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Particle swarm optimization (PSO) has been widely used in various optimization fields because of its easy implementation and high efficiency. However, it suffers from some limitations like slow convergence and premature convergence when solving high-dimensional optimization problems. This paper attempts to address these open issues. Firstly, a new method of parameter adjustment named piecewise nonlinear acceleration coefficients is introduced to the simplified particle swarm optimization algorithm (SPSO), and an improved algorithm called piecewise-nonlinear-acceleration-coefficients-based SPSO (P-SPSO) is proposed. Then, a mean differential mutation strategy is developed for the update mechanism of P-SPSO, and another improved algorithm named mean-differential-mutation-strategy embedded P-SPSO (MP-SPSO) is proposed. To validate the performance of the proposed algorithms, four different sets of experiments are carried out in this paper. The results show that, 1) the proposed P-SPSO can get better solutions than other four classic improved SPSO with different acceleration coefficients, 2) the proposed MP-SPSO algorithm shows better optimization performance than P-SPSO and mean-differential-mutation-strategy-based SPSO (M-SPSO), 3) the proposed MP-SPSO is clearly seen to be more successful than other eight well-known PSO variants, 4) compared to other nine intelligent optimization algorithms, MP-SPSO achieves better performance in terms of solution quality and robustness. Moreover, the proposed MP-SPSO algorithm is successfully applied to a real constrained engineering problem and provides better solutions than other methods.

Improved Simplified Particle Swarm Optimization Based on Piecewise Nonlinear Acceleration Coefficients and Mean Differential Mutation Strategy