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New results can be obtained about performance and vulnerability of complex networks through the common intersection of the fields of graph theory, information theory, and optimization theory. Graph theory provides a basis of architecture and also constraint relationships for key flow variables. Information theory provides measures and metrics of flow performance. The optimization of complex networks is accomplished via genetic algorithms on the flow variables. By performing a minimum flow and maximum flow optimization, a sensitivity matrix of vulnerabilities of a network can be ascertained. Thus the most vulnerable set of nodes can be determined. This procedure is first applied to a logistics network. The generalization to communication's networks and other distributed complex systems is discussed.