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Testing Surrogate-Based Optimization with the Fortified Branin-Hoo Extended to Four Dimensions
arXiv - CS - Neural and Evolutionary Computing Pub Date : 2021-07-16 , DOI: arxiv-2107.08035
Charles F. Jekel, Raphael T. Haftka

Some popular functions used to test global optimization algorithms have multiple local optima, all with the same value, making them all global optima. It is easy to make them more challenging by fortifying them via adding a localized bump at the location of one of the optima. In previous work the authors illustrated this for the Branin-Hoo function and the popular differential evolution algorithm, showing that the fortified Branin-Hoo required an order of magnitude more function evaluations. This paper examines the effect of fortifying the Branin-Hoo function on surrogate-based optimization, which usually proceeds by adaptive sampling. Two algorithms are considered. The EGO algorithm, which is based on a Gaussian process (GP) and an algorithm based on radial basis functions (RBF). EGO is found to be more frugal in terms of the number of required function evaluations required to identify the correct basin, but it is expensive to run on a desktop, limiting the number of times the runs could be repeated to establish sound statistics on the number of required function evaluations. The RBF algorithm was cheaper to run, providing more sound statistics on performance. A four-dimensional version of the Branin-Hoo function was introduced in order to assess the effect of dimensionality. It was found that the difference between the ordinary function and the fortified one was much more pronounced for the four-dimensional function compared to the two dimensional one.

中文翻译:

使用扩展到四个维度的强化 Branin-Hoo 测试基于代理的优化

一些用于测试全局优化算法的流行函数具有多个局部最优值,它们都具有相同的值,使它们都是全局最优值。通过在优化点之一的位置添加局部凹凸来强化它们,很容易使它们更具挑战性。在之前的工作中,作者针对 Branin-Hoo 函数和流行的差分进化算法说明了这一点,表明强化的 Branin-Hoo 需要一个数量级的函数评估。本文研究了强化 Branin-Hoo 函数对基于代理的优化的影响,该优化通常通过自适应采样进行。考虑了两种算法。EGO算法,基于高斯过程(GP)和基于径向基函数(RBF)的算法。发现 EGO 在识别正确盆地所需的所需函数评估数量方面更加节俭,但在台式机上运行成本高昂,限制了重复运行的次数以建立有关数量的可靠统计数据所需的功能评估。RBF 算法运行成本更低,提供了更多关于性能的可靠统计数据。为了评估维度的影响,引入了 Branin-Hoo 函数的四维版本。结果发现,与二维函数相比,四维函数的普通函数和强化函数之间的差异要明显得多。限制可以重复运行的次数,以建立有关所需函数评估数量的可靠统计数据。RBF 算法运行成本更低,提供了更多关于性能的可靠统计数据。为了评估维度的影响,引入了 Branin-Hoo 函数的四维版本。结果发现,与二维函数相比,四维函数的普通函数和强化函数之间的差异要明显得多。限制可以重复运行的次数,以建立有关所需函数评估数量的可靠统计数据。RBF 算法运行成本更低,提供了更多关于性能的可靠统计数据。为了评估维度的影响,引入了 Branin-Hoo 函数的四维版本。结果发现,与二维函数相比,四维函数的普通函数和强化函数之间的差异要明显得多。
更新日期:2021-07-19
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