Limited memory, limited arity unbiased black-box complexity: first insights
Pages 2020 - 2023
Abstract
Limited arity unbiased black-box complexity was proven to be a successful tool for understanding the working principles of randomized search heuristics and delivered insights to develop new efficient algorithms. While good upper bounds for simple problems were found long time ago, there are still no matching lower bounds.
On a road towards closing this gap, we introduce the notion of limited-memory, limited arity unbiased black-box complexity. We show that some efficient binary unbiased algorithms (almost) satisfy the memory-2 requirement, and present an algorithm to compute, for a given problem size, the exact lower bound on the runtime of any memory-m k-ary algorithm on any unimodal function.
References
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Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. 2001. Introduction to Algorithms, 2nd Ed. MIT Press, Cambridge, Massachusetts.
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Benjamin Doerr, Carola Doerr, and Franziska Ebel. 2015. From black-box complexity to designing new genetic algorithms. Theoretical Computer Science 567 (2015), 87--104.
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Benjamin Doerr, Carola Doerr, and Jing Yang. 2016. Optimal Parameter Choices via Precise Black-Box Analysis. In Proceedings of Genetic and Evolutionary Computation Conference. 1123--1130.
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Benjamin Doerr, Daniel Johannsen, Timo Kötzing, Per Kristian Lehre, Markus Wagner, and Carola Winzen. 2011. Faster black-box algorithms through higher arity operators. In Proceedings of Foundations of Genetic Algorithms. 163--172.
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Benjamin Doerr and Carola Winzen. 2014. Playing Mastermind with Constant-Size Memory. Theory of Computing Systems 55, 4 (2014), 658--684.
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Benjamin Doerr and Carola Winzen. 2014. Ranking-Based Black-Box Complexity. Algorithmica 68, 3 (2014), 571--609.
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Benjamin Doerr and Carola Winzen. 2014. Reducing the arity in unbiased black-box complexity. Theoretical Computer Science 545 (2014), 108--121.
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Per Kristian Lehre and Carsten Witt. 2012. Black-box Search by Unbiased Variation. Algorithmica 64 (2012), 623--642.32
Index Terms
- Limited memory, limited arity unbiased black-box complexity: first insights
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Published In
July 2019
2161 pages
ISBN:9781450367486
DOI:10.1145/3319619
- Editor:
- Manuel López-Ibáñez,
- General Chairs:
- Anne Auger,
- Thomas Stützle
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Publication History
Published: 13 July 2019
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