In this paper, we propose a Web service composition framework that uses Integer Linear Programming with non-functional objectives and constraints, in addition to the syntactic matching of Web services features. We envision that when Web services are fully deployed and commercialized in the near future, the criteria of Web service composition to achieve objectives will vary depending on users' needs or preferences from the number of Web services to non-functional objectives, such as costs, time, and/or reputation. Such non-functional attributes cannot be readily considered in planning-graph, constraint satisfaction, or propositional satisfiability techniques, which are predominantly logic-based. This paper shows how the proposed Integer Linear Programming framework can be utilized to compose Web services with non-functional attributes. This framework enables our composition software agent to identify the best composition result that satisfies both non-functional requirements as well as functional ones, namely, parameter matching. A preliminary implementation of the proposed idea and further research directions are also discussed.