Data centers are critical to the commercial and social activities of modern society but are also major electricity consumers. To minimize their environmental impact, it is imperative to make data centers more energy efficient while maintaining a high quality of service (QoS). Bearing this consideration in mind, we develop an analytical model using queueing theory for evaluating the QoS of a data center. Furthermore, based on this model, we develop a domain-specific evolutionary optimization framework featuring a tailored solution representation and a constraint-aware initialization operator for finding the optimal placement of virtual network functions in a data center that optimizes multiple conflicting objectives with regard to energy consumption and QoS. In particular, our framework is applicable to any existing evolutionary multi-objective optimization algorithm in a plug-in manner. Extensive experiments validate the efficiency and accuracy of our QoS model as well as the effectiveness of our tailored algorithms for virtual network function placement problems at various scales.