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The continuously increasing complexity of communication networks and the increasing diversity and unpredictability of traffic demand has led to a consensus view that the automation of the management process is inevitable. Currently, network and service management techniques are mostly manual, requiring human intervention, and leading to slow response times, high costs, and customer dissatisfaction. In this paper we present AutoNet, a self-organizing management system for core networks where robustness to environmental changes, namely traffic shifts, topology changes, and community of interest is viewed as critical. A framework to design robust control strategies for autonomic networks is proposed. The requirements of the network are translated to graph-theoretic metrics and the management system attempts to automatically evolve to a stable and robust control point by optimizing these metrics. The management approach is inspired by ideas from evolutionary science where a metric, network criticality, measures the survival value or robustness of a particular network configuration. In our system, network criticality is a measure of the robustness of the network to environmental changes. The control system is designed to direct the evolution of the system state in the direction of increasing robustness. As an application of our framework, we propose a traffic engineering method in which different paths are ranked based on their robustness measure, and the best path is selected to route the flow. The choice of the path is in the direction of preserving the robustness of the network to the unforeseen changes in topology and traffic demands. Furthermore, we develop a method for capacity assignment to optimize the robustness of the network.