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How To Analyse Evolutionary Algorithms
, 2002
"... Many variants of evolutionary algorithms have been designed and applied. The ..."
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Cited by 26 (1 self)
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Many variants of evolutionary algorithms have been designed and applied. The
Bistability in a Gene Pool GA with Mutation
 In Foundations of genetic algorithms (FOGA7
, 2003
"... It is possible for a GA to have two stable fixed points on a singlepeak fitness landscape. ..."
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Cited by 7 (4 self)
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It is possible for a GA to have two stable fixed points on a singlepeak fitness landscape.
On the finitetime dynamics of ant colony optimization
 Methodol. Comput. Appl. Probab
"... Abstract. An analytical framework for investigating the finitetime dynamics of ant colony optimization (ACO) under a fitnessproportional pheromone update rule on arbitrary construction graphs is developed. A limit theorem on the approximation of the stochastic ACO process by a deterministic proces ..."
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Cited by 4 (1 self)
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Abstract. An analytical framework for investigating the finitetime dynamics of ant colony optimization (ACO) under a fitnessproportional pheromone update rule on arbitrary construction graphs is developed. A limit theorem on the approximation of the stochastic ACO process by a deterministic process is demonstrated, and a system of ordinary differential equations governing the process dynamics is identified. As an example for the application of the presented theory, the behavior of ACO on three different construction graphs for subset selection problems is analyzed and compared for some basic test functions. The theory enables first rough theoretical predictions of the convergence speed of ACO.
How to analyze evolutionary algorithms
 Theoretical Computer Science
"... Many variants of evolutionary algorithms have been designed and applied. The experimental knowledge is immense. The rigorous analysis of evolutionary algorithms is difficult, but such a theory can help to understand, design, and teach evolutionary algorithms. In this survey, first the history of att ..."
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Cited by 4 (1 self)
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Many variants of evolutionary algorithms have been designed and applied. The experimental knowledge is immense. The rigorous analysis of evolutionary algorithms is difficult, but such a theory can help to understand, design, and teach evolutionary algorithms. In this survey, first the history of attempts to analyse evolutionary algorithms is described and then new methods for continuous as well as discrete search spaces are presented and discussed.
Bistability of the needle function in the presence of truncation selection
, 2003
"... Abstract. It is possible for a GA to have two stable fixed points on a singlepeak fitness landscape. These can correspond to metastable finite populations. This phenomenon is called bistability, and is only known to happen in the presence of recombination, selection, and mutation. This paper model ..."
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Cited by 3 (2 self)
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Abstract. It is possible for a GA to have two stable fixed points on a singlepeak fitness landscape. These can correspond to metastable finite populations. This phenomenon is called bistability, and is only known to happen in the presence of recombination, selection, and mutation. This paper models the bistability phenomenon using an infinite population model of a GA based on gene pool recombination. Fixed points and their stability are explicitly calculated. This is possible since the infinite population model of the gene pool GA is much more tractable than the infinite population model for the standard simple GA. For the needleinthehaystack fitness function, the fixed point equations reduce to a single variable polynomial equation, and stability of fixed points can be determined from the derivative of the single variable equation. 1
Bistability of the Needle Function in the Presence of Truncation Selection Genetic Algorithms Track
"... Abstract. It is possible for a GA to have two stable fixed points on a singlepeak fitness landscape. These can correspond to metastable finite populations. This phenomenon is called bistability, and is only known to happen in the presence of recombination, selection, and mutation. This paper model ..."
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Abstract. It is possible for a GA to have two stable fixed points on a singlepeak fitness landscape. These can correspond to metastable finite populations. This phenomenon is called bistability, and is only known to happen in the presence of recombination, selection, and mutation. This paper models the bistability phenomenon using an infinite population model of a GA based on gene pool recombination. Fixed points and their stability are explicitly calculated. This is possible since the infinite population model of the gene pool GA is much more tractable than the infinite population model for the standard simple GA. For the needleinthehaystack fitness function, the fixed point equations reduce to a single variable polynomial equation, and stability of fixed points can be determined from the derivative of the single variable equation. 1
Abbreviations: GAs
"... Abstract. It is known that modelling a finite population genetic algorithm as a Markov chain requires a prohibitively large number of states. In an attempt to resolve this problem, a number of state aggregation techniques have been proposed. We consider two different strategies for aggregating popul ..."
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Abstract. It is known that modelling a finite population genetic algorithm as a Markov chain requires a prohibitively large number of states. In an attempt to resolve this problem, a number of state aggregation techniques have been proposed. We consider two different strategies for aggregating populations, one using equal average fitness and the other using equal best fitness. We examine how the approximation scales with population size, in addition to studying the effects of other parameters (such as mutation rate). We find that a large reduction in the number of states is possible, sometimes with surprisingly small loss of accuracy.