The recent migration towards Internet of Things determined the rise of a Computing Continuum paradigm where Edge and Cloud resources coordinate to support the execution of Artificial Intelligence (AI) applications, becoming the foundation of use-cases spanning from predictive maintenance to machine vision and healthcare. This generates a fragmented scenario where computing and storage power are distributed among multiple devices with highly heterogeneous capacities. The runtime management of AI applications executed in the Computing Continuum is challenging, and requires ad-hoc solutions. We propose SPACE4AI-R, which combines Random Search and Stochastic Local Search algorithms to cope with workload fluctuations by identifying the minimum-cost reconfiguration of the initial production deployment, while providing performance guarantees across heterogeneous resources including Edge devices and servers, Cloud GPU-based Virtual Machines and Function as a Service solutions. Experimental results prove the efficacy of our tool, yielding up to 60% cost reductions against a static design-time placement, with a maximum execution time under 1.5s in the most complex scenarios
