SIAM Journal on Scientific Computing, Volume 43, Issue 2, Page A1527-A1554, January 2021.
Finding optimal (or low energy) centroidal Voronoi tessellations (CVTs) on a two-dimensional domain is a challenging problem. One must navigate an energy landscape whose desirable critical points have sufficiently small basins of attractions that are inaccessible with Monte Carlo initialized gradient descent methods. We present a simple deterministic method for efficiently navigating the energy landscape in order to access these low energy CVTs. The method has two parameters and is based upon each generator moving away from the closest neighbor by a certain distance. We give a statistical analysis of the performance of this hybrid method comparing with the results of a large number of runs for both Lloyd's method and state-of-the-art quasi-Newton methods. Stochastic alternatives are also considered.

中文翻译：

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导航Voronoi质心镶嵌能量景观的一种简单几何方法。

SIAM科学计算杂志，第43卷，第2期，第A1527-A1554页，2021年1月。
在二维域中找到最佳（或低能量）质心Voronoi镶嵌（CVT）是一个具有挑战性的问题。必须浏览一种能源景观，其理想的临界点具有足够小的吸引力盆地，而蒙特卡洛初始化梯度下降方法无法达到这些吸引力。我们提出了一种简单的确定性方法，可以有效地浏览能源格局，以访问这些低能耗CVT。该方法具有两个参数，并且基于每个发电机从最近的邻居移开一定的距离。我们对这种混合方法的性能进行了统计分析，并与劳埃德方法和最新的拟牛顿方法的大量运行结果进行了比较。还考虑了随机替代方案。