Volume

Dagstuhl Seminar Proceedings, Volume 6061



Publication Details

  • published at: 2006-07-07
  • Publisher: Schloss-Dagstuhl - Leibniz Zentrum für Informatik

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Document
06061 Abstracts Collection – Theory of Evolutionary Algorithms

Authors: Dirk V. Arnold, Thomas Jansen, Jonathan E. Rowe, and Michael D. Vose


Abstract
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.

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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
06061 Executive Summary – Theory of Evolutionary Algoritms

Authors: Dirk V. Arnold, Thomas Jansen, Jonathan E. Rowe, and Michael D. Vose


Abstract
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.

Cite as

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
A Mathematical Modelling Technique for the Analysis of the Dynamics of a Simple Continuous EDA

Authors: Marcus Gallagher and Bo Yuan


Abstract
We describe a mathematical model for the infinite-population dynamics of a simple continuous EDA: UMDAc. Using this model, it is possible to numerically generate the dynamics of the algorithm on a fitness function of known form. The technique is compared with existing analysis and illustrated on a number of simple test problems. The model is also used to examine the effect of adding an amplification constant to the variance parameter of the UMDAc model.

Cite as

Marcus Gallagher and Bo Yuan. A Mathematical Modelling Technique for the Analysis of the Dynamics of a Simple Continuous EDA. In Theory of Evolutionary Algorithms. Dagstuhl Seminar Proceedings, Volume 6061, pp. 1-7, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2006)


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@InProceedings{gallagher_et_al:DagSemProc.06061.3,
  author =	{Gallagher, Marcus and Yuan, Bo},
  title =	{{A Mathematical Modelling Technique for the Analysis of the Dynamics of a Simple Continuous EDA}},
  booktitle =	{Theory of Evolutionary Algorithms},
  pages =	{1--7},
  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.06061.3},
  URN =		{urn:nbn:de:0030-drops-5940},
  doi =		{10.4230/DagSemProc.06061.3},
  annote =	{Keywords: Estimation of Distribution Algorithms}
}
Document
A New Quartet Tree Heuristic for Hierarchical Clustering

Authors: Rudi Cilibrasi and Paul M. B. Vitany


Abstract
We present a new quartet heuristic for hierarchical clustering from a given distance matrix. We determine a dendrogram (ternary tree) by a new quartet method and a fast heuristic to implement it. We do not assume that there is a true ternary tree that generated the distances and which we with to recover as closeley as possible. Our aim is to model the distance matrix as faithfully as possible by the dendrogram. Our algorithm is essentially randomized hill-climbing, using parallellized Genetic Programming, where undirected trees evolve in a random walk driven by a prescribed fitness function. Our method is capable of handling up to 60--80 objects in a matter of hours, while no existing quartet heuristic can directly compute a quartet tree of more than about 20--30 objects without running for years. The method is implemented and available as public software at www.complearn.org. We present applications in many areas like music, literature, bird-flu (H5N1) virus clustering, and automatic meaning discovery using Google.

Cite as

Rudi Cilibrasi and Paul M. B. Vitany. A New Quartet Tree Heuristic for Hierarchical Clustering. In Theory of Evolutionary Algorithms. Dagstuhl Seminar Proceedings, Volume 6061, pp. 1-13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2006)


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@InProceedings{cilibrasi_et_al:DagSemProc.06061.4,
  author =	{Cilibrasi, Rudi and Vitany, Paul M. B.},
  title =	{{A New Quartet Tree Heuristic for Hierarchical Clustering}},
  booktitle =	{Theory of Evolutionary Algorithms},
  pages =	{1--13},
  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.06061.4},
  URN =		{urn:nbn:de:0030-drops-5985},
  doi =		{10.4230/DagSemProc.06061.4},
  annote =	{Keywords: Genetic programming, hierarchical clustering, quartet tree method}
}
Document
How fast does the stationary distribution of the Markov chain modelling EAs concentrate on the homogeneous populations for small mutation rate?

Authors: Boris S. Mitavskiy and Jonathan E. Rowe


Abstract
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.

Cite as

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}
}
Document
On Complexity of Optimized Crossover for Binary Representations

Authors: Anton Eremeev


Abstract
We consider the computational complexity of producing the best possible offspring in a crossover, given two solutions of the parents. The crossover operators are studied on the class of Boolean linear programming problems, where the Boolean vector of variables is used as the solution representation. By means of efficient reductions of the optimized gene transmitting crossover problems (OGTC) we show the polynomial solvability of the OGTC for the maximum weight set packing problem, the minimum weight set partition problem and for one of the versions of the simple plant location problem. We study a connection between the OGTC for linear Boolean programming problem and the maximum weight independent set problem on 2-colorable hypergraph and prove the NP-hardness of several special cases of the OGTC problem in Boolean linear programming.

Cite as

Anton Eremeev. On Complexity of Optimized Crossover for Binary Representations. In Theory of Evolutionary Algorithms. Dagstuhl Seminar Proceedings, Volume 6061, pp. 1-13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2006)


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@InProceedings{eremeev:DagSemProc.06061.6,
  author =	{Eremeev, Anton},
  title =	{{On Complexity of Optimized Crossover for Binary Representations}},
  booktitle =	{Theory of Evolutionary Algorithms},
  pages =	{1--13},
  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.06061.6},
  URN =		{urn:nbn:de:0030-drops-5932},
  doi =		{10.4230/DagSemProc.06061.6},
  annote =	{Keywords: Genetic Algorithm, Optimized Crossover, Complexity}
}
Document
On Turing complete T7 and MISC F--4 program fitnes landscapes

Authors: William B. Langdon and Riccardo Poli


Abstract
We use the minimal instruction set F-4 computer to define a minimal Turing complete T7 computer suitable for genetic programming (GP) and amenable to theoretical analysis. Experimental runs and mathematical analysis of the T7, show the fraction of halting programs is drops to zero as bigger programs are run.

Cite as

William B. Langdon and Riccardo Poli. On Turing complete T7 and MISC F--4 program fitnes landscapes. In Theory of Evolutionary Algorithms. Dagstuhl Seminar Proceedings, Volume 6061, pp. 1-28, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2006)


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@InProceedings{langdon_et_al:DagSemProc.06061.7,
  author =	{Langdon, William B. and Poli, Riccardo},
  title =	{{On Turing complete T7 and MISC F--4 program fitnes landscapes}},
  booktitle =	{Theory of Evolutionary Algorithms},
  pages =	{1--28},
  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.06061.7},
  URN =		{urn:nbn:de:0030-drops-5956},
  doi =		{10.4230/DagSemProc.06061.7},
  annote =	{Keywords: Genetic programming}
}
Document
Runtime Analysis of a Simple Ant Colony Optimization Algorithm

Authors: Frank Neumann and Carsten Witt


Abstract
Ant Colony Optimization (ACO) has become quite popular in recent years. In contrast to many successful applications, the theoretical foundation of this randomized search heuristic is rather weak. Building up such a theory is demanded to understand how these heuristics work as well as to come up with better algorithms for certain problems. Up to now, only convergence results have been achieved showing that optimal solutions can be obtained in a finite amount of time. We present the first runtime analysis of a simple ACO algorithm that transfers many rigorous results with respect to the expected runtime of a simple evolutionary algorithm to our algorithm. In addition, we examine the choice of the evaporation factor, which is a crucial parameter in such an algorithm, in greater detail and analyze its effect with respect to the runtime.

Cite as

Frank Neumann and Carsten Witt. Runtime Analysis of a Simple Ant Colony Optimization Algorithm. In Theory of Evolutionary Algorithms. Dagstuhl Seminar Proceedings, Volume 6061, pp. 1-17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2006)


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@InProceedings{neumann_et_al:DagSemProc.06061.8,
  author =	{Neumann, Frank and Witt, Carsten},
  title =	{{Runtime Analysis of  a Simple Ant Colony Optimization Algorithm}},
  booktitle =	{Theory of Evolutionary Algorithms},
  pages =	{1--17},
  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.06061.8},
  URN =		{urn:nbn:de:0030-drops-5928},
  doi =		{10.4230/DagSemProc.06061.8},
  annote =	{Keywords: Randomized Search Heuristics, Ant Colony Optimization, Runtime Analysis}
}
Document
The Factorized Distribution Algorithm and the Minimum Relative Entropy Principle

Authors: Heinz Mühlenbein and Robin Höns


Abstract
We assume that the function to be optimized is additively decomposed (ADF). Then the interaction graph $G_{ADF}$ can be used to compute exact or approximate factorizations. For many practical problems only approximate factorizations lead to efficient optimization algorithms. The relation between the approximation used by the FDA algorithm and the minimum relative entropy principle is discussed. A new algorithm is presented, derived from the Bethe-Kikuchi approach in statistical physics. It minimizes the relative entropy to a Boltzmann distribution with fixed $eta$. We shortly compare different factorizations and algorithms within the FDA software. We use 2-d Ising spin glass problems and Kaufman's n-k function as examples.

Cite as

Heinz Mühlenbein and Robin Höns. The Factorized Distribution Algorithm and the Minimum Relative Entropy Principle. In Theory of Evolutionary Algorithms. Dagstuhl Seminar Proceedings, Volume 6061, pp. 1-27, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2006)


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@InProceedings{muhlenbein_et_al:DagSemProc.06061.9,
  author =	{M\"{u}hlenbein, Heinz and H\"{o}ns, Robin},
  title =	{{The Factorized Distribution Algorithm and the Minimum Relative Entropy Principle}},
  booktitle =	{Theory of Evolutionary Algorithms},
  pages =	{1--27},
  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.06061.9},
  URN =		{urn:nbn:de:0030-drops-5973},
  doi =		{10.4230/DagSemProc.06061.9},
  annote =	{Keywords: Junction tree, minimum relative entropy, maximum likelihood, Bethe-Kikuchi approximation}
}

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