated networks, when the optimization is applied. Large
ensembles of optimized networks are obtained and their statistical properties
are investigated.
