ROCEWEA. low-discrepancy sequence
Authors: Feng. Wu, Yuelin Zhao, Ke Zhao, Wanxie ZhongIn this paper, we proposed an assumption that the static solution to the multi-bodies problem is a low-discrepancy sequence, and established a dynamical evolutionary model (DEM) based on the minimum potential energy to find out the static solution. We also discussed some coefficients to ensure the convergence of the evolutionary iteration. Based on the DEM, the relationship between the potential energy and the discrepancy during the evolutionary iteration process is studied. It is found that there is a significant positive correlation between them, which confirms the proposed assumptions. We also combined the DEM with the restarting technique to generate a series of low-discrepancy sequences. These sequences are unbiased and perform better than other low-discrepancy sequences in terms of the discrepancy, the potential energy, integrating eight test functions and computing the statistical moments for two practical stochastic problems. Numerical examples also show that the DEM can not only generate uniformly distributed sequences in cubes, but also in non-cubes.