  Network's resilience to the malfunction of its components has been of great
concern. The goal of this work is to determine the network design guidelines,
which maximizes the network efficiency while keeping the cost of the network
(that is the average connectivity) constant. With a global optimization method,
memory tabu search (MTS), we get the optimal network structure with the
approximately best efficiency. We analyze the statistical characters of the
network and find that a network with a small quantity of hub nodes, high degree
of clustering may be much more resilient to perturbations than a random network
and the optimal network is one kind of highly heterogeneous networks. The
results strongly suggest that networks with higher efficiency are more robust
to random failures. In addition, we propose a simple model to describe the
statistical properties of the optimal network and investigate the
synchronizability of this model.
