The goal of data centers in the cloud computing environment is to provision the workloads and the computing resources as demanded by the users without the intervention of the providers. To achieve this, virtualization based server consolidation acts as a vital part in virtual machine placement process. Consolidating the Virtual Machines (VMs) on the Physical Machines (PMs) cuts down the unused physical servers, decreasing the energy consumption, while keeping the constraints for CPU and memory utilization. This technique also reduces the resource wastage and optimizes the available resources efficiently. Ant Colony Optimization (ACO) that is a well-known multi objective heuristic algorithm and Grey Wolf Algorithm (GWO) has been used to consolidate the servers used in the virtual machine placement problem. The proposed Fuzzy HAGA algorithm outperforms the other algorithms MMAS, ACS, FFD and Fuzzy ACS compared against it as the number of processors and memory utilization are lesser than these algorithms. © 2020 C. Vijaya et al., published by Sciendo 2020.