A summary-attainment-surface plotting method for visualizing the performance of stochastic multiobjective optimizers
A summary-attainment-surface plotting method for visualizing the performance of stochastic multiobjective optimizers
复制标题
DOI：
10.1109/isda.2005.15
复制
发表时间：
2005-09
期刊：
影响因子：
--
通讯作者：
Joshua D. Knowles
中科院分区：
文献类型：
--
作者：
Joshua D. Knowles
在评估随机优化器的性能时，有时需要用在某一部分样本运行中获得的质量来表示性能。例如，样本中位数质量是在50%的运行中期望达到的最佳估计量，对于其他分位数也是如此。在多目标优化中，这个概念仍然适用，但运行的结果不是作为标量（即最佳解的成本）来测量的，而是作为k维空间中的到达曲面（其中k是目标的数量）。在本文中，我们报告了一种算法，可以方便地用于绘制任何数量的维度（虽然它是特别适合于三个）的总结达到表面。汇总实现面定义为在n次运行的样本中的s次运行中（独立地）实现的所有最严格目标的并集，对于任何s/spl isin/1.。n，对于任意k。我们还讨论了该算法的计算复杂性，并给出了一些例子，它的使用。该算法的C代码可从作者处获得。
When evaluating the performance of a stochastic optimizer it is sometimes desirable to express performance in terms of the quality attained in a certain fraction of sample runs. For example, the sample median quality is the best estimator of what one would expect to achieve in 50% of runs, and similarly for other quantiles. In multiobjective optimization, the notion still applies but the outcome of a run is measured not as a scalar (i.e. the cost of the best solution), but as an attainment surface in k-dimensional space (where k is the number of objectives). In this paper we report an algorithm that can be conveniently used to plot summary attainment surfaces in any number of dimensions (though it is particularly suited for three). A summary attainment surface is defined as the union of all tightest goals that have been attained (independently) in precisely s of the runs of a sample of n runs, for any s/spl isin/1..n, and for any k. We also discuss the computational complexity of the algorithm and give some examples of its use. C code for the algorithm is available from the author.