  We construct and investigate Boolean networks that follow a given reliable
trajectory in state space, which is insensitive to fluctuations in the updating
schedule, and which is also robust against noise. Robustness is quantified as
the probability that the dynamics return to the reliable trajectory after a
perturbation of the state of a single node. In order to achieve high
robustness, we navigate through the space of possible update functions by using
an evolutionary algorithm. We constrain the networks to having the minimum
number of connections required to obtain the reliable trajectory. Surprisingly,
we find that robustness always reaches values close to 100 percent during the
evolutionary optimization process. The set of update functions can be evolved
such that it differs only slightly from that of networks that were not
optimized with respect to robustness. The state space of the optimized networks
is dominated by the basin of attraction of the reliable trajectory.
