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Journal Articles Algorithmica Year : 2014

Ranking-Based Black-Box Complexity

Abstract

Randomized search heuristics such as evolutionary algorithms, simulated annealing, and ant colony optimization are a broadly used class of general-purpose algorithms. Analyzing them via classical methods of theoretical computer science is a growing field. While several strong runtime analysis results have appeared in the last 20 years, a powerful complexity theory for such algorithms is yet to be developed. We enrich the existing notions of black-box complexity by the additional restriction that not the actual objective values, but only the relative quality of the previously evaluated solutions may be taken into account by the black-box algorithm. Many randomized search heuristics belong to this class of algorithms.We show that the new ranking-based model can give more realistic complexity estimates. The class of all binary-value functions has a black-box complexity of O(logn) in the previous black-box models, but has a ranking-based complexity of Θ(n).On the other hand, for the class of all OneMax functions, we present a ranking-based black-box algorithm that has a runtime of Θ(n/logn), which shows that the OneMax problem does not become harder with the additional ranking-basedness restriction.

Dates and versions

hal-01086508 , version 1 (24-11-2014)

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Cite

Benjamin Doerr, Carola Doerr. Ranking-Based Black-Box Complexity. Algorithmica, 2014, 68, pp.571-609. ⟨10.1007/s00453-012-9684-9⟩. ⟨hal-01086508⟩
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