Skip to main content
SpringerLink
Log in

A Survey of Optimization by Building and Using Probabilistic Models

  • Published:
Computational Optimization and Applications Aims and scope Submit manuscript

Abstract

This paper summarizes the research on population-based probabilistic search algorithms based on modeling promising solutions by estimating their probability distribution and using the constructed model to guide the exploration of the search space. It settles the algorithms in the field of genetic and evolutionary computation where they have been originated, and classifies them into a few classes according to the complexity of models they use. Algorithms within each class are briefly described and their strengths and weaknesses are discussed.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S. Baluja, “Population-based incremental learning: A method for integrating genetic search based function optimization and competitive learning,” Tech. Rep. No. CMU-CS-94-163, Carnegie Mellon University, Pittsburgh, PA, 1994.

    Google Scholar 

  2. S. Baluja and S. Davies, “Using optimal dependency-trees for combinatorial optimization: Learning the structure of the search space,” in Proceedings of the 14th International Conference on Machine Learning, 1997, pp. 30–38.

  3. P.A. Bosman, “Continuous iterated density estimation evolutionary algorithms within the IDEA framework,” Personal communication, 2000.

  4. P.A.N. Bosman and D. Thierens, “Linkage information processing in distribution estimation algorithms,” in Proceedings of the Genetic and Evolutionary Computation Conference GECCO-99, Orlando, FL, W. Banzhaf, J. Daida, A.E. Eiben, M.H. Garzon, V. Honavar, M. Jakiela, and R.E. Smith (Eds.), 1999, vol. I, pp. 60–67.

  5. J.S. De Bonet, C.L. Isbell, and P. Viola, “MIMIC: Finding optima by estimating probability densities,” in Advances in Neural Information Processing Systems, M.C. Mozer, M.I. Jordan, and T. Petsche (Eds.), 1997, vol. 9, p. 424.

  6. K. Deb and R.B. Agrawal, “Simulated binary crossover for continuous search space,” Complex Systems, vol. 9, pp. 115–148, 1995.

    Google Scholar 

  7. J. Edmonds, “Optimum branching,” J. Res. NBS, vol. 71B, pp. 233–240, 1967.

    Google Scholar 

  8. L.J. Eshelman and J.D. Schaffer, “Real-coded genetic algorithms and interval-schemata,” in Foundations of Genetic Algorithms Workshop (FOGA-92), D. Whitley (Ed.), Vail; Colorado, 1992.

    Google Scholar 

  9. R. Etxeberria and P. Larrañaga, “Global optimization using Bayesian networks,” in Second Symposium on Artificial Intelligence (CIMAF-99), Habana, Cuba, 1999, pp. 332–339.

  10. M. Gallagher, M. Frean, and T. Downs, “Real-valued evolutionary optimization using a flexible probability density estimator,” in Proceedings of the Genetic and Evolutionary Computation Conference, W. Banzhaf, J. Daida, A.E. Eiben, M.H. Garzon, V. Honavar, M. Jakiela, and R.E. Smith (Eds.), Orlando, Florida, USA, 1999, vol. 1, pp. 840–846.

  11. D.E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley: Reading, MA, 1989.

    Google Scholar 

  12. D.E. Goldberg, “Genetic and evolutionary algorithms in the real world,” University of Illinois at Urbana-Champaign, Illinois Genetic Algorithms Laboratory, Urbana, IlliGAL Report No. 99013, 1999.

    Google Scholar 

  13. S. Handley, “On the use of a directed acyclic graph to represent a population of computer programs,” in Proceedings of the First IEEE Conference on Evolutionary Computation, Piscataway, NJ, 1994, pp. 154–159.

  14. G. Harik, “Linkage learning via probabilistic modeling in the ECGA,” University of Illinois at Urbana-Champaign, Illinois Genetic Algorithms Laboratory, Urbana, IL, IlliGAL Report No. 99010, 1999.

    Google Scholar 

  15. G. Harik, E. Cantú-Paz, D.E. Goldberg, and B.L. Miller, “The gambler's ruin problem, genetic algorithms, and the sizing of populations,” in Proceedings of the International Conference on Evolutionary Computation (ICEC'97), Piscataway, NJ, 1997, pp. 7–12.

  16. G.R. Harik, F.G. Lobo, and D.E. Goldberg, “The compact genetic algorithm,” in Proceedings of the International Conference on Evolutionary Computation (ICEC'98), Piscataway, NJ, 1998, pp. 523–528.

  17. D. Heckerman, D. Geiger, and M. Chickering, “Learning Bayesian networks: The combination of knowledge and statistical data,” Microsoft Research, Redmond, WA, Technical Report MSR-TR-94-09, 1994.

  18. J.H. Holland, Adaptation in Natural and Artificial Systems, University of Michigan Press: Ann Arbor, MI, 1975.

    Google Scholar 

  19. D. Knjazew and D.E. Goldberg, “OMEGA—Ordering messy GA: Solving permutation problems with the fast messy genetic algorithm and random keys,” University of Illinois at Urbana-Champaign, Illinois Genetic Algorithms Laboratory, Urbana, IL, IlliGAL Report No. 2000004, 2000.

    Google Scholar 

  20. J.R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection, The MIT Press: Cambridge, MA, 1992.

    Google Scholar 

  21. S. Kullback and R.A. Leibler, “On information and sufficiency,” Annals of Math. Stats., vol. 22, pp. 79–86, 1951.

    Google Scholar 

  22. V. Kvasnicka, M. Pelikan, and J. Pospichal, “Hill climbing with learning (an abstraction of genetic algorithm),” Neural Network World, vol. 6, pp. 773–796, 1996.

    Google Scholar 

  23. L.A. Marascuilo and M. McSweeney, Nonparametric and Distribution-Free Methods for the Social Sciences, Brooks/Cole Publishing Company: CA, 1977.

    Google Scholar 

  24. T.M. Mitchell, Machine Learning, McGraw-Hill: New York, 1997.

    Google Scholar 

  25. H. Mühlenbein, “The equation for response to selection and its use for prediction,” Evolutionary Computation, vol. 5, no. 3, pp. 303–346, 1997.

    Google Scholar 

  26. H. Mühlenbein and T. Mahnig, “Convergence theory and applications of the factorized distribution algorithm,” Journal of Computing and Information Technology, vol. 7, no. 1, pp. 19–32, 1998.

    Google Scholar 

  27. H. Mühlenbein and T. Mahnig “FDA—A scalable evolutionary algorithm for the optimization of additively decomposed functions,” Evolutionary Computation, vol. 7, no. 4, pp. 353–376, 1999.

    Google Scholar 

  28. H.Mühlenbein, T. Mahnig, and A.O. Rodriguez, “Schemata, distributions and graphical models in evolutionary optimization,” Journal of Heuristics, vol. 5, pp. 215–247, 1999.

    Google Scholar 

  29. H. Mühlenbein and G. Paaß, “From recombination of genes to the estimation of distributions I. Binary parameters,” in Parallel Problem Solving from Nature—PPSN IV, Berlin, A. Eiben, T. Bäck, M. Shoenauer, and H. Schwefel (Eds.), 1996, pp. 178–187.

  30. I. Ono and S. Kobayashi, “A real-coded genetic algorithm for function optimization using unimodal normal distribution crossovers,” in Proceedings of the Seventh International Conference on Genetic Algorithms, San Francisco, T. Bäck (Ed.), 1997, pp. 246–253.

  31. M. Pelikan, D.E. Goldberg, and E. Cantú-Paz, “Linkage problem, distribution estimation, and Bayesian networks,” University of Illinois at Urbana-Champaign, Illinois Genetic Algorithms Laboratory, Urbana, IL, IlliGAL Report No. 98013, 1998.

    Google Scholar 

  32. M. Pelikan, D.E. Goldberg, and E. Cantú-Paz, “BOA: The Bayesian optimization algorithms,” in Proceedings of the Genetic and Evolutionary Computation Conference GECCO-99, Orlando, FL, W. Banzhaf, J. Daida, A.E. Eiben, M.H. Garzon, V. Honavar, M. Jakiela, and R.E. Smith (Eds.), 1999, vol. I, pp. 525–532.

  33. M. Pelikan, D.E. Goldberg, and E.Cantú-Paz, “Bayesian optimization algorithm, population sizing, and time to convergence,” University of Illinois at Urbana-Champaign, Illinois Genetic Algorithms Laboratory, Urbana, IL, IlliGAL Report No. 2000001, 2000.

    Google Scholar 

  34. M. Pelikan, D.E. Goldberg, and E. Cantú-Paz, “Hierarchical problem solving by the Bayesian optimization algorithms,” University of Illinois at Urbana-Champaign, Illinois Genetic Algorithms Laboratory, Urbana, IL, IlliGAL Report No. 2000002, 2000.

    Google Scholar 

  35. M. Pelikan, D.E. Goldberg, and E.Cantú-Paz, “Linkage problem, distribution estimation, and Bayesian networks,” Evolutionary Computation, vol. 8, no. 3, pp. 311–341, 2000.

    Google Scholar 

  36. M. Pelikan and H. Mühlenbein, “The bivariate marginal distribution algorithm,” in Advances in Soft Computing—Engineering Design and Manufacturing, London, R. Roy, T. Furuhashi, and P.K. Chawdhry (Eds.), 1999, pp. 521–535.

  37. I. Rechenberg, Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution, Frommann-Holzboog: Stuttgart, 1973.

    Google Scholar 

  38. F. Rothlauf, D.E. Goldberg, and A. Heinzl, “Bad codings and the utility of well-designed genetic algorithms,” University of Illinois at Urbana-Champaign, Illinois Genetic Algorithms Laboratory, Urbana, IL, IlliGAL Report No. 200007, 2000.

    Google Scholar 

  39. S. Rudlof and M. Köppen, “Stochastic hill climbing with learning by vectors of normal distributions,” in First On-line Workshop on Soft Computing, Nagoya, Japan, 1996.

  40. R.P. Salustowicz and J. Schmidhuber, “Probabilistic incremental program evolution: Stochastic search through program space,” in Machine Learning: ECML-97, M. van Someren and G. Widmer (Eds.), vol. 1224 of Lecture Notes in Artificial Intelligence, 1997, pp. 213–220.

  41. J. Schwarz and J. Ocenasek, “Experimental study: Hypergraph partitioning based on the simple and advanced algorithms BMDA and BOA,” in Proceedings of the Fifth International Conference on Soft Computing, Brno, Czech Republic, 1999, pp. 124–130.

  42. M. Sebag and A. Ducoulombier, “Extending population-based incremental learning to continuous search spaces,” in Parallel Problem Solving from Nature—PPSN V, Berlin Heidelberg, 1998, pp. 418–427.

  43. I. Servet, L. Trave-Massuyes, and D. Stern, “Telephone network traffic overloading diagnosis and evolutionary computation techniques,” in Proceedings of the Third European Conference on Artificial Evolution (AE'97), NY, G. Goos, J. Hartmanis, and J. Leeuwen (Eds.), 1997, pp. 137–144.

  44. R. Shachter and D. Heckerman, “Thinking backwards for knowledge acquisition,” AI Magazine, vol. 7, pp. 55–61, 1987.

    Google Scholar 

  45. D. Thierens, “Analysis and design of genetic algorithm,” Ph.D. thesis, Katholieke Universiteit Leuven, Leuven, Belgium, 1995.

    Google Scholar 

  46. H.-M. Voigt, H. Múhlenbein, and D. Cvetkovíc, “Fuzzy recombination for the breeder genetic algorithm,” in Proceedings of the Sixth International Conference on Genetic Algorithms, 1995, pp. 104–111.

Download references

Author information

Authors and Affiliations

  1. Illinois Genetic Algorithms Laboratory, Department of General Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

    Martin Pelikan, David E. Goldberg & Fernando G. Lobo

Authors
  1. Martin Pelikan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David E. Goldberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fernando G. Lobo
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pelikan, M., Goldberg, D.E. & Lobo, F.G. A Survey of Optimization by Building and Using Probabilistic Models. Computational Optimization and Applications 21, 5–20 (2002). https://doi.org/10.1023/A:1013500812258

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1013500812258

Search

Navigation