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As the Internet expands in reach and capacity, the energy consumption of network equipment increases. To date, the cost of transmission and switching equipment has been considered to be the major barrier to growth of the Internet. But energy consumption rather than cost of the component equipment may eventually become a barrier to continued growth. Research efforts on ldquogreening the Internetrdquo have been initiated in recent years, aiming to develop energy-efficient network architectures and operational strategies so as to reduce the energy consumption of the Internet. The direct benefits of such efforts are to reduce the operational costs in the network and cut the greenhouse footprint of the network. Second, from an engineering point of view, energy efficiency will assist in reducing the thermal issues associated with heat dissipation in large data centers and switching nodes. In the present research, we concentrate on minimizing the energy consumption of an IP over WDM network. We develop efficient approaches ranging from mixed integer linear programming (MILP) models to heuristics. These approaches are based on traditional virtual-topology and traffic grooming designs. The novelty of the framework involves the definition of an energy-oriented model for the IP over WDM network, the incorporation of the physical layer issues such as energy consumption of each component and the layout of optical amplifiers in the design, etc. Extensive optimization and simulation studies indicate that the proposed energy-minimized design can significantly reduce energy consumption of the IP over WDM network, ranging from 25% to 45%. Moreover, the proposed designs can also help equalize the power consumption at each network node. This is useful for real network deployment, in which each node location may be constrained by a limited electricity power supply. Finally, it is also interesting and useful to find that an energy-efficient network design is also a cost-efficient design - because of the fact that IP router ports play a dominating role in both energy consumption and network cost in the IP over WDM network.