Skip to main content
SpringerLink
Log in

A probabilistic database approach to the analysis of genetic algorithms

  • Theoretical Foundations of Evolutionary Computation
  • Conference paper
  • First Online:
Parallel Problem Solving from Nature — PPSN IV (PPSN 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1141))

Included in the following conference series:

  • 148 Accesses

Abstract

This paper takes a fresh look at some of the key ideas of genetic algorithms, using concepts drawn from the theory of majorization and probabilistic databases. We show the intimate relationships between GAs and the theory of probabilistic databases. We show how deception is well described using Saari's theorem, and its relationships with the Simpson and other paradoxes in decision theory. Reconstructability, a concept of fundamental importance in databases, is proposed as a useful substitute for deception. The database projection operator is connected with hyperplane partitions, and is used to show the nexus between point crossover operators and the join operator. Using results from probabilistic databases, we show that crossover may be considered as a majorization operator.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Cavallo and M. Pittarelli. The theory of probabilistic databases. In P. M. Stocker, W. Kent, and P. Hammersley, editors, Proceedings of the 13th International Conference on Very Large Data Bases, pages 71–81. Morgan Kaufmann, 1987.

    Google Scholar 

  2. J. E. Cohen. An uncertainly principle in demography and the unisex issue. The American Statistician, 40(1):32–39, 1986.

    PubMed  Google Scholar 

  3. R. Fagin. Degrees of acyclicity for hypergraphs and relational database schemes. J. of the ACM, 30(3):514–550, 1983.

    Article  Google Scholar 

  4. D. E. Goldberg. Simple genetic algorithms and the minimal decptive problem. In L. Davis, editor, Genetic algorithms and simulated annealing, pages 74–78. Pitman, London, 1987.

    Google Scholar 

  5. J. Grefenstette. Deception considered harmful. In L. Whitley, Darrell, editor, Foundation of Genetic Algorithms, Vol. 2, pages 75–92. Morgan Kaufmann, 1993.

    Google Scholar 

  6. J. Grefenstette and J. Baker. How genetic algorithms work: a critical look at implicit parallelism. In G. J. E. Rawlins, editor, Foundation of Genetic Algorithms. Morgan Kaufmann, 1989.

    Google Scholar 

  7. A. W. Marshall and I. Olkin. Inequalities: Theory of majorization and its Applications. Academic Press, New York, 1979.

    Google Scholar 

  8. A. Menon. Mathematical Models of Evolutionary Algorithms. PhD thesis, School of Computer Science, Syracuse University, 1996 (forthcoming).

    Google Scholar 

  9. A. Menon, K. Mehrotra, C. Mohan, and S. Ranka. Selection, majorization and replicators. In IEEE 3rd International Conference on Evolutionary Computation, pages 606–610. IEEE Press, 1996.

    Google Scholar 

  10. A. Menon, K. Mehrotra, C. Mohan, and S. Ranka. Replicators, majorization and genetic algorithms: New models, connections and analytical tools. In Foundations of Genetic Algorithms. Morgan Kaufman, 1996 (to appear).

    Google Scholar 

  11. H. Mühlenbein. Evolution in time and space — the parallel genetic algorithm. In G. J. E. Rawlins, editor, Foundation of Genetic Algorithms, pages 316–338. Morgan Kaufmann, San Mateo, CA, 1991.

    Google Scholar 

  12. Y. Rabinovich, A. Sinclair, and A. Wigderson. Quadratic dynamical systems (preliminary version). In Proc. 33rd Annual Symp. Foundations of Computer Science, pages 304–313, Pittsburgh, 1992.

    Google Scholar 

  13. D. G. Saari. The source of some paradoxes from social choice and probability. J. of Economic Theory, 41:1–22, 1987.

    Article  Google Scholar 

  14. S. Sunder. Simpson's reversal paradox and cost allocation. J. of Accounting Research, 21(1):223–233, 1983.

    Google Scholar 

  15. D. L. Whitley. Fundamental principles of deception in genetic search. In G. J. E. Rawlins, editor, Foundation of Genetic Algorithms. Morgan Kaufmann, San Mateo, CA, 1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer & Information Science, 2-120 Center for Science and Technology, Syracuse University, 13244, Syracuse, NY

    Anil Menon, Kishan Mehrotra & Chilukuri K. Mohan

  2. Department of CISE, University of Florida, 301 CSE Bldg, 32611, Gainesville, FL

    Sanjay Ranka

Authors
  1. Anil Menon
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kishan Mehrotra
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chilukuri K. Mohan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sanjay Ranka
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Hans-Michael Voigt Werner Ebeling Ingo Rechenberg Hans-Paul Schwefel

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Menon, A., Mehrotra, K., Mohan, C.K., Ranka, S. (1996). A probabilistic database approach to the analysis of genetic algorithms. In: Voigt, HM., Ebeling, W., Rechenberg, I., Schwefel, HP. (eds) Parallel Problem Solving from Nature — PPSN IV. PPSN 1996. Lecture Notes in Computer Science, vol 1141. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61723-X_980

Download citation

  • DOI: https://doi.org/10.1007/3-540-61723-X_980

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61723-5

  • Online ISBN: 978-3-540-70668-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation