扩展维度空间中的低差异采样：一种粒子群优化化的加速技术
Low-discrepancy Sampling in the Expanded Dimensional Space: An Acceleration Technique for Particle Swarm Optimization
AI总结：
本研究基于Niderreiter定理分析PSO误差，提出在扩展维度空间中采用低差异采样的加速技术，该技术可降低样本离散度与每次迭代误差，结合标准PSO与CLPSO后，在同等精度下显著提升收敛速度。
摘要：
与随机采样相比，低差异采样在覆盖搜索空间方面更有效效。然而，现有研究无法明确断定低差异采样对粒子群优化（PSO）的影响是正面还是负面。利用Niderreiter定理，本研究完成了PSO的误差分析，揭示出PSO每次迭代的误差界取决于样本集在扩展维度空间中的离散度。离散度越小，误差越小。基于该误差分析，提出了一种在扩展维度空间中采用低差异采样的PSO类算法加速技术。与随机采样相比，该加速技术能在扩展维度空间中生成离散度更小的低差异样本集；同时降低每次迭代的误差，从而提高收敛速度。将加速技术与标准PS0及综合学习粒子群优化相结合，比较改进算法与原始算法的性能。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更快。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
