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Particle swarm optimization (PSO) is characterized as simple in concept, easy to implement, and efficient in computation, but some enhancements to its basic algorithm's stability and global convergence still need to be investigated. A number of improvements on the PSO algorithm are summarized to overcome its shortcomings. Then, an improved PSO (IPSO) algorithm is proposed to move a particle in the swarm to the best position along the direction of its updated velocity with an optimized time step. Subsequently, a hybrid PSO (HPSO) algorithm based on the parallel collaboration is presented, which is a combination of Powell, pattern search and IPSO. Finally, the performances of the IPSO and HPSO are tested through numerical simulation, in which the global optimum solutions of four typical test functions need to be searched for. The results show that the IPSO method increases the stability of the basic PSO and results in faster convergence to the global optimum solution, and the HPSO does better in solving complex global optimization problems and carrying out parallel operations.