Cloud federation enables service providers to collaborate to provide better services to customers. For cloud storage services, optimizing customer object placement for a member of a federation is a real challenge. Storage, migration, and latency costs need to be considered. These costs are contradictory in some cases. In this article, 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
IR
, a Constraint Data Placement matheuristic based on NSGAII with Injection and Repair functions. The injection function aims 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 ensures that the solutions obey the problem constraints and so prevents from exploring large sets of unfeasible solutions. It reduces drastically the execution time of NSGAII. 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%.