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Many problems in cloud computing are not solvable in polynomial time and only option left is to choose approximate solution instead of optimum. Virtual Machine placement is one of such problem with resource constraints in which overall objective is to optimize multiple resources of hosts during placement process. In this paper we have addressed this problem with large size NP-Hard instances and proposed novel local search-based approximation algorithm. This problem is not yet studied in the research community with NP hard instances. A new proposed algorithm is empirically evaluated with state-of-the-art techniques. and our algorithm has improved placement result by 18% in CPU utilization, 21% in resource contention and 26% in overall resource utilization for benchmark instances collected from azure private cloud data center.