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This paper presents an efficient particle swarm optimization (PSO) based search algorithm for solving the single source all destination shortest paths or what is called the shortest-paths tree (SPT), commonly encountered in graph theory. A new particle encoding/decoding scheme has been devised for particle-representation of the SPT parameters. This encoding/decoding exploits the sub-optimality feature of the shortest path. In the proposed algorithm, the solution, the shortest path tree, is not represented by one particle, but it is the solution that is contributed by the complete swarm population. Numerical computation results on several networks with random topologies illustrate the efficiency of the proposed PSO method for computation of shortest paths in networks.