This paper highlights a novel approach to address multiple networking-based VM allocation and migration objectives at the cloud data center. The proposed approach in this paper is structured into three distinct phases: firstly, we employ a Bi-Directional Long Short Term Memory (BiLSTM) model to predict Virtual Machines (VMs) instance’s prices. Subsequently, we formulate the problem of allocating VMs to Physical Machines (PMs) and switches in a network-aware cloud data center environment as a multi-objective optimization task, employing Linear Programming (LP) techniques. For optimal allocation of VMs, we leverage the Branch-and-Bound (BaB) technique. In the third phase, we implement a VM migration strategy sensitive to SLA requirements and energy consumption considerations. The results, conducted using the CloudSim simulator, demonstrate the efficacy of our approach, showcasing a substantial 35% reduction in energy consumption, a remarkable decrease in SLA violations, and a notable 18% increase in the cloud data center’s profit. Finally, the proposed multi-objective approach reduces energy consumption and SLA violation and makes the data center sustainable.