TL;DR
This paper introduces Affine OneMax functions, a new class of test functions for black box optimization, analyzing their complexity and demonstrating their properties through theoretical bounds and experiments.
Contribution
It defines Affine OneMax functions, studies their black box complexity, and explores tunable complexity via invertible affine maps, supported by theoretical analysis and experiments.
Findings
Black box complexity is polynomial in dimension.
Complexity can be tuned using transvections.
Search algorithms perform variably on AOM functions.
Abstract
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.
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Taxonomy
TopicsMetaheuristic Optimization Algorithms Research · Optical Network Technologies · Quantum Computing Algorithms and Architecture