摘要： This paper proposes a novel bi-velocity discrete particle swarm optimization (BVDPSO) approach and extends its application to the nondeterministic polynomial (NP) complete multicast routing problem (MRP). The main contribution is the extension of particle swarm optimization (PSO) from the continuous domain to the binary or discrete domain. First, a novel bi-velocity strategy is developed to represent the possibilities of each dimension being 1 and 0. This strategy is suitable to describe the binary characteristic of the MRP, where 1 stands for a node being selected to construct the multicast tree, whereas 0 stands for being otherwise. Second, BVDPSO updates the velocity and position according to the learning mechanism of the original PSO in the continuous domain. This maintains the fast convergence speed and global search ability of the original PSO. Experiments are comprehensively conducted on all of the 58 instances with small, medium, and large scales in the Operation Research Library (OR-library). The results confirm that BVDPSO can obtain optimal or near-optimal solutions rapidly since it only needs to generate a few multicast trees. BVDPSO outperforms not only several state-of-the-art and recent heuristic algorithms for the MRP problems, but also algorithms based on genetic algorithms, ant colony optimization, and PSO.