Enterprise Application Integration deals with the problem of connecting heterogeneous applications, and is the centerpiece of current on-premise, cloud and device integration scenarios. For integration scenarios, structurally correct composition of patterns into processes and improvements of integration processes are crucial. In order to achieve this, we formalize compositions of integration patterns based on their characteristics, and describe optimization strategies that help to reduce the model complexity, and improve the process execution efficiency using design time techniques. Using the formalism of timed DB-nets - a refinement of Petri nets - we model integration logic features such as control- and data flow, transactional data storage, compensation and exception handling, and time aspects that are present in reoccurring solutions as separate integration patterns. We then propose a realization of optimization strategies using graph rewriting, and prove that the optimizations we consider preserve both structural and functional correctness. We evaluate the improvements on a real-world catalog of pattern compositions, containing over 900 integration processes, and illustrate the correctness properties in case studies based on two of these processes.