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Empirical analysis of ideal recombination on random decomposable problems

Published: 07 July 2007 Publication History

Abstract

This paper analyzes the behavior of a selectorecombinative genetic algorithm (GA) with an ideal crossover on a class of random additively decomposable problems (rADPs). Specifically, additively decomposable problems of order k whose subsolution fitnesses are sampled from the standard uniform distribution U[0,1] are analyzed. The scalability of the selectorecombinative GA is investigated for 10,000 rADP instances. The validity of facetwise models in bounding the population size, run duration, and the number of function evaluations required to successfully solve the problems is also verified. Finally, rADP instances that are easiest and most difficult are also investigated.

References

[1]
D. H. Ackley. A connectionist machine for genetic hill climbing. Kluwer Academic Publishers, 1987.
[2]
H. Asoh and H. Mühlenbein. On the mean convergence time of evolutionary algorithms without selection and mutation. Parallel Problem Solving from Nature, 3:98--107, 1994.
[3]
T. Bäck. Generalized convergence models for tournament -- and (μ, λ) -- selection. Proceedings of the Sixth International Conference on Genetic Algorithms, pages 2--8, 1995.
[4]
N. Balakrishnan and W. W. S. Chen. Handbook of tables for order statistics from lognormal distributions with applications. Kluwer Academic Publishers, Amsterdam, Netherlands, 1999.
[5]
N. Balakrishnan and A. C. Cohen. Order statistics and inference. Academic Press, New York, NY, 1991.
[6]
N. Balakrishnan and C. R. Rao, editors. Order statistics: Applications . Elsevier, Amsterdam, Netherlands, 1999.
[7]
N. Balakrishnan and C. R. Rao, editors. Order statistics: Theory and methods . Elsevier, Amsterdam, Netherlands, 1999.
[8]
A. D. Bethke. Genetic algorithms as function Re-optimizers . PhD thesis, University of Michigan, Ann Arbor, MI, 1981. (University Microfilms No. 8106101).
[9]
M. G. Bulmer. The Mathematical Theory of Quantitative Genetics. Oxford University Press, Oxford, 1985.
[10]
K. Deb and D. E. Goldberg. Analyzing deception in trap functions. Foundations of Genetic Algorithms, 2:93--108, 1992. (Also IlliGAL Report No. 91009).
[11]
W. Feller. An Introduction to Probability Theory and its Applications. Wiley, New York, NY, 1970.
[12]
D. E. Goldberg. Simple genetic algorithms and the minimal deceptive problem. In L. Davis, editor, Genetic algorithms and simulated annealing, chapter 6, pages 74--88. Morgan Kaufmann, Los Altos, CA, 1987.
[13]
D. E. Goldberg. Design of innovation:Lessons from and for competent genetic algorithms. Kluwer Academic Publishers, Boston, MA, 2002.
[14]
D. E. Goldberg, K. Deb, and J. H. Clark. Genetic algorithms, noise, and the sizing of populations. Complex Systems, 6:333--362, 1992. (Also IlliGAL Report No. 91010).
[15]
D. E. Goldberg, B. Korb, and K. Deb. Messy genetic algorithms: Motivation, analysis, and first results. Complex Systems, 3(5):493--530, 1989. (Also IlliGAL Report No. 89003).
[16]
D. E. Goldberg and P. Segrest. Finite Markov chain analysis of genetic algorithms. Proceedings of the Second International Conference on Genetic Algorithms, pages 1--8, 1987.
[17]
G. Harik, E. Cantú-Paz, D. E. Goldberg, and B. L. Miller. The gambler's ruin problem, genetic algorithms, and the sizing of populations. Evolutionary Computation, 7(3):231--253, 1999. (Also IlliGAL Report No. 96004).
[18]
R. V. Hogg and A. T. Craig. Introduction to Mathematical Statistics . Macmillan, New York, NY, 5th edition, 1995.
[19]
M. Kimura. Diffusion models in population genetics. Journal of Applied Probability, 1:177--232, 1964.
[20]
G. E. Liepins and M. D. Vose. Representational issues in genetic optimization. Journal of Experimental and Theoretical Artificial Intelligence, 2:101--115, 1990.
[21]
B. L. Miller and D. E. Goldberg. Genetic algorithms, tournament selection, and the effects of noise. Complex Systems, 9(3):193--212, 1995. (Also IlliGAL Report No. 95006).
[22]
H. Mühlenbein and D. Schlierkamp-Voosen. Predictive models for the breeder genetic algorithm: I. continous parameter optimization. Evolutionary Computation, 1(1):25--49, 1993.
[23]
M. Pelikan, K. Sastry, M. V. Butz, and D. E. Goldberg. Hierarchical BOA on random decomposable problems. IlliGAL Report No. 2006002, University of Illinois at Urbana Champaign, Urbana, IL, January 2006.
[24]
K. Sastry. Evaluation-relaxation schemes for genetic and evolutionary algorithms. Master's thesis, University of Illinois at Urbana-Champaign, Urbana, IL, 2001. (Also IlliGAL Report No. 2002004).
[25]
K. Sastry and D. E. Goldberg. Modeling tournament selection with replacement using apparent added noise. Intelligent Engineering Systems Through ArtificialNeuralNetworks, 11:129--134, 2001. (Also IlliGAL Report No. 2001014).
[26]
K. Sastry and D. E. Goldberg. Let's get ready to rumble: Crossover versus mutation head to head. Proceedings of the 2004 Genetic and Evolutionary Computation Conference, 2:126--137, 2004. Also IlliGAL Report No. 2004005.
[27]
K. Sastry, M. Pelikan, and D. E. Goldberg. Analysis of ideal recombination on random decomposable problems. IlliGAL Report No. 2006016, University of Illinois at Urbana-Champaign, Urbana, IL, April 2006.
[28]
D. Thierens and D. E. Goldberg. Convergence models of genetic algorithm selection schemes. Parallel Problem Solving from Nature, 3:116--121, 1994.
[29]
L. D. Whitley. Fundamental principles of deception in genetic search. Foundations of Genetic Algorithms, pages 221--241, 1991.

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cover image ACM Conferences
GECCO '07: Proceedings of the 9th annual conference on Genetic and evolutionary computation
July 2007
2313 pages
ISBN:9781595936974
DOI:10.1145/1276958
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: 07 July 2007

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Author Tags

  1. additively-decomposable problems
  2. building blocks
  3. convergence time
  4. empirical analysis
  5. genetic algorithms
  6. ideal crossover
  7. population sizing
  8. problem difficulty
  9. scalability analysis
  10. test problems

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GECCO '07 Paper Acceptance Rate 266 of 577 submissions, 46%;
Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

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