A new class of test functions for black box optimization is introduced. Affine OneMax (AOM) functions are defined as compositions of OneMax and invertible affine maps on bit vectors. The black box complexity of the class is upper bounded by a polynomial of large degree in the dimension. The proof relies on discrete Fourier analysis and the Kushilevitz-Mansour algorithm. Tunable complexity is achieved by expressing invertible linear maps as finite products of transvections. The black box complexity of sub-classes of AOM functions is studied. Finally, experimental results are given to illustrate the performance of search algorithms on AOM functions.
翻译：引入了黑盒优化的新测试功能类别。 Affine OneMax(AOM) 函数的定义是: OneMax 的构成和位矢量上的不可倒置的离子形形形形形形形形形形形形形色色图的构成。 等级的黑盒复杂程度在维度上被一个多面形形形形形形形形形色色体的上层框复杂程度。 证据依赖于离散的 Fourier 分析和 Kushilevitz-Mansour 算法。 将不可倒置的线形图作为穿透的有限产品来表达, 实现可图的复杂性。 正在研究 AOM 函数亚类的黑盒复杂程度。 最后, 实验结果用来说明对 AOM 函数的搜索算法的性。
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