Data centers must provide sufficient resources to ensure smooth operation of the applications hosted in them under variable workload. In addition to traditional Internet applications, the number of applications requiring high-performance computing, such as machine learning, big data processing, and virtual desktop infrastructure applications is growing. Due to the high parallel computing requirements of such applications, the demand for servers with graphics processing units (GPUs) is increasing. Data centers are becoming heterogeneous, including traditional non-GPU servers and GPU servers. Many works are devoted to the problem of virtual machine placement in homogeneous cloud data centers, but for heterogeneous data centers, the distribution and provision of GPUs to virtual machines requires further study. This paper presents a formulation of the problem of GPU-aware multi-criteria placement of virtual machines to improve the energy efficiency of the data centers, while providing sufficient resources for the operation of virtual machines.