skip to main content
10.1145/1389095.1389339acmconferencesArticle/Chapter ViewAbstractPublication PagesgeccoConference Proceedingsconference-collections
research-article

Analysis of a genetic programming algorithm for association studies

Published: 12 July 2008 Publication History

Abstract

In this paper a Genetic Programming algorithm for genetic association studies is reconsidered. It is shown, that the application field of the algorithm is not restricted to genetic association studies, but that the algorithm can also be applied to logic minimization problems. In the context of multi-valued logic minimization on incompletely specified truth tables it outperforms existing algorithms. In addition, the facilities of the algorithm in the original application field are complemented by new results and experiments. This includes answers to the open questions of how to automatically choose the best individual in the last population and whether crossover is necessary for the algorithm.

References

[1]
W. Banzhaf, F. D. Francone, R. E. Keller, and P. Nordin. Genetic programming: an introduction: on the automatic evolution of computer programs and its applications. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 1998.
[2]
R. K. Brayton, A. L. Sangiovanni-Vincentelli, C. T. McMullen, and G. D. Hachtel. Logic Minimization Algorithms for VLSI Synthesis. Kluwer Academic Publishers, Norwell, MA, USA, 1984.
[3]
L. Breiman. Bagging predictors. Mach. Learn., 26:123--140, 1996.
[4]
L. Breiman. Random Forests. Mach. Learn., 45:5--32, 2001.
[5]
L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stone. Classification and regression trees. Wadsworth, Belmont, CA, 1984.
[6]
W. J. Conover. Practical Nonparametric Statistics. John Wiley and Sons, third edition, 1999.
[7]
M. de Berg, M. van Krefeld, M. Overmars, and O. Schwarzkopf. Computational Geometry - Algorithms and Applications. Springer, 1997.
[8]
S. Droste. Efficient genetic programming for finding good generalizing Boolean functions. In J. R. Koza, K. Deb, M. Dorigo, D. B. Fogel, M. Garzo, H. Iba, and R. L. Riolo, editors, Proceedings of the Second Annual Conference on Genetic Programming, pages 82--87, San Francisco CA, 1997. Morgan Kaufmann Publishers, Inc.
[9]
J. Dussault, G. Metze, and M. Krieger. A multivalued switching algebra with boolean properties. In Proceedings of the sixth international symposium on Multiple-valued logic, pages 68--73, Los Alamitos, CA, USA, 1976. IEEE Computer Society Press.
[10]
G. A. Heidema, J. M. A. Boer, N. Nagelkerke, E. C. M. Mariman, D. L. van der A, and E. J. M. Feskens. The challenge for genetic epidemiologists: How to analyze large numbers of SNPs in relation to complex diseases. BioMed Genet., 7(23), 2006.
[11]
J. Hoh and J. Ott. Mathematical multi-locus approaches to localizing complex human trait genes. Nat. Rev. Genet., 4:701--709, 2003.
[12]
M. Hollander and D. A. Wolfe. Nonparametric Statistical Methods. John Wiley and Sons, second edition, 1999.
[13]
J. R. Koza. Genetic Programming. The MIT Press, Cambridge. Massachusetts, 1992.
[14]
J. R. Koza. Genetic Programming II. The MIT Press, Cambridge. Massachusetts, 1994.
[15]
J. T. Kristensen and P. B. Miltersen. Finding small obdds for incompletely specified truth tables is hard. In Proceedings of COCOON 2006, volume 4112 of Lecture Notes in Computer Science, pages 489--496. Springer, 2006.
[16]
R. Nunkesser. RFreak: R/FrEAK interface, 2007. R package version 0.2-0.
[17]
R. Nunkesser, T. Bernholt, H. Schwender, K. Ickstadt, and I. Wegener. Detecting high-order interactions of single nucleotide polymorphisms using genetic programming. Bioinformatics, 23(24):3280--3288, 2007.
[18]
R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2007.
[19]
I. Ruczinski, C. Kooperberg, and M. LeBlanc. Logic regression. J. Comput. Graph. Stat., 12:475--511, 2003.
[20]
R. L. Rudell and A. Sangiovanni-Vincentelli. Multiple-valued minimization for pla optimization. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 6(5):727--750, 1987.
[21]
T. Sasao. Multiple-valued decomposition of generalized boolean functions and the complexity of programmable logic arrays. IEEE Trans. Comput., 30(9):635--643, 1981.
[22]
H. Schwender and A. Fritsch. scrime: Analysis of High-Dimensional Categorical Data such as SNP Data, 2008. R package version 1.0.0.
[23]
S. Y. H. Su and A. A. Sarris. The relationship between multivalued switching algebra and boolean algebra under different definitions of complement. IEEE Trans. Comput., 21(5):479--485, 1972.
[24]
R. Tibshirani, G. Walther, and T. Hastie. Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 63(2):411--423, 2001.
[25]
E. Zitzler and L. Thiele. Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans. Evolutionary Computation, 3(4):257--271, 1999.

Recommendations

Comments

Information & Contributors

Information

Published In

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]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 12 July 2008

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. association studies
  2. genetic programming
  3. logic minimization

Qualifiers

  • Research-article

Conference

GECCO08
Sponsor:

Acceptance Rates

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

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • 0
    Total Citations
  • 155
    Total Downloads
  • Downloads (Last 12 months)1
  • Downloads (Last 6 weeks)0
Reflects downloads up to 08 Mar 2025

Other Metrics

Citations

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media