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Affine OneMax

Published: 08 July 2021 Publication History

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. Tunable complexity is achieved by expressing invertible linear maps as finite products of transvections. Finally, experimental results are given to illustrate the performance of search algorithms on AOM functions.

References

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Carola Doerr. Complexity theory for discrete black-box optimization heuristics. In Benjamin Doerr and Frank Neumann, editors, Theory of Evolutionary Computation: Recent Developments in Discrete Optimization, pages 133--212, Cham, 2020. Springer International Publishing.
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Stefan Droste, Thomas Jansen, and Ingo Wegener. Upper and lower bounds for randomized search heuristics in black-box optimization. Theory of Computing Systems, 39(4):525--544, 2006.
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HNCO. https://github.com/courros/hnco. v0.16.
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Eyal Kushilevitz and Yishay Mansour. Learning decision trees using the Fourier spectrum. SIAM Journal on Computing, 22(6):1331--1348, 1993.
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Gunar Liepins and Michael Vose. Representational issues in genetic optimization. J. Exp. Theor. Artif. Intell., 2:101--115, 1990.
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Gunar Liepins and Michael Vose. Polynomials, basis sets, and deceptiveness in genetic algorithms. Complex Systems, 5, 1991.
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Sancho Salcedo-Sanz and Carlos Bousoño-Calzón. On the application of linear transformations for genetic algorithms optimization. KES Journal, 11:89--104, 2007.
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Christopher Schumacher, Michael Vose, and Darrell Whitley. The no free lunch and problem description length. In Proc. of the 3rd Annual Conf. on Genetic and Evolutionary Computation (GECCO'01), pages 565--570, San Francisco, CA, USA, 2001. Morgan Kaufmann Publishers Inc.

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cover image ACM Conferences
GECCO '21: Proceedings of the Genetic and Evolutionary Computation Conference Companion
July 2021
2047 pages
ISBN:9781450383516
DOI:10.1145/3449726
Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

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Publication History

Published: 08 July 2021

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Author Tags

  1. black box complexity
  2. black box optimization
  3. combinatorial optimization
  4. discrete fourier analysis
  5. linear group
  6. test functions
  7. transvections
  8. tunable complexity

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