The rise of the Internet of Things (IoT) paradigm has led to an interest in applying it not only in tasks for the general public but also to stringent domains such as healthcare. However, the developers of these next-generation IoT applications must consider additional non-functional requirements related to the criticality of the processes they automate, such as low response times or low deployment costs, as well as technical constraints, which include organizational, legal and policy-related constraints on where data can be processed or stored. While the Computing Continuum paradigm emerges as a valuable alternative for placing such applications, identifying the deployments that satisfy all these requirements becomes a tough challenge. The NP-hard nature of the problem makes it impractical to manually find such a deployment, and traditional approaches fail to consider the technical constraints. In this paper, we present the Genetic Algorithm for Application Placement (GAAP), an evolutionary computing-based meta-heuristic designed to help IoT application developers find deployments that satisfy their Quality of Service, business and technical constraints. Our evaluation of an Internet of Medical Things use case shows that GAAP supports larger scenarios than traditional approaches and gives IoT application developers more options while providing better scalability.