Ranking-Based Black-Box Complexity
| Autor: | Doerr, Benjamin, Winzen, Carola |
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| Rok vydání: | 2011 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00453-012-9684-9 |
| Popis: | 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 gives more realistic complexity estimates for some problems. For example, the class of all binary-value functions has a black-box complexity of $O(\log n)$ in the previous black-box models, but has a ranking-based complexity of $\Theta(n)$. For the class of all OneMax functions, we present a ranking-based black-box algorithm that has a runtime of $\Theta(n / \log n)$, which shows that the OneMax problem does not become harder with the additional ranking-basedness restriction. Comment: This is an extended version of our CSR 2011 paper. 31 pages. The journal version is to appear in Algorithmica, DOI: 10.1007/s00453-012-9684-9 |
| Databáze: | arXiv |
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