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A PSO with increasing inertia weight, distinct from a widely used PSO with decreasing inertia weight, is proposed in this paper. Far from drawing conclusions from sole empirical study or rule of thumb, this algorithm is derived from particle trajectory study and convergence analysis. Four standard test functions are used to confirm its validity finally. From the experiments, it is clear that a PSO with increasing inertia weight outperforms the one with decreasing inertia weight, both in convergent speed and solution precision, with no additional computing load.