Data centers are a critical and ubiquitous resource for providing infrastructure for banking, Internet and electronic commerce. One way of managing the data centers efficiently is to minimize a cost function that takes into account the load of the machines, the balance among a set of available resources of the machines, and the costs of moving processes while respecting a set of constraints. This problem is called machine re-assignment problem. An instance of this online problem can have several tens of thousands of processes. Therefore, the challenge is to solve a very large size instance in a very limited time. In this paper, we describe a constraint programming based Large Neighborhood Search (LNS) approach for solving this problem. The values of the parameters of LNS can have a significant impact on the performance of LNS when solving an instance. We, therefore, employ the Instance Specific Algorithm Configuration methodology, where a clustering of the instances is maintained in the offline phase and the parameters of LNS are automatically tuned for each cluster. When a new instance arrives the values of the parameters of the closest cluster are used for solving the instance in the online phase. Results confirm that our CP-based LNS approach with high quality parameter settings finds good quality solutions for very large size instances in very limited time. Our results also significantly outperform the hand-tuned settings of the parameters selected by a human expert.