The run-time binding of web services has been recently put forward in order to support rapid and dynamic web service compositions. With the growing number of alternative web services that provide the same functionality but differ in quality parameters, the service composition becomes a decision problem on which component services should be selected such that user's end-to-end QoS requirements (e.g. availability, response time) and preferences (e.g. price) are satisfied. Although very efficient, local selection strategy fails short in handling global QoS requirements. Solutions based on global optimization, on the other hand, can handle global constraints, but their poor performance renders them inappropriate for applications with dynamic and realtime requirements. In this paper we address this problem and propose a solution that combines global optimization with local selection techniques to benefit from the advantages of both worlds. The proposed solution consists of two steps: ...