Technology providers heavily exploit the usage of edge‐cloud data centers (ECDCs) to meet user demand while the ECDCs are large energy consumers. Concerning the decrease of the energy expenditure of ECDCs, task placement is one of the most prominent solutions for effective allocation and consolidation of such tasks onto physical machine (PM). Such allocation must also consider additional optimizations beyond power and must include other objectives, including network‐traffic effectiveness. In this study, we present a multi‐objective virtual machine (VM) placement scheme (considering VMs as fog tasks) for ECDCs called TRACTOR, which utilizes an artificial bee colony optimization algorithm for power and network‐aware assignment of VMs onto PMs. The proposed scheme aims to minimize the network traffic of the interacting VMs and the power dissipation of the data center's switches and PMs. To evaluate the proposed VM placement solution, the Virtual Layer 2 (VL2) and three‐tier network topologies are modeled and integrated into the CloudSim toolkit to justify the effectiveness of the proposed solution in mitigating the network traffic and power consumption of the ECDC. Results indicate that our proposed method is able to reduce power energy consumption by 3.5% while decreasing network traffic and power by 15% and 30%, respectively, without affecting other QoS parameters.