The process of mapping virtual machines to physical machines is known as virtual machine placement. In cloud computing environment optimal placement plays an important role for the improvement in power efficiency and resource utilization. In this paper, the authors study the ant colony optimization and multi-objective genetic algorithm for the virtual machine placement problem. They propose an algorithm that combines both multi-objective algorithm and ant colony optimization. They also have designed an architecture for the proposed system. The algorithms were tested using some instances from the literature.