This study aims to develop a digital retrieval system for art museums to solve the problems of inaccurate information and low retrieval efficiency in the digital management of cultural heritage. By introducing an improved Genetic Algorithm (GA), digital management and access efficiency are enhanced, to bring substantial optimization and innovation to the digital management of cultural heritage. Based on the collection of art museums, this study first integrates the collection’s images, texts, and metadata with multi-source intelligent information to achieve a more accurate and comprehensive description of digital content. Second, a GA is introduced, and a GA 2 Convolutional Neural Network (GA2CNN) optimization model combining domain knowledge is proposed. Moreover, the convergence speed of traditional GA is improved to adapt to the characteristics of cultural heritage data. Lastly, the Convolutional Neural Network (CNN), GA, and GA2CNN are compared to verify the proposed system’s superiority. The results show that in all models, the sample output results’ actual value is 2.62, which represents the real data observation results. For sample number 5, compared with the actual value of 2.62, the predicted values of the GA2CNN and GA models are 2.6177 and 2.6313, and their errors are 0.0023 and 0.0113. The CNN model’s predicted value is 2.6237, with an error of 0.0037. It can be found that the network fitting accuracy after optimization of the GA2CNN model is high, and the predicted value is very close to the actual value. The digital retrieval system integrated with the GA2CNN model has a good performance in enhancing retrieval efficiency and accuracy. This study provides technical support for the digital organization and display of cultural heritage and offers valuable references for innovative exploration of museum information management in the digital era.