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arXiv · 2511.07836

Hyperellipsoid Density Sampling: Exploitative Sequences to Accelerate High-Dimensional Numerical Optimization

Julian G. Soltes
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Abstract

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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BibTeXRIS

Julian G. Soltes. 2025-11-11. Hyperellipsoid Density Sampling: Exploitative Sequences to Accelerate High-Dimensional Numerical Optimization. https://arxiv.org/abs/2511.07836

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