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 interplay between the distribution network and distributed resources introduces complexity, manifesting in the intricate response of distributed resources to system incentive, thereby challenging their unified management. Leveraging machine learning and optimization theories, this chapter firstly introduces 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 chapter discusses the fusing learning and optimization for distribution network operation framework 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 can ensure the secure and economical operation of the distribution system but also addresses carbon emission management. Finally, through comprehensive case studies, the precision of constraint learning for distributed resource assimilation and the effectiveness of the integrated machine learning-optimization distribution network operational model are demonstrated in this chapter.