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IEEE World Congress on Computational Intelligence

WCCI 2012: Advances in Computational Intelligence pp 122–144Cite as

Probabilistic Graphical Approaches for Learning, Modeling, and Sampling in Evolutionary Multi-objective Optimization

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Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 7311))

Abstract

Multi-objective optimization is widely found in many fields, such as logistics, economics, engineering, or whenever optimal decisions need to be made in the presence of tradeoff between two or more conflicting objectives. The synergy of probabilistic graphical approaches in evolutionary mechanism may enhance the iterative search process when interrelationships of the archived data has been learned, modeled, and used in the reproduction. This paper presents the implementation of probabilistic graphical approaches in solving multi-objective optimization problems under the evolutionary paradigm. First, the existing work on the synergy between probabilistic graphical models and evolutionary algorithms in the multi-objective framework will be presented. We will then show that the optimization problems can be solved using a restricted Boltzmann machine (RBM). The learning, modeling as well as sampling mechanisms of the RBM will be highlighted. Lastly, five studies that implement the RBM for solving multi-objective optimization problems will be discussed.

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References

  1. Deb, K.: Multi-objective Optimization using Evolutionary Algorithms. John Wiley & Sons, Chichester (2001)

    MATH  Google Scholar 

  2. Tan, K.C., Khor, E.F., Lee, L.H.: Multiobjective Evolutionary Algorithms and Applications. Springer (2005)

    Google Scholar 

  3. Larrañaga, P., Lozano, J.A.: Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Kluwer, Norwell (2001)

    MATH  Google Scholar 

  4. Lozano, J.A., Larran̈aga, P., Bengoetxea, E.: Towards a New Evolutionary Computation: Advances on Estimation of Distribution Algorithms. STUDFUZZ. Springer, New York (2006)

    Book  Google Scholar 

  5. Neri, F., Mininno, E.: Memetic Compact Differential Evolution for Cartesian Robot Control. IEEE Computational Intelligence Magazine 5(2), 54–65 (2010)

    Article  Google Scholar 

  6. Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. MIT Press (2009)

    Google Scholar 

  7. Larrañaga, P.: Probabilistic Graphical Models and Evolutionary Computation. In: Plenary Lecturer in 2010 IEEE World Congress on Computational Intelligence (2010)

    Google Scholar 

  8. Ting, C.K., Zeng, W.M., Lin, T.C.: Linkage Discovery Through Data Mining. IEEE Computational Intelligence Magazine 5(1), 10–13 (2010)

    Article  Google Scholar 

  9. Pelikan, M., Sastry, K., Goldberg, D.E.: Multiobjective Estimation of Distribution Algorithm. In: Scalable Optimization via Probabilistic Modeling, pp. 223–248. Springer (2006)

    Google Scholar 

  10. Bosman, P.A.N., Thierens, D.: Multi-objective Optimization with Diversity Preserving Mixture-based Iterated Density Estimation Evolutionary Algorithms. International Journal of Approximate Reasoning 31(3), 259–289 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Laumanns, M., Ocenasek, J.: Bayesian Optimization Algorithms for Multi-objective Optimization. In: Proceedings of the 7th International Conference on Parallel Problem Solving from Nature, pp. 298–307 (2002)

    Google Scholar 

  12. Costa, M., Minisci, E.: MOPED: A Multi-objective Parzen-Based Estimation of Distribution Algorithm for Continuous Problems. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 282–294. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  13. Li, H., Zhang, Q., Tsang, E., Ford, J.A.: Hybrid Estimation of Distribution Algorithm for Multiobjective Knapsack Problem. In: Gottlieb, J., Raidl, G.R. (eds.) EvoCOP 2004. LNCS, vol. 3004, pp. 145–154. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  14. Okabe, T., Jin, Y., Sendhoff, B., Olhofer, M.: Voronoi-based Estimation of Distribution Algorithm for Multi-objective Optimization. In: IEEE Congress on Evolutionary Computation, pp. 1594–1601 (2004)

    Google Scholar 

  15. 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)

    Article  Google Scholar 

  16. Pelikan, M., Sastry, K., Goldberg, D.E.: Multiobjective hBOA, Clustering, and Scalability. In: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, pp. 663–670 (2005)

    Google Scholar 

  17. Sastry, K., Goldberg, D.E., Pelikan, M.: Limits of Scalability of Multiobjective Estimation of Distribution Algorithms. In: IEEE Congress on Evolutionary Computation, pp. 2217–2224 (2005)

    Google Scholar 

  18. Soh, H., Kirley, M.: moPGA: Towards a New Generation of Multi-objective Genetic Algorithms. In: IEEE Congress on Evolutionary Computation, pp. 1702–1709 (2006)

    Google Scholar 

  19. Bosman, P.A.N., Thierens, D.: Adaptive Variance Scaling in Continuous Multi-objective Estimation of Distribution Algorithms. In: Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, pp. 500–507 (2007)

    Google Scholar 

  20. Zhong, X., Li, W.: A Decision-tree-based Multi-objective Estimation of Distribution Algorithm. In: Proceedings of the 2007 International Conference on Computational Intelligence and Security, pp. 114–118 (2007)

    Google Scholar 

  21. Zhang, Q., Zhou, Z., Jin, Y.: RM-MEDA: A Regularity Model-based Multiobjective Estimation of Distribution Algorithm. IEEE Transactions on Evolutionary Computation 12(1), 41–63 (2008)

    Article  Google Scholar 

  22. Zhou, A., Zhang, Q., Jin, Y.: Approximating the Set of Pareto-optimal Solutions in Both the Decision and Objective Spaces by an Estimation of Distribution Algorithm. IEEE Transactions on Evolutionary Computation 13(5), 1167–1189 (2009)

    Article  Google Scholar 

  23. Martí, L., García, J., Berlanga, A., Molina, J.: Solving Complex High-dimensional Problems with the Multi-objective Neural Estimation of Distribution Algorithm. In: Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation, pp. 619–626 (2009)

    Google Scholar 

  24. Huband, S., Hingston, P., Barone, L., While, L.: A Review of Multiobjective Test Problems and a Scalable Test Problem Toolkit. IEEE Transactions on Evolutionary Computation 10(5), 477–506 (2006)

    Article  MATH  Google Scholar 

  25. Gao, Y., Hu, X., Liu, H., Feng, Y.: Multiobjective Estimation of Distribution Algorithm Combined with PSO for RFID Network Optimization. In: International Conference on Measuring Technology and Mechatronics Automation, pp. 736–739 (2010)

    Google Scholar 

  26. Li, X.: Niching Without Niching Parameters: Particle Swarm Optimization Using a Ring Topology. IEEE Transactions on Evolutionary Computation 14(1), 150–169 (2010)

    Article  Google Scholar 

  27. Salakhutdinov, R., Mnih, A., Hinton, G.: Restricted Boltzmann Machines for Collaborative Filtering. In: Proceedings of the 24th International Conference on Machine Learning, pp. 791–798 (2007)

    Google Scholar 

  28. Hinton, G.E.: Training Products of Experts by Minimizing Contrastive Divergence. Neural Computation 14(8), 1771–1800 (2002)

    Article  MATH  Google Scholar 

  29. Hinton, G.E., Salakhutdinov, R.: Reducing the Dimensionality of Data with Neural Networks. Science 313(5786), 504–507 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  30. Tieleman, T.: Training Restricted Boltzmann Machines Using Approximations to the Likelihood Gradient. In: Proceedings of the 25th International Conference on Machine Learning, pp. 1064–1071 (2008)

    Google Scholar 

  31. Carreira-Perpiñán, M., Hinton, G.: On Contrastive Divergence Learning. In: 10th International Workshop on Artificial Intelligence and Statistics, pp. 59–66 (2005)

    Google Scholar 

  32. Lu, K., Yen, G.G.: Rank-density-based multiobjective genetic algorithm and benchmark test function study. IEEE Transactions on Evolutionary Computation 7(4), 325–343 (2003)

    Article  Google Scholar 

  33. Deb, K., Sinha, A., Kukkonen, S.: Multi-objective Test Problems, Linkages, and Evolutionary Methodologies. In: Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, pp. 1141–1148 (2006)

    Google Scholar 

  34. Tang, H., Shim, V.A., Tan, K.C., Chia, J.Y.: Restricted Boltzmann Machine Based Algorithm for Multi-objective Optimization. In: IEEE Congress on Evolutionary Computation, pp. 3958–3965 (2010)

    Google Scholar 

  35. Shim, V.A., Tan, K.C., Chia, J.Y.: An Investigation on Sampling Technique for Multi-objective Restricted Boltzmann Machine. In: IEEE Congress on Evolutionary Computation, pp. 1081–1088 (2010)

    Google Scholar 

  36. Shim, V.A., Tan, K.C., Chia, J.Y., Al Mamun, A.: Multi-objective Optimization with Estimation of Distribution Algorithm in a Noisy Environment. Evolutionary Computation (accepted)

    Google Scholar 

  37. Beyer, H.G.: Evolutionary Algorithms in Noisy Environments: Theoretical Issues and Guidelines for Practice. Computer Methods in Applied Mechanics and Engineering 186(2), 239–267 (2000)

    Article  MATH  Google Scholar 

  38. Goh, C.K., Tan, K.C.: An Investigation on Noisy Environments in Evolutionary Multiobjective Optimization. IEEE Transactions on Evolutionary Computation 11(3), 354–381

    Google Scholar 

  39. Darwen, P., Pollack, J.: Coevolutionary learning on Noisy Tasks. In: IEEE Congress on Evolutionary Computation, pp. 1724–1731 (1999)

    Google Scholar 

  40. Hughes, E.J.: Evolutionary Multi-objective Ranking with Uncertainy and Noise. In: Proceedings of the First International Conference on Evolutionary Multi-Criterion Optimization, pp. 329–343 (2001)

    Google Scholar 

  41. Storn, R., Price, K.: Differential Evolution - A Simple and Efficient Heuristic for Global Optimization Over Continuous Spaces. Journal of Global Optimization 11(4), 341–359 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  42. Shim, V.A., Tan, K.C., Cheong, C.Y.: A Hybrid Estimation of Distribution Algorithm with Decomposition for Solving the Multi-objective Multiple Traveling Salesmen Problem. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews (accepted)

    Google Scholar 

  43. Ishibuchi, H., Yoshida, T., Murata, T.: A Multi-objective Genetic Local Search Algorithm and Its Application to Flowshop Scheduling. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews 28(3), 204–223 (1998)

    Article  Google Scholar 

  44. Zhang, Q., Li, H.: MOEA/D: A Multiobjective Evolutinoary Algorithm Based On Decomposition. IEEE Transactions on Evolutionary Computation 11(6), 712–731 (2007)

    Article  MathSciNet  Google Scholar 

  45. Okonjo, C.: An Effective Method of Balancing the Workload Amongst Salesmen. Omega 16(2), 159–163 (1998)

    Article  Google Scholar 

  46. Goh, C.K., Ong, Y.S., Tan, K.C., Teoh, E.J.: An Investigation on Evolutionary Gradient Search for Multi-objective Optimization. In: IEEE Congress on Evolutionary Computation, pp. 3741–3746 (2008)

    Google Scholar 

  47. Shim, V.A., Tan, K.C.: A Hybrid Adaptive Evolutionary Algorithm in the Domination-based and Decomposition-based Frameworks of Multi-objective Optimization. In: IEEE Congress on Evolutionary Computation (accepted, 2012)

    Google Scholar 

  48. Abbass, H.A., Sarker, R.: The Pareto Differential Evolution Algorithm. International Journal of Artificial Intelligence Tools 11(4), 531–552 (2002)

    Article  Google Scholar 

  49. Kukkonen, S., Lampinen, J.: GDE3: The Third Evolution Step of Generalized Differential Evolution. In: IEEE Congress on Evolutionary Computation, pp. 443–450 (2005)

    Google Scholar 

  50. Li, H., Zhang, Q.: Multiobjective Optimization Problems with Complicated Pareto Sets, MOEA/D and NSGA-II. IEEE Transactions on Evolutionary Computation 13(2), 284–302 (2009)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, 117576, Singapore

    Vui Ann Shim & Kay Chen Tan

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  1. Vui Ann Shim
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  2. Kay Chen Tan
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Editor information

Editors and Affiliations

  1. Key Lab of Intelligent Perception and Image Understanding of Ministry of Education of China, Xidian University, 710071, Xi’an, Shaanxi, China

    Jing Liu

  2. Dipartimento di Elettronica e Informazione, Politecnico di Milano, 20133, Milano, Italy

    Cesare Alippi

  3. Université Pierre et Marie Curie - Paris 6, LIP6, 4 place Jussieu, 75005, Paris, France

    Bernadette Bouchon-Meunier

  4. Department of Electrical & Computer Engineering, Portland State University, 97207, Portland, OR, USA

    Garrison W. Greenwood

  5. School of Engineering and Information Technology, University of New South Wales, 2600, Canberra, ACT, Australia

    Hussein A. Abbass

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© 2012 Springer-Verlag Berlin Heidelberg

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Shim, V.A., Tan, K.C. (2012). Probabilistic Graphical Approaches for Learning, Modeling, and Sampling in Evolutionary Multi-objective Optimization. In: Liu, J., Alippi, C., Bouchon-Meunier, B., Greenwood, G.W., Abbass, H.A. (eds) Advances in Computational Intelligence. WCCI 2012. Lecture Notes in Computer Science, vol 7311. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30687-7_7

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  • DOI: https://doi.org/10.1007/978-3-642-30687-7_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30686-0

  • Online ISBN: 978-3-642-30687-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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