A stream application may allocate processing elements to one or more compute nodes (or hosts) to achieve a desired optimization goal. Each optimization mode may define processing element selection criteria and/or host selection criteria. When allocating a processing element to a host, a scheduler may place each processing element individually. Accordingly, the scheduler may use the processing element selection criteria for selecting which processing element in the stream application to allocate next. The scheduler may then determine, based on one or more constraints, which host the processing element can be placed on. If the scheduler determines that multiple hosts are suitable candidates for the processing element, it may use the host selection criteria to pick one of the candidate hosts that further optimize the stream application to meet the desired goal. Examples of different optimization goals that may be achieved using processing element and host selection criteria include optimizing performance, decreasing maintenance and operating costs, increasing solvability, sharing limited computer resources with other applications, and the like.