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In the last decade, most research in Machine Learning contributed to the improvement of existing models, with the aim of increasing the performance of neural networks for the solution of a variety of different tasks. However, such advancements often come at the cost of an increase of model memory and computational requirements. This represents a significant limitation for the deployability of research output in realistic settings, where the cost, the energy consumption, and the complexity of the framework play a crucial role. To solve this issue, the designer should search for models that maximise the performance while limiting its footprint. Typical approaches to reach this goal rely either on manual procedures, which cannot guarantee the optimality of the final design, or upon Neural Architecture Search algorithms to automatise the process, at the expenses of extremely high computational time. This paper provides a solution for the fast identification of a neural network that maximises the model accuracy while preserving size and computational constraints typical of tiny devices. Our approach, named FreeREA, is a custom cell-based evolution NAS algorithm that exploits an optimised combination of training-free metrics to rank architectures during the search, thus without need of model training. Our experiments, carried out on the common benchmarks NAS-Bench-101 and NATS-Bench, demonstrate that i) FreeREA is a fast, efficient, and effective search method for models automatic design; ii) it outperforms State of the Art training-based and training-free techniques in all the datasets and benchmarks considered, and iii) it can easily generalise to constrained scenarios, representing a competitive solution for fast Neural Architecture Search in generic constrained applications. The code is available at \url{https://github.com/NiccoloCavagnero/FreeREA}.