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The effects of randomness of control coefficients in particle swarm optimization (PSO) are investigated through empirical studies. The PSO is viewed as a method to solve a coverage problem in the solution space when the global-best particle is reported as the solution. Randomness of the control coefficients, therefore, plays a crucial role in providing an efficient and effective algorithm. Comparisons of performances are made between the uniform and Gaussian distributed random coefficients in adjusting particle velocities. Alternative strategies are also tested, they include: i) pre-assigned randomness through the iterations, ii) selective hybrid random adjustment based on the fitness of the particles. Furthermore, the effect of velocity momentum factor is compared between a constant and random momentum. Numerical results show that performances of the proposed variations are comparable to the conventional implementation for simple test functions. However, enhanced performances using the selective and hybrid strategy are observed for complicate functions.