基于空间分割的代理模型并行序列采样方法

A parallel sequential sampling method for surrogate modeling based on design space partition

针对当前代理模型序列采样缺少并行采样策略、无法有效利用并行计算资源的问题,提出了一种基于空间分割的代理模型并行序列采样方法.利用Voronoi图将设计空间分割为与样本数量相同的子空间,每个样本的交叉验证误差作为对应子空间的误差指标,利用蒙特卡罗法计算每个子空间的尺寸作为稀疏性指标.以两种指标的权重和计算子空间的样本需求度,确定须要增加样本的目标子空间.每个目标子空间增加一个样本,新增样本同时考虑与该子空间中已有样本及与本次迭代中已加入样本的空间距离,避免样本聚集.通过测试不同权重系数对采样结果的影响得出较优参数,通过对比并行采样与随机采样策略验证其效果.最后,通过与一次性采样和若干序列采样方法对比,验证了所提出并行采样方法的有效性.

Most sequential sampling methods cannot choose sample points in parallel,and then effectively utilize parallel computing resources.A parallel sequential sampling method for surrogate modeling based on design space partition(PSS-DSP) was proposed.PSS-DSP divided design space into a number of subspaces by using Voronoi diagram,and the number of subspaces was the same as that of sample points.The cross-validation error of each point was regarded as the error index of each subspace.The size of each subspace was evaluated by Monte Carlo method,which was regarded as the sparsity index.The targeted subspaces were determined by calculating the weight sum of the two indexes.Each targeted subspace added a new point at one iteration.A newly added point was chosen based on the distances to the existing point in this subspace and to the points that have been chosen in this iteration.The strategy avoided the aggregation of the new points. The better value of the weight was investigated by comparing the results on different test problems.The effectiveness of the parallel sampling strategy was validated by comparing it with a random sampling strategy.Finally,the superiority of PSS-DSP was verified by comparing it with one-step and sequential sampling methods.