Advertisement

Annals of Operations Research

, Volume 131, Issue 1–4, pp 373–395 | Cite as

Model-Based Search for Combinatorial Optimization: A Critical Survey

  • Mark Zlochin
  • Mauro Birattari
  • Nicolas Meuleau
  • Marco Dorigo
Article

Abstract

In this paper we introduce model-based search as a unifying framework accommodating some recently proposed metaheuristics for combinatorial optimization such as ant colony optimization, stochastic gradient ascent, cross-entropy and estimation of distribution methods. We discuss similarities as well as distinctive features of each method and we propose some extensions.

ant colony optimization cross-entropy method stochastic gradient ascent estimation of distribution algorithms adaptive optimization metaheuristics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aarts, E.H.L. and J.K. Lenstra. (1997). Local Search in Combinatorial Optimization. Chichester, UK: Wiley.Google Scholar
  2. Baluja, S. (1994). “Population-Based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning.” Technical Report CMU-CS-94-163, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA.Google Scholar
  3. Baluja, S. and R. Caruana. (1995). “Removing the Genetics from the Standard Genetic Algorithm.” In Proceedings of the Twelfth International Conference on Machine Learning (ML-95). Palo Alto, CA: Morgan Kaufmann, pp. 38–46.Google Scholar
  4. Baluja, S. and S. Davies. (1997). “Using Optimal Dependency-Trees for Combinatorial Optimization: Learning the Structure of the Search Space.” In Proceedings of the Fourteenth International Conference on Machine Learning (ML-97). Palo Alto, CA: Morgan Kaufmann, pp. 30–38.Google Scholar
  5. Bertsekas, D.P. (1995). Nonlinear Programming. Belmont, MA: Athena Scientific.Google Scholar
  6. Blum, C., A. Roli, and M. Dorigo. (2001). “HC-ACO: The Hyper-Cube Framework for Ant Colony Optimization.” In Proceedings of MIC'2001-Meta-Heuristics International Conference, Vol. 2, Porto, Portugal, pp. 399–403.Google Scholar
  7. Blum, C. and M. Dorigo. (2004). “The Hyper-Cube Framework for Ant Colony Optimization.” IEEE Transactions on Systems, Man, and Cybernetics, Part B 34(2), 1161–1172.Google Scholar
  8. De Boer, P.T., D.P. Kroese, S. Mannor, and R.Y. Rubinstein. (2001). “A Tutorial on the Cross-Entropy Method.” <http://wwwhome.cs.utwente.nl/~ptdeboer/ce/tutorial.pdf> Google Scholar
  9. De Bonet, J.S., C.L. Isbell, and P. Viola. (1997). “MIMIC: Finding Optima by Estimating Probability Densities.” In Advances in Neural Information Processing Systems, Vol. 9. Cambridge, MA: MIT Press, pp. 424–431.Google Scholar
  10. Dorigo, M. (1992). “Optimization, Learning and Natural Algorithms," Ph.D. Thesis, Dipartimento di Elettronica, Politecnico di Milano, Italy (in Italian).Google Scholar
  11. Dorigo, M. and G. Di Caro. (1999). “The Ant Colony Optimization Meta-Heuristic.” In New Ideas in Optimization. London, UK: McGraw Hill, pp. 11–32.Google Scholar
  12. Dorigo, M., G. Di Caro, and L.M. Gambardella. (1999). “Ant Algorithms for Discrete Optimization.” Arti-ficial Life 5(2), 137–172.Google Scholar
  13. Dorigo, M. and L.M. Gambardella. (1997). “Ant Colony System: A Cooperative Learning Approach to the Traveling Salesman Problem.” IEEE Transactions on Evolutionary Computation 1(1), 53–66.CrossRefGoogle Scholar
  14. Dorigo, M., V. Maniezzo, and A. Colorni. (1991). “The Ant System: An Autocatalytic Optimizing Process.” Technical Report 91-016 Revised, Dipartimento di Elettronica, Politecnico di Milano, Italy.Google Scholar
  15. Dorigo, M., V. Maniezzo, and A. Colorni. (1996). “Ant System: Optimization by a Colony of Cooperating Agents.” IEEE Transactions on Systems, Man, and Cybernetics-Part B 26(1), 29–41.Google Scholar
  16. Dorigo, M. and T. Stützle. (2002). “The Ant Colony Optimization Metaheuristic: Algorithms, Applications and Advances.” In Handbook of Metaheuristics, International Series in Operations Research & Management Science, Vol. 57. Norwell, MA: Kluwer Academic, pp. 251–285.Google Scholar
  17. Dorigo, M. and T. Stützle. (2004). Ant Colony Optimization. Cambridge, MA: MIT Press.Google Scholar
  18. Etxeberria, R. and P. Larrañaga. (1999). “Global Optimization with Bayesian Networks.” In Proceedings of the Second Symposium on Artificial Intelligence, La Habana, Cuba, pp. 332–339.Google Scholar
  19. Goldberg, D. and P. Segrest. (1987). “Finite Markov Chain Analysis of Genetic Algorithms.” In Proceedings of the Second International Conference on Genetic Algorithms. Hillsdale, NJ: Lawrence Erlbaum Associates, pp. 1–8.Google Scholar
  20. Harik, G.R. (1999). “Linkage Learning via Probabilistic Modeling in the ECGA.” Technical Report Illi-GAL, 99010, University of Illinois at Urbana-Champaign, Urbana, IL.Google Scholar
  21. Harik, G.R., F.G. Lobo, and D.E. Goldberg. (1999). “The Compact Genetic Algorithm.” IEEE Transactions on Evolutionary Computation 3(4), 287–297.CrossRefGoogle Scholar
  22. Heckerman, D. (1995). “A Tutorial on Learning with Bayesian Networks.” Technical Report MSR-TR-95-06, Microsoft Research, Redmond, WA.Google Scholar
  23. Holland, J. (1975). Adaptation in Natural and Artificial Systems.Ann Arbor, MI: University of Michigan Press.Google Scholar
  24. Kullback, S. (1959). Information Theory and Statistics. New York: Wiley.Google Scholar
  25. Larrañaga, P. and J.A. Lozano. (2001). Estimation of Distribution Algorithms. A New Tool for Evolutionary Computation. Boston, MA: Kluwer Academic.Google Scholar
  26. Lieber, D. (1999). “The Cross-Entropy Method for Estimating Probabilities of Rare Events.” Ph.D. Thesis, William Davidson Faculty of Industrial Engineering and Management, Technion, Haifa, Israel.Google Scholar
  27. Maniezzo, V. (1999). “Exact and Approximate Nondeterministic Tree-Search Procedures for the Quadratic Assignment Problem.” INFORMS Journal on Computing 11(4), 358–369.Google Scholar
  28. Marascuilo, L. and M. McSweeney. (1977). Nonparametric and Distribution-Free Methods for the Social Sciences. Monterey, CA: Brooks/Cole.Google Scholar
  29. Meuleau, N. and M. Dorigo. (2002). “Ant Colony Optimization and Stochastic Gradient Descent.” Artificial Life 8(2), 103–121.CrossRefGoogle Scholar
  30. Mitchell, T.M. (1997). Machine Learning. New-York: McGraw-Hill.Google Scholar
  31. Mühlenbein, H., J. Bendisch, and H.-M. Voigt. (1996). “From Recombination of Genes to the Estimation of Distributions. I. Binary Parameters.” In Proceedings of PPSN-I, First International Conference on Parallel Problem Solving from Nature. Berlin, Germany: Springer, pp. 178–187.Google Scholar
  32. Pelikan, M., D.E. Goldberg, and E. Cantú-Paz. (1998). “Linkage Problem, Distribution Estimation, and Bayesian Networks.” Technical Report IlliGAL, 98013, University of Illinois at Urbana-Champaign, Urbana, IL.Google Scholar
  33. Pelikan, M., D.E. Goldberg, and F. Lobo. (1999). “A Survey of Optimization by Building and Using Probabilistic Models.” Technical Report IlliGAL, 99018, University of Illinois at Urbana-Champaign, Urbana, IL.Google Scholar
  34. Pelikan, M. and H. Mühlenbein. (1999). “The Bivariate Marginal Distribution Algorithm.” In Advances in Soft Computing-Engineering Design and Manufacturing. London, UK: Springer, pp. 521–535.Google Scholar
  35. Quinlan, J. (1993). “Combining Instance-Based and Model-Based Learning.” In Proceedings of the Tenth International Conference on Machine Learning (ML-93). San Mateo, CA: Morgan Kaufmann, pp. 236–243.Google Scholar
  36. Robbins, H. and S. Monro. (1951). “A Stochastic Approximation Method.” Annals of Mathematical Statistics 22, 400–407.Google Scholar
  37. Rubinstein, R.Y.: 1999a, “The Cross-Entropy Method for Combinatorial and Continuous Optimization.” Methodology and Computing in Applied Probability 1(2), 127–190.CrossRefGoogle Scholar
  38. Rubinstein, R.Y.: 1999b, “Rare Event Simulation via Cross-Entropy and Importance Sampling.” In Second International Workshop on Rare Event Simulation, RESIM'99, pp. 1–17.Google Scholar
  39. Rubinstein, R.Y. (2001). “Combinatorial Optimization, Cross-Entropy, Ants and Rare Events.” In Stochastic Optimization: Algorithms and Applications. Dordrecht, The Netherlands: Kluwer Academic, pp. 303–364.Google Scholar
  40. Stützle, T. and H.H. Hoos. (1997). “The MAX-MIN Ant System and Local Search for the Traveling Salesman Problem.” In Proceedings of ICEC'97-1997 IEEE 4th International Conference on Evolutionary Computation. Piscataway, NJ: IEEE Press, pp. 308–313.Google Scholar
  41. Stützle, T. and H.H. Hoos. (2000). “MAX-MINAnt System.” Future Generation Computer Systems 16(8), 889–914.Google Scholar
  42. Sutton, R. and A. Barto. (1998). Reinforcement Learning. An Introduction. Cambridge, MA: MIT Press.Google Scholar
  43. Syswerda, G. (1993). “Simulated Crossover in Genetic Algorithms.” In Foundations of Genetic Algorithms, Vol. 2. San Mateo, CA: Morgan Kaufmann, pp. 239–255.Google Scholar
  44. Zlochin, M. and M. Dorigo. (2002). “Model-Based Search for Combinatorial Optimization: A Comparative Study.” In Proceedings of PPSN-VII, Seventh International Conference on Parallel Problem Solving from Nature, Lecture Notes in Computer Science, Vol. 2439. Berlin, Germany: Springer, pp. 651–661.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Mark Zlochin
    • 1
  • Mauro Birattari
    • 2
  • Nicolas Meuleau
    • 3
  • Marco Dorigo
    • 2
  1. 1.Dept. of Applied Mathematics and Computer ScienceThe Weizmann Institute of ScienceIsrael
  2. 2.IRIDIAUniversité Libre de BruxellesBelgium
  3. 3.NASA Ames Research CenterMoffett FieldUSA

Personalised recommendations