用非均匀采样聚焦高维优化关键区域，提速显著。
Hyperellipsoid Density Sampling: Exploitative Sequences to Accelerate High-Dimensional Numerical Optimization
- 以超椭球体重叠方式生成非均匀采样序列，聚焦参数空间内部。
- 在29个CEC2017测试函数上，10维平均提速37%，100维仍达11%。
- 适合有先验信息的高维优化，尤其适用于难以采样的复杂问题。
维度灾难仍是现代优化问题的持续挑战。将搜索空间扩展至高维会指数级加剧均匀采样分布的稀疏性，使传统准蒙特卡洛（QMC）序列效率下降。本文提出一种非均匀采样策略——超椭球密度采样（HDS），通过一系列无监督学习技术生成重叠的超椭球样本，聚焦超体积内部区域。若已知最优区域，可偏置分布以提升效率，适用性广。在29个广泛使用的CEC2017测试函数上，以差分进化（DE）为优化器，与高度均匀的Sobol序列对比，结果显示最终解的几何均值误差具有统计显著性改进（p<0.05），10维平均性能提升37%，100维仍达11%。本研究验证了HDS作为非均匀采样替代方案的有效性。
原文摘要 · Abstract (English)
The curse of dimensionality remains a persistent challenge in modern optimization problems. Expanding the search space into higher dimensions exponentiates the sparsity of uniform sample distributions, rendering traditional quasi-Monte Carlo (QMC) sequences increasingly inefficient. This paper introduces a non-uniform sampling strategy to accelerate high-dimensional optimization. This method, Hyperellipsoid Density Sampling (HDS), generates samples as hyperellipsoids overlapping throughout the parameter space. Utilizing a series of unsupervised learning techniques, a non-uniform sequence is generated to exploit the interior regions of the hypervolume. If prior information about optima is known, the distribution can be biased towards the known regions, making HDS versatile for many numerical applications. HDS was evaluated against Sobol, a highly uniform QMC sampling method, using differential evolution (DE) on the challenging and widely benchmarked set of 29 CEC2017 test functions. The results show statistically significant improvements in final solution geometric mean error (p<0.05), with average performance gains ranging from 37% in 10D to 11% in 100D. This paper demonstrates the efficacy of HDS as an exploitative alternative to uniform QMC sampling.
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