The analysis of the Quality of Service (QoS) level in a Cloud Computing environment becomes an attractive researchdomain as the utilization rate is daily higher and higher. Its management has a huge impact on the performance ofboth services and global Cloud infrastructures. Thus, in order to nd a good trade-o, a Cloud provider has to takeinto account many QoS objectives, and also the manner to optimize them during the virtual machines allocationprocess. To tackle this complex challenge, this article proposed a multiobjective optimization of four relevantCloud QoS objectives, using two different optimization methods: a Genetic Algorithm (GA) and a Mixed IntegerLinear Programming (MILP) approach. The complexity of the virtual machine allocation problem is increasedby the modeling of Dynamic Voltage and Frequency Scaling (DVFS) for energy saving on hosts. A global mixed-integer non linear programming formulation is presented and a MILP formulation is derived by linearization. Aheuristic decomposition method, which uses the MILP to optimize intermediate objectives, is proposed. Numerousexperimental results show the complementarity of the two heuristics to obtain various trade-os between the differentQoS objectives.