Abstract: The proposed energy-saving routing algorithms for data center networks can be broadly classified into two categories: traffic-awareness and topology-awareness. The performance of the former depends largely on the accuracy of the predicted traffic patterns. However, the traffic patterns in the actual network change dynamically, and the predicted traffic patterns might not accord with the real-time traffic patterns of the network. It is often difficult for the traffic-aware energy-saving routing algorithms to guarantee reliable transmission of burst flows. On the other hand, the latter has to ensure the connectivity of the network topology, which does not consider the traffic load. Therefore, there are often lots of idle devices during low traffic load that result in energy waste. For this reason, for a software-defined data center network (SDCN) with fat-tree topology, we combine the advantages of the two kinds of energy-saving routing algorithms, and propose some concepts including equivalent nodes, the minimum subset for network connectivity, isolated switch and invalid link, auxiliary graph model and SDCN connectivity conditions in this paper. On this basis, a multi-constrained energy-saving routing optimization model is described. Moreover, a multi-constrained energy-saving routing algorithm (MER) is also proposed. In order to reduce the network energy consumption, MER algorithm can sleep as many redundant switches and links as possible while guaranteeing the requirements of the flows in delay and reliability. Finally, the performance of the proposed algorithm is evaluated by using Mininet and Floodlight, and the simulation results show that MER has lower average packet delay and packet loss rate than the existing algorithms in the literature with a desired energy saving rate.