Application of Threshold-Accepting to the Evaluation of the Discrepancy of a Set of Points
Application of Threshold-Accepting to the Evaluation of the Discrepancy of a Set of Points
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DOI：
10.1137/s0036142995286076
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发表时间：
1997-10
影响因子：
2.9
通讯作者：
P. Winker;K. Fang
中科院分区：
文献类型：
--
作者：
P. Winker;K. Fang
准蒙特卡罗方法提供了多维数值积分的有效例程。这些方法基于在积分区域的一组代表点处评估被积函数。如果一个集合显示出较低的差异，则可以称为具有代表性。然而，在高于二维的维度和大量点的情况下，差异的评估变得不可行。使用高效的多用途启发式阈值接受提供了获得给定点集差异的至少良好近似的可能性。本文介绍了阈值接受启发式的实现，对其一些小示例的性能进行了评估，以及具有未知差异的较大点集的结果。
Efficient routines for multidimensional numerical integration are provided by quasi--Monte Carlo methods. These methods are based on evaluating the integrand at a set of representative points of the integration area. A set may be called representative if it shows a low discrepancy. However, in dimensions higher than two and for a large number of points the evaluation of discrepancy becomes infeasible. The use of the efficient multiple-purpose heuristic threshold-accepting offers the possibility to obtain at least good approximations to the discrepancy of a given set of points. This paper presents an implementation of the threshold-accepting heuristic, an assessment of its performance for some small examples, and results for larger sets of points with unknown discrepancy.