In pursuit of efficient and scalable data analytics, the insight that "one size does not fit all" has given rise to a plethora of specialized data processing platforms and today's complex data analytics are moving beyond the limits of a single platform. In this paper, we present the cost-based optimizer of Rheem, an open-source cross-platform system that copes with these new requirements. The optimizer allocates the subtasks of data analytic tasks to the most suitable platforms. Our main contributions are: (i)~a mechanism based on graph transformations to explore alternative execution strategies; (ii)~a novel graph-based approach to efficiently plan data movement among subtasks and platforms; and (iii)~an efficient plan enumeration algorithm, based on a novel enumeration algebra. We extensively evaluate our optimizer under diverse real tasks. The results show that our optimizer is capable of selecting the most efficient platform combination for a given task, freeing data analysts from the need to choose and orchestrate platforms. In addition, our optimizer allows tasks to run more than one order of magnitude faster by using multiple platforms instead of a single platform.