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Convolutional neural networks have a broad spectrum of practical applications in computer vision. Currently, much of the data come from images, and it is crucial to have an efficient technique for processing these large amounts of data. Convolutional neural networks have proven to be very successful in tackling image processing tasks. However, the design of a network structure for a given problem entails a fine-tuning of the hyperparameters in order to achieve better accuracy. This process takes much time and requires effort and expertise from the domain. Designing convolutional neural networks' architecture represents a typical NP-hard optimization problem, and some frameworks for generating network structures for a specific image classification tasks have been proposed. To address this issue, in this paper, we propose the hybridized monarch butterfly optimization algorithm. Based on the observed deficiencies of the original monarch butterfly optimization approach, we performed hybridization with two other state-of-the-art swarm intelligence algorithms. The proposed hybrid algorithm was firstly tested on a set of standard unconstrained benchmark instances, and later on, it was adapted for a convolutional neural network design problem. Comparative analysis with other state-of-the-art methods and algorithms, as well as with the original monarch butterfly optimization implementation was performed for both groups of simulations. Experimental results proved that our proposed method managed to obtain higher classification accuracy than other approaches, the results of which were published in the modern computer science literature. [ABSTRACT FROM AUTHOR]