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Particle swarm optimization (PSO) is a population-based optimization technique that can be applied to a wide range of problems. Here, we first investigate the behavior of particles in the PSO using a Monte Carlo method. The results reveal the essence of the trajectory of particles during iterations and the reasons why the PSO lacks a global search ability in the last stage of iterations. Then, we report a novel PSO with a moderate-random-search strategy (MRPSO), which enhances the ability of particles to explore the solution spaces more effectively and increases their convergence rates. Furthermore, a new mutation strategy is used, which makes it easier for particles in hybrid MRPSO (HMRPSO) to find the global optimum and which also seeks a balance between the exploration of new regions and the exploitation of the already sampled regions in the solution spaces. Thirteen benchmark functions are employed to test the performance of the HMRPSO. The results show that the new PSO algorithm performs much better than other PSO algorithms for each multimodal and unimodal function. Furthermore, compared with recent evolutionary algorithms, experimental results empirically demonstrate that the proposed framework yields promising search performance.