Data centers are critical to the commercial and social activities of modern society but are also major consumers of electricity. The challenge of providing high quality, low energy services is inspiring an overhaul of data centers and the wider telecommunications network. In this thesis we develop accurate analytical models for evaluating the quality of service of future data centers. Furthermore, based on these models, we develop domain-specific optimisation algorithms for finding the optimal placement of virtual network functions - a key component of future data centers. Our key contributions are the identification and correction of issues with popular models of the data centre, a new metaheuristic approach to placement that outperforms the current state of the art, and refinements to our algorithm to allow it to solve very large problem instances.