Nowadays, Web services are growing very fast and are usually aggregated into a composite one to satisfy customer?s more and more complex requirements. Generally, there may be several different candidate services to carry out one task in a composite service, so a choice needs to be made for helping users select the most suitable one to satisfy their end-to-end constraints. This paper addresses this issue as a multistage decision problem Based on the quality and attribute value of services, this paper generates a Weighted Multistage Graph for composite service, and transform the problem of services selection into the one of how to get a longest path under a given end-toend constraints. Considering the problem of Interface Matching, this paper presents a 3-layer Web service organization model (WS3LM), which can help getting executable composite service with well matching. This paper describes and compares two of global optimal selection approaches: Dynamic Programming and Genetic Algorithm.