Virtual machine placement in the cloud infrastructure is an important problem that remains to be effectively addressed.The mapping problem between virtual machines and physical nodes is to decide how to allocate virtualized resources on the cloud to many Web applications,thus it greatly impacts on the performance,cost and QoS guaranteed service.An adaptive management framework for virtual machine placement in the cloud is proposed.A multi-objective optimization genetic algorithm is presented to determine placement strategy in the framework,which is subject to application service level objects(SLOs) constraint.It encodes the chromosome using the group method,and crossover and mutation operations deal with the chromosome which length is varying.It decodes the chromosome using three-dimensional split method.The experimental results show that,the proposed solution could effectively reduce the number of used nodes and virtual machine migration,and minimize violation of many application SLOs,compared with traditional heuristic methods and single objective solution.