Edge storage, as a supplement to cloud storage, reduces latency by providing services in a timely and efficient manner near the source. In a collaborative edge storage datacenter network (CESN), not only does the edge storage datacenter (ESDC) that is closest to the user provide services, but multiple ESDCs work together to provide better services. In this collaborative work mechanism, different application session requests create large persistent multicast flows with diverse performance requirements. Existing multicast scheduling methods such as unicast shortest path (USP) and static single tree (SST) do not consider flow characteristics or performance requirements. In this paper, we first modeled the multicast flow scheduling problem in a CESN. The model is based on different types of flows with diverse network requirements. Then, we tailored a multicast flow scheduling method based on multiple-attribute decisionmaking and a genetic algorithm (MDGA). MDGA selects appropriate multicast routing paths for flows in a CESN by considering the requested flow types and network status. The experimental results show that the proposed MDGA method can balance network loads and reduce the average transmission delay for highpriority flows better than USP and SST.INDEX TERMS collaborative edge storage, datacenter network, multicast flow, multiple-attribute decision-making, genetic algorithm.