The poor timeliness of routing has always been an urgent problem in practical operator networks, especially in situations with large-scale networks and multiple network domains. In this article, a pruning idea of routing integrated with Dijkstra’s shortest path searching is utilized to accelerate the process of routing in large-scale multi-domain elastic optical networks (EONs). The layered-graph approach is adopted in the spectrum allocation stage. To this end, an efficient heuristic algorithm is proposed, called “Branch-and-Bound based Routing and Layered Graph based Spectrum Allocation algorithm (BBR-LGSA)”, which is an integrated RSA algorithm. Notably, the significant reduction in algorithm time complexity is not only reflected in the pruning method used in the routing stage but also in the construction of auxiliary graphs during the spectrum allocation stage utilizing the Branch-and-Bound method. Simulation results show that the proposed BBR-LGSA significantly reduces the average running time by nearly 78% with higher spectrum utilization in large-scale multi-domain EONs, compared with benchmark algorithms. In addition, the impact of key parameters on performance comparisons of different algorithms is evaluated.