Cloud Computing, as a distributed computingparadigm, consists in provisioning infrastructure, software, andplatform resources as services. This paradigm is being increasinglyused for the deployment and execution of servicebasedapplications. To efficiently manage them according to theautonomic computing paradigm, service-based applications canbe associated with autonomic manager (AM) components thatmonitor, analyze monitoring data, plan and execute configurationactions on them. Since an autonomic manager is composed offour basic components, then autonomic management of newapplications lies on determining how many instance of each AMcomponent to use in order to minimize the cost and maximize themanagement performance. In this paper, we propose both exactand approximate approaches that aim to choose the right numberof AM components for managing service-based applications.Experiments shows the efficiency of our approach.Index Terms-Cloud computing, Service-based.