使用遗传算法构造低星偏差点集
Constructing Low Star Discrepancy Point Sets with Genetic Algorithms
AI总结：
提出一种基于进化原理的遗传算法，通过优化和评估两个组件，高效构造低星偏差点集，显著优于现有方法，并可扩展优化逆星偏差。
摘要：
几何偏差是衡量分布不规则性的标准度量，在数值积分中具有重要意义。其中最重要的偏差概念之一是所谓的“星偏差”。粗略地说，具有低星偏差值的点集可以在拟蒙特卡洛积分中实现较小的近似误差，因此它是研究最多的偏差概念。本文提出了一种计算低星偏差点集的新算法。该算法的两个组件（分别用于优化和评估）基于进化原理。我们的算法明显优于现有方法。据我们所知，它也是第一个可以轻松适应优化逆星偏差的算法。
英文摘要：
Geometric discrepancies are standard measures to quantify the irregularity of distributions. They are an important notion in numerical integration. One of the most important discrepancy notions is the so-called \emph{star discrepancy}. Roughly speaking, a point set of low star discrepancy value allows for a small approximation error in quasi-Monte Carlo integration. It is thus the most studied discrepancy notion. In this work we present a new algorithm to compute point sets of low star discrepancy. The two components of the algorithm (for the optimization and the evaluation, respectively) are based on evolutionary principles. Our algorithm clearly outperforms existing approaches. To the best of our knowledge, it is also the first algorithm which can be adapted easily to optimize inverse star discrepancies.
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