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An efficient heuristic multicast routing algorithm based on simulated annealing named SADDVS is proposed to solve delay and delay variation-bounded Steiner tree problem. This problem is known to be NP-complete. The proposed heuristic algorithm uses a procedure called paths switching to construct, neighbors in feasible region, which greatly reduces the search area and running time. We also give a method to dynamically reorganize the multicast tree in response to changes for the destinations. Simulations demonstrate that our algorithm is better in terms of tree cost as compared to the existing algorithms. Further, it performs excellent performance of delay and delay variation, high success ratio, rapid convergence and better real-time property.