Real royal road functions for constant population size

Storch, Tobias; Wegener, Ingo

doi:10.1016/j.tcs.2004.03.047

Cited by 59 publications

(12 citation statements)

References 6 publications

(8 reference statements)

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“…Nevertheless, this mechanism makes the individuals spread on a certain fitness level such that crossover is able to find suitable parents to recombine. Storch and Wegener [14] presented a similar result for populations of constant size. They used a stronger mechanism that prevents duplicates from entering the population, regardless of their fitness.…”

Section: Introductionmentioning

confidence: 52%

Theoretical analysis of diversity mechanisms for global exploration

Friedrich

Oliveto

Sudholt

et al. 2008

Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation

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Maintaining diversity is important for the performance of evolutionary algorithms. Diversity mechanisms can enhance global exploration of the search space and enable crossover to find dissimilar individuals for recombination. We focus on the global exploration capabilities of mutation-based algorithms. Using a simple bimodal test function and rigorous runtime analyses, we compare well-known diversity mechanisms like deterministic crowding, fitness sharing, and others with a plain algorithm without diversification. We show that diversification is necessary for global exploration, but not all mechanisms succeed in finding both optima efficiently.

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Section: Introductionmentioning

confidence: 52%

Theoretical analysis of diversity mechanisms for global exploration

Friedrich

Oliveto

Sudholt

et al. 2008

Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation

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“…Storch and Wegener [8] present another class of real royal road functions for constant population size where a genetic algorithm with the smallest possible population size, namely 2, suffices to obtain a polynomial expected runtime.…”

Section: Introductionmentioning

confidence: 99%

Crossover is provably essential for the Ising model on trees

Sudholt

2005

Proceedings of the 7th Annual Conference on Genetic and Evolutionary Computation

105

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Diese Arbeit ist im Sonderforschungsbereich 531, "Computational Intelligence", der Universität Dortmund entstanden und wurde auf seine Veranlassung unter Verwendung der ihm von der Deutschen Forschungsgemeinschaft zur Verfügung gestellten Mittel gedruckt. Crossover is Provably Essential for the Ising Model on TreesDirk Sudholt * FB Informatik, Univ. Dortmund, 44221 Dortmund, GermanyDirk.Sudholt@uni-dortmund.de Abstract Due to experimental evidence it is incontestable that crossover is essential for some fitness functions. However, theoretical results without assumptions are difficult. So-called real royal road functions are known where crossover is proved to be essential, i. e., mutation-based algorithms have an exponential expected runtime while the expected runtime of a genetic algorithm is polynomially bounded. However, these functions are artificial and have been designed in such a way that crossover is essential only at the very end (or at other well-specified points) of the optimization process.Here, a more natural fitness function based on a generalized Ising model is presented where crossover is essential throughout the whole optimization process. Mutation-based algorithms such as (µ+λ) EAs with constant population size are proved to have an exponential expected runtime while the expected runtime of a simple genetic algorithm with population size 2 and fitness sharing is polynomially bounded.

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“…This helps to isolate the influences of population size and selection pressure that are beyond the scope of this paper. Note that as used in [19,15], though the population size of two is small, it is sufficient for showing the effect of recombination operators. …”

Section: The Evolutionary Algorithmmentioning

confidence: 99%

Towards Analyzing Recombination Operators in Evolutionary Search

Qian

Zhou

2010

Parallel Problem Solving From Nature, PPSN XI

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Abstract. Recombination (also called crossover) operators are widely used in EAs to generate offspring solutions. Although the usefulness of recombination has been well recognized, theoretical analysis on recombination operators remains a hard problem due to the irregularity of the operators and their complicated interactions to mutation operators. In this paper, as a step towards analyzing recombination operators theoretically, we present a general approach which allows to compare the runtime of an EA turning the recombination on and off, and thus helps to understand when a recombination operator works. The key of our approach is the Markov Chain Switching Theorem which compares two Markov chains for the first hit of the target.As an illustration, we analyze some recombination operators in evolutionary search on the LeadingOnes problem using the proposed approach. The analysis identifies some insight on the choice of recombination operators, which is then verified in experiments.

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Real royal road functions for constant population size

Cited by 59 publications

References 6 publications

Theoretical analysis of diversity mechanisms for global exploration

Theoretical analysis of diversity mechanisms for global exploration

Crossover is provably essential for the Ising model on trees

Towards Analyzing Recombination Operators in Evolutionary Search

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