Halton sequences are d–dimensional quasirandom sequences that fill the d–dimensional hyperspace in a uniform way. They can be used in a variety of applications such as multidimensional integration, uniform sampling, and, e.g., quasi–Monte Carlo simulations. Generalized Halton sequences improve the space–filling properties of original Halton sequences in higher dimensions by digit scrambling. In this work, an evolutionary optimization algorithm, the differential evolution, is used to optimize scrambling permutations of a d–dimensional generalized Halton sequence so that the discrepancy of the generated point set is minimized.

中文翻译：

---

低差异广义Halton序列优化的差分进化

Halton序列是以统一方式填充d维超空间的d维拟随机序列。它们可以用于多种应用中，例如多维积分，统一采样和准蒙特卡洛模拟。广义的Halton序列通过数字加扰改善了更高维度上原始Halton序列的空间填充特性。在这项工作中，使用进化优化算法（差分进化）来优化d维广义Halton序列的加扰排列，以使生成的点集的差异最小化。