Traditional design optimization methods rely on engineering experience and exhibit low computational efficiency and accuracy when addressing optimization problems. Deep learning has attracted considerable attention for its excellent performance in solving optimization problems. On this basis, deep learning optimization methods suitable for single-objective and multi-objective scenarios are developed. The first method is a single-objective optimization approach based on the Transformer architecture. The design and optimization process aims to minimize the equipment volume under a specified power constraint by pre-training a Transformer model and employing a discrete grid search strategy. The second method is a multi-objective optimization approach that integrates a Graph Neural Network model. Complex relationships among design parameters are represented by constructing a graph structure. A multi-task uncertainty weighting strategy is adopted to achieve comprehensive performance optimization. In addition, an automatic parameter search based on gradient descent is utilized to complete the design optimization process. Experimental results demonstrate that, compared with the method based on a multilayer perceptron model, the proposed method achieves lower prediction error. The coefficient of determination \({R}^{2}\) increases from 0.92 to 0.94 while the mean absolute error (MAE) decreases from 0.078 to 0.065. In terms of design optimization, a reduction in equipment volume by 2% to 7% is realized.