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Removing redundant features and improving classifier performance necessitates the use of meta-heuristic and deep learning (DL) algorithms in feature selection and classification problems. With the maturity of DL tools, many data-driven polarimetric synthetic aperture radar (POLSAR) representation models have been suggested, most of which are based on deep convolutional neural networks (DCNNs). In this paper, we propose a hybrid approach of a new multi-objective binary chimp optimization algorithm (MOBChOA) and DCNN for optimal feature selection. We implemented the proposed method to classify POLSAR images from San Francisco, USA. To do so, we first performed the necessary preprocessing, including speckle reduction, radiometric calibration, and feature extraction. After that, we implemented the proposed MOBChOA for optimal feature selection. Finally, we trained the fully connected DCNN to classify the pixels into specific land-cover labels. We evaluated the performance of the proposed MOBChOA-DCNN in comparison with nine competitive methods. Our experimental results with the POLSAR image datasets show that the proposed architecture had a great performance for different important optimization parameters. The proposed MOBChOA-DCNN provided fewer features (27) and the highest overall accuracy. The overall accuracy values of MOBChOA-DCNN on the training and validation datasets were 96.89% and 96.13%, respectively, which were the best results. The overall accuracy of SVM was 89.30%, which was the worst result. The results of the proposed MOBChOA on two real-world benchmark problems were also better than the results with the other methods. Furthermore, it was shown that the MOBChOA-DCNN performed better than methods from previous studies. [ABSTRACT FROM AUTHOR]