Wide-Area Power System Stabilizers (WAPSSs) are damping controllers used in power systems that employ data from Phasor Measurement Units (PMUs). WAPSSs are capable of providing high damping rates for the low-frequency oscillation modes, especially the inter-area modes. Oscillation modes can destabilize power systems if they are not correctly identified and adequately damped. However, WAPSS communication channels may be subject to failures or cyber-attacks that affect their proper operation and may even cause system instability. This research proposes a method based on an optimization model for the design of a WAPSS robust to multiple permanent communication failures. The results of applications of the proposed method in the IEEE 68-bus system show the ability of the WAPSS design to be robust to a possible number of permanent communication failures. Above this value, the combinations of failures and processing time are high and they make it difficult to obtain high damping rates for the closed-loop control system. The application and comparison of different optimization techniques are valid and showed a superior performance of the Grey Wolf Optimizer in solving the optimization problem.