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**Published in:** Dagstuhl Seminar Proceedings, Volume 8051, Theory of Evolutionary Algorithms (2008)

From Jan. 27, 2008 to Feb. 1, 2008, the Dagstuhl Seminar 08051 ``Theory of Evolutionary Algorithms'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available.

Dirk V. Arnold, Anne Auger, Carsten Witt, and Jonathan E. Rowe. 08051 Abstracts Collection – Theory of Evolutionary Algorithms. In Theory of Evolutionary Algorithms. Dagstuhl Seminar Proceedings, Volume 8051, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{arnold_et_al:DagSemProc.08051.1, author = {Arnold, Dirk V. and Auger, Anne and Witt, Carsten and Rowe, Jonathan E.}, title = {{08051 Abstracts Collection – Theory of Evolutionary Algorithms}}, booktitle = {Theory of Evolutionary Algorithms}, pages = {1--15}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2008}, volume = {8051}, editor = {Dirk V. Arnold and Anne Auger and Jonathan E. Rowe and Carsten Witt}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08051.1}, URN = {urn:nbn:de:0030-drops-15242}, doi = {10.4230/DagSemProc.08051.1}, annote = {Keywords: Evolutionary Computation, Theory of Evolutionary Algorithms} }

Document

**Published in:** Dagstuhl Seminar Proceedings, Volume 8051, Theory of Evolutionary Algorithms (2008)

The 2008 Dagstuhl Seminar "Theory of Evolutionary Algorithms" was the fifth in a firmly established series of biannual events. In the week from Jan. 27, 2008 to Feb. 1, 2008, 47 researchers from nine countries discussed their recent work and trends in evolutionary computation.

Dirk V. Arnold, Anne Auger, Jonathan E. Rowe, and Carsten Witt. 08051 Executive Summary – Theory of Evolutionary Algorithms. In Theory of Evolutionary Algorithms. Dagstuhl Seminar Proceedings, Volume 8051, pp. 1-5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{arnold_et_al:DagSemProc.08051.2, author = {Arnold, Dirk V. and Auger, Anne and Rowe, Jonathan E. and Witt, Carsten}, title = {{08051 Executive Summary – Theory of Evolutionary Algorithms}}, booktitle = {Theory of Evolutionary Algorithms}, pages = {1--5}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2008}, volume = {8051}, editor = {Dirk V. Arnold and Anne Auger and Jonathan E. Rowe and Carsten Witt}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08051.2}, URN = {urn:nbn:de:0030-drops-14812}, doi = {10.4230/DagSemProc.08051.2}, annote = {Keywords: Evolutionary Algorithms, Theory of Evolutionary Algorithms} }

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**Published in:** LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008)

We analyze a simple random process in which a token is moved in the
interval $A={0,dots,n$: Fix a probability distribution $mu$
over ${1,dots,n$. Initially, the token is placed in a random
position in $A$. In round $t$, a random value $d$ is chosen
according to $mu$. If the token is in position $ageq d$, then it
is moved to position $a-d$. Otherwise it stays put. Let $T$ be
the number of rounds until the token reaches position 0. We show
tight bounds for the expectation of $T$ for the optimal
distribution $mu$. More precisely, we show that
$min_mu{E_mu(T)=Thetaleft((log n)^2
ight)$. For the
proof, a novel potential function argument is introduced. The
research is motivated by the problem of approximating the minimum
of a continuous function over $[0,1]$ with a ``blind'' optimization
strategy.

Martin Dietzfelbinger, Jonathan E. Rowe, Ingo Wegener, and Philipp Woelfel. Tight Bounds for Blind Search on the Integers. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 241-252, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{dietzfelbinger_et_al:LIPIcs.STACS.2008.1348, author = {Dietzfelbinger, Martin and Rowe, Jonathan E. and Wegener, Ingo and Woelfel, Philipp}, title = {{Tight Bounds for Blind Search on the Integers}}, booktitle = {25th International Symposium on Theoretical Aspects of Computer Science}, pages = {241--252}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-06-4}, ISSN = {1868-8969}, year = {2008}, volume = {1}, editor = {Albers, Susanne and Weil, Pascal}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1348}, URN = {urn:nbn:de:0030-drops-13486}, doi = {10.4230/LIPIcs.STACS.2008.1348}, annote = {Keywords: } }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 6061, Theory of Evolutionary Algorithms (2006)

From 05.02.06 to 10.02.06, the Dagstuhl Seminar 06061 ``Theory of Evolutionary Algorithms'' was held in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available.

Dirk V. Arnold, Thomas Jansen, Jonathan E. Rowe, and Michael D. Vose. 06061 Abstracts Collection – Theory of Evolutionary Algorithms. In Theory of Evolutionary Algorithms. Dagstuhl Seminar Proceedings, Volume 6061, pp. 1-16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{arnold_et_al:DagSemProc.06061.1, author = {Arnold, Dirk V. and Jansen, Thomas and Rowe, Jonathan E. and Vose, Michael D.}, title = {{06061 Abstracts Collection – Theory of Evolutionary Algorithms}}, booktitle = {Theory of Evolutionary Algorithms}, pages = {1--16}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2006}, volume = {6061}, editor = {Dirk V. Arnold and Thomas Jansen and Michael D. Vose and Jonathan E. Rowe}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06061.1}, URN = {urn:nbn:de:0030-drops-6009}, doi = {10.4230/DagSemProc.06061.1}, annote = {Keywords: Evolutionary algorithms, evolutionary computation, theory} }

Document

**Published in:** Dagstuhl Seminar Proceedings, Volume 6061, Theory of Evolutionary Algorithms (2006)

The 2006 Dagstuhl Seminar ``Theory of Evolutionary Algorithms'' carried forward a series of Dagstuhl seminars that started in 2000 and has become an established event in the community. In the week from from 05.02.2006 to 10.02.2006, 56 researchers from 12 countries discussed their recent work and recent trends in evolutionary computation.

Dirk V. Arnold, Thomas Jansen, Jonathan E. Rowe, and Michael D. Vose. 06061 Executive Summary – Theory of Evolutionary Algoritms. In Theory of Evolutionary Algorithms. Dagstuhl Seminar Proceedings, Volume 6061, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{arnold_et_al:DagSemProc.06061.2, author = {Arnold, Dirk V. and Jansen, Thomas and Rowe, Jonathan E. and Vose, Michael D.}, title = {{06061 Executive Summary – Theory of Evolutionary Algoritms}}, booktitle = {Theory of Evolutionary Algorithms}, pages = {1--2}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2006}, volume = {6061}, editor = {Dirk V. Arnold and Thomas Jansen and Michael D. Vose and Jonathan E. Rowe}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06061.2}, URN = {urn:nbn:de:0030-drops-5995}, doi = {10.4230/DagSemProc.06061.2}, annote = {Keywords: Evolutionary algorithms, evolutionary computation, theory} }

Document

**Published in:** Dagstuhl Seminar Proceedings, Volume 6061, Theory of Evolutionary Algorithms (2006)

The state space of the Markov chain modelling an evolutionary algorithm
is quite large especially if the population space and the search space are
large. I shell introduce an appropriate notion of "coarse graining" for
such Markov chains. Indeed, from the mathematical point of view, this can
be called a quotient of a Markov chain by an equivalence relation over the
state space. The newly obtained Markov chain has a significantly smaller
state space and it's stationary distribution is "coherent" with the
initial large chain. Although the transition probabilities of the
coarse-grained Markov chain are defined in terms of the stationary
distribution of the original big chain, in some cases it is possible to
deduce interesting information about the stationary distribution of the
original chain in terms of the quatient chain. I will demonstrate how
this method works. I shell also present some simple results and open
questions.

Boris S. Mitavskiy and Jonathan E. Rowe. How fast does the stationary distribution of the Markov chain modelling EAs concentrate on the homogeneous populations for small mutation rate?. In Theory of Evolutionary Algorithms. Dagstuhl Seminar Proceedings, Volume 6061, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{mitavskiy_et_al:DagSemProc.06061.5, author = {Mitavskiy, Boris S. and Rowe, Jonathan E.}, title = {{How fast does the stationary distribution of the Markov chain modelling EAs concentrate on the homogeneous populations for small mutation rate?}}, booktitle = {Theory of Evolutionary Algorithms}, pages = {1--9}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2006}, volume = {6061}, editor = {Dirk V. Arnold and Thomas Jansen and Michael D. Vose and Jonathan E. Rowe}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06061.5}, URN = {urn:nbn:de:0030-drops-5964}, doi = {10.4230/DagSemProc.06061.5}, annote = {Keywords: Markov chains, Evolutionary algorithms, coarse graining quotients of irreducible Markov chains, concentration on the uniform populations} }

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