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Designing EDAs by using the elitist convergent EDA concept and the boltzmann distribution

Published: 12 July 2008 Publication History

Abstract

This paper presents a theoretical definition for designing EDAs called Elitist Convergent Estimation of Distribution Algorithm (ECEDA), and a practical implementation: the Boltzmann Univariate Marginal Distribution Algorithm (BUMDA). This proposal computes a Gaussian model which approximates a Boltzmann distribution via the minimization of the Kullback Leibler divergence. The resulting approach needs only one parameter: the population size. A set of problems is presented to show advantages and comparative performance of this approach with state of the art continuous EDAs.

References

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P. A. N. Bosman and D. Thierens. Expanding from discrete to continuous estimation of distribution algorithms: The idea. In PPSN VI: Proceedings of the 6th International Conference on Parallel Problem Solving from Nature, pages 767--776, London, UK, 2000. Springer-Verlag.]]
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M. Gallagher$^1$ and M. Frean$^2$. Population-based continuous optimization and probabilistic modelling. Technical report, $^1$School of computer Science and Electrical Engineering, Univerity of Queensland, Australia. $^2$School of Mathematical and Computing Sciences, Victoria Univerty, New Zealand., University of Queensland. 4072 Australia., 2001.]]
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J. Grahl, P. A. N. Bosman, and S. Minner. Convergence phases, variance trajectories, and runtime analysis of continuos edas. In GECCO '07: Proceedings of the 8th annual conference on Genetic and evolutionary computation, pages 516--522. ACM, 2007.]]
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P. Larra\ naga and J. A. Lozano. Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Kluwer Academic Publishers, Norwell, MA, USA, 2001.]]
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T. Mahnig and H. Mühlenbein. Comparing the adaptive boltzmann selection schedule sds to truncation selection. In Proceedings of the Third International Symposium on Adaptive Systems ISAS 2001, Evolutionary Computation and Probabilistic Graphical Models, pages 121--128, La Habana, Cuba, 2001.]]
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H. Mühlenbein. The equation for response to selection and its use for prediction. Evolutionary Computation, 5(3):303--346, 1997.]]
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H. Mühlenbein, T. Mahnig, and A. O. Rodriguez. Schemata, distributions and graphical models in evolutionary optimization. Journal of Heuristics, 5(2):215--247, 1999.]]
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C. Yunpeng, S. Xiaomin, and J. Peifa. Probabilistic modeling for continuous eda with boltzmann selection and kullback-leibeler divergence. In GECCO '06: Proceedings of the 8th annual conference on Genetic and evolutionary computation, pages 389--396, New York, NY, USA, 2006. ACM.]]
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  • (2019)Symmetric-Approximation Energy-Based Estimation of Distribution (SEED): A Continuous Optimization AlgorithmIEEE Access10.1109/ACCESS.2019.29481997(154859-154871)Online publication date: 2019

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  1. Designing EDAs by using the elitist convergent EDA concept and the boltzmann distribution

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    cover image ACM Conferences
    GECCO '08: Proceedings of the 10th annual conference on Genetic and evolutionary computation
    July 2008
    1814 pages
    ISBN:9781605581309
    DOI:10.1145/1389095
    • Conference Chair:
    • Conor Ryan,
    • Editor:
    • Maarten Keijzer
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Published: 12 July 2008

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    Author Tags

    1. boltzmann distribution
    2. estimation of distribution algorithms
    3. kullback-leibler divergence
    4. performance analysis

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    • (2019)Symmetric-Approximation Energy-Based Estimation of Distribution (SEED): A Continuous Optimization AlgorithmIEEE Access10.1109/ACCESS.2019.29481997(154859-154871)Online publication date: 2019

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