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Deep learning methods have become very successful at solving many complex tasks such as image classification and segmentation, speech recognition and machine translation. Nevertheless, manually designing a neural network for a specific problem is very difficult and time-consuming due to the massive hyperparameter search space, long training times, and lack of technical guidelines for the hyperparameter selection. Moreover, most networks are highly complex, task specific and over-parametrized. Recently, multiobjective neural architecture search (NAS) methods have been proposed to automate the design of accurate and efficient architectures. However, they only optimize either the macro- or micro-structure of the architecture requiring the unset hyperparameters to be manually defined, and do not use the information produced during the optimization process to increase the efficiency of the search. In this work, we propose EMONAS, an Efficient MultiObjective Neural Architecture Search framework for the automatic design of neural architectures while optimizing the network's accuracy and size. EMONAS is composed of a search space that considers both the macro- and micro-structure of the architecture, and a surrogate-assisted multiobjective evolutionary based algorithm that efficiently searches for the best hyperparameters using a Random Forest surrogate and guiding selection probabilities. EMONAS is evaluated on the task of 3D cardiac segmentation from the MICCAI ACDC challenge, which is crucial for disease diagnosis, risk evaluation, and therapy decision. The architecture found with EMONAS is ranked within the top 10 submissions of the challenge in all evaluation metrics, performing better or comparable to other approaches while reducing the search time by more than 50% and having considerably fewer number of parameters.