Compared with random sampling, low-discrepancy sampling is more effective in covering the search space. However, the existing research cannot definitely state whether the impact of a low-discrepancy sample on particle swarm optimization (PSO) is positive or negative. Using Niderreiter's theorem, this study completes an error analysis of PSO, which reveals that the error bound of PSO at each iteration depends on the dispersion of the sample set in an expanded dimensional space. Based on this error analysis, an acceleration technique for PSO-type algorithms is proposed with low-discrepancy sampling in the expanded dimensional space. The acceleration technique can generate a low-discrepancy sample set with a smaller dispersion, compared with a random sampling, in the expanded dimensional space; it also reduces the error at each iteration, and hence improves the convergence speed. The acceleration technique is combined with the standard PSO and the comprehensive learning particle swarm optimization, and the performance of the improved algorithm is compared with the original algorithm. The experimental results show that the two improved algorithms have significantly faster convergence speed under the same accuracy requirement.

翻译：与随机采样相比，低差异采样在覆盖搜索空间方面更为有效。然而，现有研究无法明确判断低差异采样对粒子群优化（PSO）的影响是正向还是负向。本研究借助Niederreiter定理完成了PSO的误差分析，揭示了每次迭代中PSO的误差界取决于样本集在扩展维度空间中的分散度。基于该误差分析，提出了一种在扩展维度空间中进行低差异采样的PSO类算法加速技术。该技术能在扩展维度空间中生成比随机采样分散度更小的低差异样本集，从而降低每次迭代的误差，进而提升收敛速度。将该加速技术与标准PSO及综合学习粒子群优化相结合，并将改进算法与原算法进行性能对比。实验结果表明，在相同精度要求下，两种改进算法的收敛速度显著提升。