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:与随机抽样相比,低差异抽样在覆盖搜索空间方面更有效。然而,现有的研究无法肯定地说明低差异抽样对粒子群优化(PSO)的影响是正的还是负的。使用 Niderreiter 的定理,本研究完成了对 PSO 的错误分析,该分析显示,PSO 在每个迭代过程中的误差取决于在扩大的维度空间中所设定的样本的分布。根据这一错误分析,提出了PSO 型算法的加速技术,在扩大的维度空间中采用低差异抽样。加速技术可以产生低差异抽样,在扩大的维度空间中,与随机抽样相比,分布较小;它也可以减少每次迭代的误差,从而提高趋同速度。加速技术与标准的PSOO和全面学习的粒子体温优化相结合,改进的算法的性能与原始算法相比较。实验结果表明,两种改进的算法在相同的精确度要求下具有大大加快的趋同速度。</s>