Advertisement

Multi-objective Phylogenetic Algorithm: Solving Multi-objective Decomposable Deceptive Problems

  • Jean Paulo Martins
  • Antonio Helson Mineiro Soares
  • Danilo Vasconcellos Vargas
  • Alexandre Cláudio Botazzo Delbem
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6576)

Abstract

In general, Multi-objective Evolutionary Algorithms do not guarantee find solutions in the Pareto-optimal set. We propose a new approach for solving decomposable deceptive multi-objective problems that can find all solutions of the Pareto-optimal set. Basically, the proposed approach starts by decomposing the problem into subproblems and, then, combining the found solutions. The resultant approach is a Multi-objective Estimation of Distribution Algorithm for solving relatively complex multi-objective decomposable problems, using a probabilistic model based on a phylogenetic tree. The results show that, for the tested problem, the algorithm can efficiently find all the solutions of the Pareto-optimal set, with better scaling than the hierarchical Bayesian Optimization Algorithm and other algorithms of the state of art.

Keywords

Mutual Information Multiobjective Optimization Neighbor Join Distribution Algorithm Multiobjective Evolutionary Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aghagolzadeh, M., Soltanian-Zadeh, H., Araabi, B., Aghagolzadeh, A.: A hierarchical clustering based on mutual information maximization. In: IEEE International Conference on Image Processing, ICIP 2007, vol. 1 (2007)Google Scholar
  2. 2.
    Aporntewan, C., Ballard, D., Lee, J.Y., Lee, J.S., Wu, Z., Zhao, H.: Gene hunting of the Genetic Analysis Workshop 16 rheumatoid arthritis data using rough set theory. In: BMC Proceedings, vol. 3, p. S126. BioMed Central Ltd (2009)Google Scholar
  3. 3.
    Coello, C.A.C., Zacatenco, S.P., Pulido, G.T.: Multiobjective optimization using a micro-genetic algorithm (2001)Google Scholar
  4. 4.
    Day, W., Edelsbrunner, H.: Efficient algorithms for agglomerative hierarchical clustering methods. Journal of classification 1(1), 7–24 (1984)CrossRefzbMATHGoogle Scholar
  5. 5.
    Deb, K.: Multi-objective genetic algorithms: Problem difficulties and construction of test problems. Evolutionary computation 7(3), 205–230 (1999)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)CrossRefGoogle Scholar
  7. 7.
    Deb, K.: Multi-objective optimization using evolutionary algorithms (2001)Google Scholar
  8. 8.
    Dionísio, A., Menezes, R., Mendes, D.A.: Entropy-based independence test. Nonlinear Dynamics 44(1), 351–357 (2006)CrossRefzbMATHGoogle Scholar
  9. 9.
    Felsenstein, J.: Inferring Phylogenies, vol. 266. Sinauer Associates (2003)Google Scholar
  10. 10.
    Harik, G.: Learning gene linkage to efficiently solve problems of bounded difficulty using genetic algorithms. Ph.D. thesis, The University of Michigan (1997)Google Scholar
  11. 11.
    Hughes, E.: Evolutionary many-objective optimisation: many once or one many? In: The 2005 IEEE Congress on Evolutionary Computation, vol. 1, pp. 222–227. IEEE, Los Alamitos (2005)CrossRefGoogle Scholar
  12. 12.
    Johnson, S.: Hierarchical clustering schemes. Psychometrika 32(3), 241–254 (1967)CrossRefzbMATHGoogle Scholar
  13. 13.
    Kraskov, A.: Synchronization and Interdependence Measures and Their Application to the Electroencephalogram of Epilepsy Patients and Clustering of Data. Report Nr. NIC series 24 (2008)Google Scholar
  14. 14.
    Kraskov, A., Stogbauer, H., Andrzejak, R., Grassberger, P.: Hierarchical clustering based on mutual information. Arxiv preprint q-bio/0311039 (2003)Google Scholar
  15. 15.
    de Melo, V.V., Vargas, D.V., Delbem, A.C.B.: Uso de otimização contínua na resolução de problemas binários: um estudo com evolução diferencial e algoritmo filo-genético em problemas deceptivos aditivos.. In: 2a Escola Luso-Brasileira de Computação Evolutiva (ELBCE), APDIO (2010)Google Scholar
  16. 16.
    Morzy, T., Wojciechowski, M., Zakrzewicz, M.: Pattern-oriented hierarchical clustering. In: Eder, J., Rozman, I., Welzer, T. (eds.) ADBIS 1999. LNCS, vol. 1691, pp. 179–190. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  17. 17.
    Pelikan, M., Goldberg, D., Lobo, F.: A survey of optimization by building and using probabilistic models. Computational optimization and applications 21(1), 5–20 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Pelikan, M., Sastry, K., Cantu-Paz, E.: Scalable optimization via probabilistic modeling: From algorithms to applications. Springer, Heidelberg (2006)CrossRefzbMATHGoogle Scholar
  19. 19.
    Pelikan, M., Sastry, K., Goldberg, D.: Multiobjective hBOA, clustering, and scalability. In: Genetic And Evolutionary Computation Conference: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, pp. 663–670. Association for Computing Machinery, Inc., New York (2005)Google Scholar
  20. 20.
    Saitou, N., Nei, M.: The neighbor-joining method: a new method for reconstructing phylogenetic trees. Molecular Biology and Evolution 4(4), 406 (1987)Google Scholar
  21. 21.
    Salemi, M., Vandamme, A.M.: The Phylogenetic Handbook: A Practical Approach to DNA and Protein Phylogeny, vol. 16. Cambridge University Press, Cambridge (2003), http://doi.wiley.com/10.1002/ajhb.20017 Google Scholar
  22. 22.
    Sastry, K., Goldberg, D., Pelikan, M.: Limits of scalability of multiobjective estimation of distribution algorithms. In: The 2005 IEEE Congress on Evolutionary Computation, vol. 3, pp. 2217–2224. IEEE, Los Alamitos (2005)CrossRefGoogle Scholar
  23. 23.
    Studier, J., Keppler, K.: A note on the neighbor-joining algorithm of Saitou and Nei. Molecular Biology and Evolution 5(6), 729 (1988)Google Scholar
  24. 24.
    Thierens, D.: Analysis and design of genetic algorithms. Katholieke Universiteit Leuven, Leuven (1995)Google Scholar
  25. 25.
    Vargas, D.V., Delbem, A.C.B.: Algoritmo filogenético. Tech. rep., Universidade de São Paulo (2009)Google Scholar
  26. 26.
    Vargas, D.V., Delbem, A.C.B., de Melo, V.V.: Algoritmo filo-genético. In: 2a Escola Luso-Brasileira de Computação Evolutiva (ELBCE), APDIO (2010)Google Scholar
  27. 27.
    Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach. IEEE Transactions on Evolutionary Computation 3(4), 257–271 (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jean Paulo Martins
    • 1
  • Antonio Helson Mineiro Soares
    • 1
  • Danilo Vasconcellos Vargas
    • 1
  • Alexandre Cláudio Botazzo Delbem
    • 1
  1. 1.Institute of Mathematics and Computer ScienceUniversity of São PauloSão CarlosBrazil

Personalised recommendations