Cloud federation enables service providers to collaborate to provide better services to customers. For cloud storage services, I/O performance and network latency are important to ensure end-to-end QoS. Therefore, effectively placing customer objects for a cloud that is a member of a federation is a real challenge. In order to optimize data placement, storage, migration and latency costs need to be considered. These costs are contradictory in some cases. In this paper, we modeled object placement as a multi-objective optimization problem. The proposed model takes into account parameters related to the local infrastructure, the federated environment, customer workloads and their SLAs. For resolving this problem, we propose CDP-NSGAII , a Constraint Data Placement matheuristic based on NSGAII with injection and repair functions. The objective of the injection function is to enhance the solutions' quality. It consists to calculate some solutions using an exact method then inject them into the initial population of NSGAII. The repair function was designed to ensure that the solutions obey the problem constraints in term of storage and so prevents from exploring large sets of infeasible solutions. It allows to reduce the execution time of NSGAII. Our experimental results show that, the injection function improves the HV of NSGAII and the exact method by up to 94% and 60% respectively while the repair function reduces the execution time by an average of 68%. CCS Concepts: • Federated cloud → Hybrid storage system; • Data placement → Cost optimization.