As high-speed networks have proliferated across the globe, their topologies have become sparser due to the increased capacity of communication media and cost considerations. Reliability has been a traditional goal within network design optimization of sparse networks. This paper proposes a genetic approach that uses network resilience as a design criterion in order to ensure the integrity of network services in the event of component failures. Network resilience measures have been previously overlooked as a network design objective in an optimization framework because of their computational complexity - requiring estimation by simulation. This paper analyzes the effect of noise in the simulation estimator used to evaluate network resilience on the performance of the proposed optimization approach.