The advent of edge devices dedicated to machine learning tasks enabled the execution of AI-based applications that efficiently process and classify the data acquired by the resource-constrained devices populating the Internet of Things. The proliferation of such applications (e.g., critical monitoring in smart cities) demands new strategies to make these systems also sustainable from an energetic point of view. In this paper, we present an energy-aware approach for the design and deployment of self-adaptive AI-based applications that can balance application objectives (e.g., accuracy in object detection and frames processing rate) with energy consumption. We address the problem of determining the set of configurations that can be used to self-adapt the system with a meta-heuristic search procedure that only needs a small number of empirical samples. The final set of configurations are selected using weighted gray relational analysis, and mapped to the operation modes of the self-adaptive application. We validate our approach on an AI-based application for pedestrian detection. Results show that our self-adaptive application can outperform non-adaptive baseline configurations by saving up to 81\% of energy while loosing only between 2% and 6% in accuracy.
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