Abstract: With the extensive integration of distributed resources into the distribution network, the operational management of the distribution system becomes pivotal to ensure its reliability, safety, and efficient operation. The intricate interplay between the distribution network and distributed resources introduces complexity, manifesting in the intricate response of distributed resources to system incentive, thereby rendering their unified management challenging. In addressing this issue, leveraging machine learning and optimization theories, this study firstly proposes a constraint learning approach tailored to clusters of distributed resources. This involves establishing a data-driven response constraint model based on neural networks. Subsequently, the fusing learning and optimization for distribution network operation framework is formulated through the lens of constraint learning. Based on the constraint model, carbon emission limitations, distribution network operational model, and bilinear relaxation strategies, an amalgamated machine learning and optimization-based distribution network operational model is constructed. This model not only ensures the secure and economical operation of the distribution system but also addresses carbon emission management. A comprehensive case study validates both the accuracy of cluster learning for distributed resource integration and the efficacy of the combined machine learning-optimization approach for distribution network operation modeling.