Image captioning has become a prominent problem in recent years, with many efficient models emerging based on generation-based methods, typically employing an encoder-decoder framework. The encoder frequently utilizes convolutional neural networks (CNNs), which are computationally intensive and time-consuming. To address this issue, we introduce the Winograd algorithm into the image captioning framework, replacing standard convolution layers with Winograd convolution layers to accelerate computation. The Winograd algorithm enables minimal complexity convolution over small tiles. For certain repetitive arithmetic procedures, our model precomputes some transformation matrices to further reduce computational complexity. Additionally, to enhance caption accuracy and reduce model size, we optimize the hyper-parameters of the image captioning model using a multi-objective Bayesian optimization algorithm. The objectives are the accuracy of captions and the number of model parameters. This algorithm continuously adjusts the model during training, ultimately identifying the most suitable hyper-parameters for the image captioning task. We evaluate our model on the MS-COCO datasets, and the experimental results demonstrate that our model achieves state-of-the-art performance and improves running speed with the integration of the Winograd algorithm.