Article

On the convergence of an estimation of distribution algorithm based on linkage discovery and factorization

Authors:

Alden H. Wright,

Sandeep PulavartyAuthors Info & Claims

GECCO '05: Proceedings of the 7th annual conference on Genetic and evolutionary computation

Pages 695 - 702

https://doi.org/10.1145/1068009.1068126

Published: 25 June 2005 Publication History

Abstract

Estimation of distribution algorithms construct an explicit model of the problem to be solved, and then use this model to guide the search for good solutions. For an important class of fitness functions, namely those with k-bounded epistasis, it is possible to construct a complete explicit representation of the fitness function by sampling the fitness function. A very natural model of the problem to be solved is the Boltzmann distribution of the fitness function, which is an exponential of the fitness normalized to a probability distribution. As the exponentiation factor (inverse temperature) of the Boltzmann distribution is increased, probability is increasingly concentrated on the set of optimal points. We show that for fitness functions of k-bounded epistasis that satisfy an additional property called the running intersection property, an explicit computable exact factorization of the Boltzmann distribution with an arbitrary exponentiation factor can be constructed. This factorization allows the Boltzmann distribution to be efficiently sampled, which leads to an algorithm which finds the optimum with high probability.

References

[1]

S. Baluja and R. Caruana. Removing the genetics from the standard genetic algorithm. In A. Prieditis and S. Russel, editors, The Int. Conf. on Machine Learning 1995, pages 38--46, San Mateo, CA, 1995. Morgan Kaufmann Publishers.

[2]

J. S. de Bonet, C. L. Isbell, Jr., and P. Viola. MIMIC: Finding optima by estimating probability densities. In M. C. M. et. al., editor, Advances in Neural Information Processing Systems, volume 9, page 424. MIT Press, 1997.

[3]

D. E. Goldberg, K. Deb, H. Kargupta, and G. Harik. Rapid, accurate optimization of difficult optimization problems using fast messy genetic algorithms. In S. Forrest, editor, Proceedings of the Fifth International Conference on Genetic Algorithms, pages 56--64, San Mateo, California, 1993. Morgan Kaufman.

Digital Library

[4]

G. R. Harik and D. E. Goldberg. Learning linkage. In R. K. Belew and M. D. Vose, editors, Foundations of Genetic Algorithms 4, pages 247--262. Morgan Kaufmann, San Francisco, CA, 1997.

[5]

G. R. Harik, F. G. Lobo, and D. E. Goldberg. The compact genetic algorithm. IEEE-EC, 3(4):287, November 1999.

Digital Library

[6]

R. E. Heckendorn and A. H. Wright. Efficient linkage discovery by limited probing. In Erick Cantú Paz et al., editor, Genetic and Evolutionary Computation - GECCO 2003, Lecture Notes in Computer Science LNCS 2724, pages 1003--10014. Springer Verlag, 2003.

Digital Library

[7]

R. E. Heckendorn and A. H. Wright. Efficient linkage discovery by limited probing. Evolutionary Computation, 12(4):517--545, 2004.

Digital Library

[8]

J. Holland. Adapdation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, Michigan, 1975.

Digital Library

[9]

C. Huang and A. Darwiche. Inference in belief networks: A procedural guide. International Journal of Approximate Reasoning, 15(3):225--263, 1996.

[10]

F. V. Jensen and F. Jensen. Optimal junction trees. In Proceedings of the 10th conference on uncertainty in artificial intelligence, pages 360--366, Seattle, 1994.

[11]

H. Kargupta. The gene expression messy genetic algorithm. In International Conference on Evolutionary Computation, pages 814--819, 1996.

[12]

H. Kargupta and B. Park. Gene expression and fast construction of distributed evolutionary representation. Evolutionary Computation, 9(1):43--69, 2001.

Digital Library

[13]

S. L. Lauritzen. Graphical Models. Clarendon Press, Oxford, 1996.

[14]

H. Mühlenbein and R. Höns. The estimation of distributions and the maximum relative entropy principle. Evolutionary Computation, 13(1):1--28, 2005.

Digital Library

[15]

H. Mühlenbein and T. Mahnig. Convergence theory and application of the factorized distribution algorithm. Journal of Computing and Information Technology, 7(1):19--32, 1999.

[16]

H. Mühlenbein and T. Mahnig. FDA - a scalable evolutionary algorithm for the optimization of additively decomposed functions. Evolutionary Computation, 7(4):353--376, 1999.

Digital Library

[17]

H. Mühlenbein and T. Mahnig. Evolutionary optimization and the estimation of search distributions with applications to graph bipartitioning. International Journal of Approximate Reasoning, 31:157--192, 2002.

[18]

H. Mühlenbein and T. Mahnig. Evolutionary algorithms and the Boltzmann distribution. In Foundations of genetic algorithms (FOGA-7), pages 133--150, San Mateo, 2003. Morgan Kaufmann.

[19]

H. Mühlenbein, T. Mahnig, and A. O. Rodriguez. Schemata, distributions and graphical models in evolutionary optimization. Journal of Heuristics, 5:215--247, 1999.

Digital Library

[20]

H. Mühlenbein and G. Paaß. From recombination of genes to the estimation of distributions I, binary parameters. In Lecture Notes in Computer Science 1411: Parallel Problem Solving from Nature PPSN IV, 1996, pages 178--187. Springer Verlag, 1996.

Digital Library

[21]

M. Munetomo and D. E. Goldberg. Linkage identification by non-monotonicity detection for overla pping functions. Evolutionary Computation, 7(4):377--398, 1999.

Digital Library

[22]

M. Pelikan, D. E. Goldberg, and E. Cantú-Paz. BOA: The Bayesian optimization algorithm. In W. Banzhaf, J. Daida, A. E. Eiben, M. H. Garzon, V. Honavar, M. Jakiela, and R. E. Smith, editors, Proceedings of the Genetic and Evolutionary Computation Conference GECCO-99, volume I, pages 525--532, Orlando, FL, 13-17 1999. Morgan Kaufmann Publishers, San Fransisco, CA.

[23]

M. Pelikan, D. E. Goldberg, and E. Cantu-Paz. Linkage problem, distribution estimation, and bayesian networks. Evolutionary Computation, 8(3):311--340, 2000.

Digital Library

[24]

M. Pelikan and H. Mühlenbein. The bivariate marginal distribution algorithm. In R. Roy, T. Furuhashi, and P. K. Chawdhry, editors, Advances in Soft Computing -Engineering Design and Manufacturing, pages 521--535, London, 1999. Springer-Verlag.

[25]

M. J. Streeter. Upper bounds on the time and space complexity of optimizing additively separable functions. In Kalyanmoy Deb et al., editor, Genetic and Evolutionary Computation - GECCO 2003, procedings part II, Lecture Notes in Computer Science LNCS 3103, pages 186--197. Springer Verlag, 2004.

[26]

D. Thierens. Analysis and design of genetic algorithms. PhD thesis, Katholieke Universiteit Leuven, Leuven, Belgium, 1995.

[27]

Q. Zhang. On stability of fixed points of limit models of univariate marginal distribution algorithm and factorized distribution algorithm. IEEE Transations on Evolutionary Computation, 8(1):80--93, 2004.

Digital Library

[28]

Q. Zhang and H. Mühlenbein. On the convergence of a class of estimation of distribution algoirthms. IEEE Transations on Evolutionary Computation, 8(2):127--136, 2004.

Digital Library

Cited By

Ceberio JMendiburu ALozano J(2022)A roadmap for solving optimization problems with estimation of distribution algorithmsNatural Computing10.1007/s11047-022-09913-223:1(99-113)Online publication date: 6-Sep-2022
https://doi.org/10.1007/s11047-022-09913-2
Strasser SSheppard JButcher S(2017)A formal approach to deriving factored evolutionary algorithm architectures2017 IEEE Symposium Series on Computational Intelligence (SSCI)10.1109/SSCI.2017.8280813(1-8)Online publication date: Nov-2017
https://doi.org/10.1109/SSCI.2017.8280813
Brownlee AMcCall JChristie L(2015)Structural coherence of problem and algorithm: An analysis for EDAs on all 2-bit and 3-bit problems2015 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC.2015.7257139(2066-2073)Online publication date: May-2015
https://doi.org/10.1109/CEC.2015.7257139
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Index Terms

On the convergence of an estimation of distribution algorithm based on linkage discovery and factorization
1. Computing methodologies
  1. Artificial intelligence
    1. Control methods
    2. Search methodologies
2. Theory of computation
  1. Design and analysis of algorithms
    1. Algorithm design techniques
      1. Dynamic programming

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cover image ACM Conferences

GECCO '05: Proceedings of the 7th annual conference on Genetic and evolutionary computation

June 2005

2272 pages

ISBN:1595930108

DOI:10.1145/1068009

Editor:
Hans-Georg Beyer
Vorarlberg University of Applied Sciences, Austria
,
General Chair:
Una-May O'Reilly
CSAIL, MIT

Copyright © 2005 ACM.

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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Publication History

Published: 25 June 2005

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GECCO05: Genetic and Evolutionary Computation Conference

June 25 - 29, 2005

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Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

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Cited By

Ceberio JMendiburu ALozano J(2022)A roadmap for solving optimization problems with estimation of distribution algorithmsNatural Computing10.1007/s11047-022-09913-223:1(99-113)Online publication date: 6-Sep-2022
https://doi.org/10.1007/s11047-022-09913-2
Strasser SSheppard JButcher S(2017)A formal approach to deriving factored evolutionary algorithm architectures2017 IEEE Symposium Series on Computational Intelligence (SSCI)10.1109/SSCI.2017.8280813(1-8)Online publication date: Nov-2017
https://doi.org/10.1109/SSCI.2017.8280813
Brownlee AMcCall JChristie L(2015)Structural coherence of problem and algorithm: An analysis for EDAs on all 2-bit and 3-bit problems2015 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC.2015.7257139(2066-2073)Online publication date: May-2015
https://doi.org/10.1109/CEC.2015.7257139
Christie LLonie DMcCall J(2013)Partial structure learning by subset walsh transform2013 13th UK Workshop on Computational Intelligence (UKCI)10.1109/UKCI.2013.6651297(128-135)Online publication date: Sep-2013
https://doi.org/10.1109/UKCI.2013.6651297
Mühlenbein H(2012)Convergence Theorems of Estimation of Distribution AlgorithmsMarkov Networks in Evolutionary Computation10.1007/978-3-642-28900-2_6(91-108)Online publication date: 2012
https://doi.org/10.1007/978-3-642-28900-2_6
Shakya SSantana R(2012)A Review of Estimation of Distribution Algorithms and Markov NetworksMarkov Networks in Evolutionary Computation10.1007/978-3-642-28900-2_2(21-37)Online publication date: 2012
https://doi.org/10.1007/978-3-642-28900-2_2
Brownlee AMcCall JShakya SZhang Q(2010)Structure Learning and Optimisation in a Markov Network Based Estimation of Distribution AlgorithmExploitation of Linkage Learning in Evolutionary Algorithms10.1007/978-3-642-12834-9_3(45-69)Online publication date: 2010
https://doi.org/10.1007/978-3-642-12834-9_3
Brownlee AMcCall JShakya SZhang Q(2009)Structure learning and optimisation in a Markov-network based estimation of distribution algorithmProceedings of the Eleventh conference on Congress on Evolutionary Computation10.5555/1689599.1689657(447-454)Online publication date: 18-May-2009
https://dl.acm.org/doi/10.5555/1689599.1689657
Choi SJung KMoon B(2009)Lower and upper bounds for linkage discoveryIEEE Transactions on Evolutionary Computation10.1109/TEVC.2008.92849913:2(201-216)Online publication date: 1-Apr-2009
https://dl.acm.org/doi/10.1109/TEVC.2008.928499
Brownlee AMcCall JShakya SZhang Q(2009)Structure learning and optimisation in a Markov-network based estimation of distribution algorithm2009 IEEE Congress on Evolutionary Computation10.1109/CEC.2009.4982980(447-454)Online publication date: May-2009
https://doi.org/10.1109/CEC.2009.4982980
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