Recent work on social networks has tackled the measurement and optimization of these networks’ robustness and resilience to both failures and attacks. Different metrics have been used to quantitatively measure the robustness of a social network. In this work, we design and apply a Genetic Algorithm that maximizes the cyclic entropy of a social network model, hence optimizing its robustness to failures. Our social network model is a scale-free network created using Barabási and Albert's generative model, since it has been demonstrated recently that many large complex networks display a scale-free structure. We compare the cycles distribution of the optimally robust network generated by our algorithm to that belonging to a fully connected network. Moreover, we optimize the robustness of a scale-free network based on the links-degree entropy, and compare the outcomes to that which is based on cycles-entropy. We show that both cyclic and degree entropy optimization are equivalent and provide the same final optimal distribution. Hence, cyclic entropy optimization is justified in the search for the optimal network distribution.