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Early diagnosis of retinal diseases such as diabetic retinopathy has had the attention of many researchers. Deep learning through the introduction of convolutional neural networks has become a prominent solution for image-related tasks such as classification and segmentation. Most tasks in image classification are handled by deep CNNs pretrained and evaluated on imagenet dataset. However, these models do not always translate to the best result on other datasets. Devising a neural network manually from scratch based on heuristics may not lead to an optimal model as there are numerous hyperparameters in play. In this paper, we use two nature-inspired swarm algorithms: particle swarm optimization (PSO) and ant colony optimization (ACO) to obtain TDCN models to perform classification of fundus images into severity classes. The power of swarm algorithms is used to search for various combinations of convolutional, pooling, and normalization layers to provide the best model for the task. It is observed that TDCN-PSO outperforms imagenet models and existing literature, while TDCN-ACO achieves faster architecture search. The best TDCN model achieves an accuracy of 90.3%, AUC ROC of 0.956, and a Cohen kappa score of 0.967. The results were compared with the previous studies to show that the proposed TDCN models exhibit superior performance.