Discrete & continuous optimization constitutes a challenging task and generally rises as an NP-hard problem. In the literature, as a derivative of this type of optimization issue, hyperparameter optimization of transfer learning (TL) architectures is not efficiently analyzed as a detailed survey in the literature. In this paper, the optimized TL-based models are effectively examined to handle this issue which constitutes the main aim of our study. For evaluation, knee osteoarthritis (KOA – a chronic degenerative joint disorder) dataset is handled to perform two challenging classification tasks which reveal the second aim of our study, i.e. binary- and multi-categorizations on KOA X-ray images. To fine-tune the hyperparameters of TL models, state-of-the-art optimization methods are chosen and compared on this competitive – NP-hard problem. Sixteen optimized architectures are designed using four efficient optimization methods (ASPSO, CDW-PSO, CSA, MSGO) and four oft-used TL models (MobileNetV2, ResNet18, ResNet50, ShuffleNet) to classify the X-ray KOA images. Regarding the experiments on both categorization tasks, the MSGO algorithm arises as more robust to be considered for hyperparameter tuning of TL-based models by achieving reliable performance. In addition, it's seen that MobileNetV2 and ResNet-based models come to the forefront for X-ray imaging-based classification by achieving high accuracy rates due to the usage of residual blocks. Consequently, in terms of mean accuracy, ResNet50-MSGO and MobileNetV2-CSA respectively record 93.15 % and 93.29 % success rates on multiclass categorization, while ResNet18-CDW-PSO and MobileNetV2-MSGO provide the same highest score of 99.43 % on binary categorization.