Faster black-box algorithms through higher arity operators

Authors:
Benjamin Doerr;Daniel Johannsen;Timo Kötzing;Per Kristian Lehre;Markus Wagner;Carola Winzen
Affiliations:
Max Planck Institut für Informatik, Saarbrücken, Germany;Max Planck Institut für Informatik, Saarbrücken, Germany;Max Planck Institut für Informatik, Saarbrücken, Germany;Technical University of Denmark, Lyngby, Denmark;Max Planck Institut für Informatik, Saarbrücken, Germany;Max Planck Institut für Informatik, Saarbrücken, Germany
Venue:
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Year:
2011

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Abstract

We extend the work of Lehre and Witt (GECCO 2010) on the unbiased black-box model by considering higher arity variation operators. In particular, we show that already for binary operators the black-box complexity of LeadingOnes drops from Θ(n2) for unary operators to O(n log n). For OneMax, the Ω(n log n) unary black-box complexity drops to O(n) in the binary case. For k-ary operators, k ≤ n, the OneMax-complexity further decreases to O(n / log k).