The hardware landscape is changing from homogeneous systems towards multiple heterogeneous computing units within one system. For database systems, this is an opportunity to accelerate query processing if the heterogeneous resources can be utilized efficiently. For this goal, we investigate novel query optimization concepts for heterogeneous resources like placement granularity, execution estimation, optimization granularity, and data handling. In the end, we combine these concepts in a specialized optimization stage during query optimization together with a unique way of evaluating our optimizations in existing database systems.