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Multiobjective hBOA, clustering, and scalability

Published: 25 June 2005 Publication History

Abstract

This paper describes a scalable algorithm for solving multiobjective decomposable problems by combining the hierarchical Bayesian optimization algorithm (hBOA) with the nondominated sorting genetic algorithm (NSGA-II) and clustering in the objective space. It is first argued that for good scalability, clustering or some other form of niching in the objective space is necessary and the size of each niche should be approximately equal. Multiobjective hBOA (mohBOA) is then described that combines hBOA, NSGA-II and clustering in the objective space. The algorithm mohBOA differs from the multiobjective variants of BOA and hBOA proposed in the past by including clustering in the objective space and allocating an approximately equally sized portion of the population to each cluster. The algorithm mohBOA is shown to scale up well on a number of problems on which standard multiobjective evolutionary algorithms perform poorly.

References

[1]
D. H. Ackley. An empirical study of bit vector function optimization. Genetic Algorithms and Simulated Annealing, pages 170--204, 1987.
[2]
C.-W. Ahn. Theory, Design, and Application of Efficient Genetic and Evolutionary Algorithms. PhD thesis, Gwangju Institute of Science and Technology, Gwangju, Republic of Korea, 2005.
[3]
C. W. Ahn, R. S. Ramakrishna, and G. Goldberg. Real-coded Bayesian optimization algorithm: Bringing the strength of BOA into the continuous world. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2004), pages 840--851, 2004.
[4]
P. A. N. Bosman and D. Thierens. Linkage information processing in distribution estimation algorithms. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-99), I:60--67, 1999.
[5]
P. A. N. Bosman and D. Thierens. Continuous iterated density estimation evolutionary algorithms within the IDEA framework. Workshop Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2000), pages 197--200, 2000.
[6]
J.-H. Chen. Theory and applications of efficient multi-objective evolutionary algorithms. PhD thesis, Feng Chia University, Taichung, Taiwan, 2004.
[7]
D. M. Chickering, D. Heckerman, and C. Meek. A Bayesian approach to learning Bayesian networks with local structure. Technical Report MSR-TR-97-07, Microsoft Research, Redmond, WA, 1997.
[8]
C. A. Coello Coello, D. A. V. Veldhuizen, and G. B. Lamont. Evolutionary algorithms for solving multi-objective problems. Kluwer Academic Publishers, 2001.
[9]
K. Deb. Multi-objective optimization using evolutionary algorithms. John Wiley & Sons, Chichester, UK, 2001.
[10]
K. Deb and D. E. Goldberg. Analyzing deception in trap functions. IlliGAL Report No. 91009, University of Illinois at Urbana-Champaign, Illinois Genetic Algorithms Laboratory, Urbana, IL, 1991.
[11]
K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 2002.
[12]
C. M. Fonseca and P. J. Fleming. Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization. Proceedings of the International Conference on Genetic Algorithms (ICGA-93), pages 416--423, 1993.
[13]
N. Friedman and M. Goldszmidt. Learning Bayesian networks with local structure. In M. I. Jordan, editor, Graphical models, pages 421--459. MIT Press, Cambridge, MA, 1999.
[14]
G. R. Harik. Finding multimodal solutions using restricted tournament selection. Proceedings of the International Conference on Genetic Algorithms (ICGA-95), pages 24--31, 1995.
[15]
J. Horn, N. Nafpliotis, and D. E. Goldberg. A niched Pareto genetic algorithm for multiobjective optimization. Proceedings of the First IEEE Conference on Evolutionary Computation (ICEC-94), pages 82--87, 1994.
[16]
N. Khan. Bayesian optimization algorithms for multiobjective and hierarchically difficult problems. Master's thesis, University of Illinois at Urbana-Champaign, Urbana, IL, 2003.
[17]
N. Khan, D. E. Goldberg, and M. Pelikan. Multi-objective Bayesian optimization algorithm. IlliGAL Report No. 2002009, University of Illinois at Urbana-Champaign, Illinois Genetic Algorithms Laboratory, Urbana, IL, 2002.
[18]
J. Knowles and D. Corne. The Pareto archived evolution strategy: A new baseline algorithm for multiobjective optimisation. Proceedings of the 1999 Congress on Evolutionary Computation (CEC-99), pages 98--105, 1999.
[19]
P. Larrañaga and J. A. Lozano, editors. Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Kluwer, Boston, MA, 2002.
[20]
M. Laumanns and J. Ocenasek. Bayesian optimization algorithms for multi-objective optimization. Parallel Problem Solving from Nature, pages 298--307, 2002.
[21]
J. B. MacQueen. Some methods for classification and analysis of multivariate observations. Proceedings of the 5th Symposium on Mathematics, Statistics and Probability, pages 281--297, 1967.
[22]
H. Mühlenbein and G. Paaβ. From recombination of genes to the estimation of distributions I. Binary parameters. Parallel Problem Solving from Nature, pages 178--187, 1996.
[23]
J. Ocenasek and J. Schwarz. Estimation of distribution algorithm for mixed continuous-discrete optimization problems. In 2nd Euro-International Symposium on Computational Intelligence, pages 227--232, 2002.
[24]
M. Pelikan. Hierarchical Bayesian optimization algorithm: Toward a new generation of evolutionary algorithms. Springer-Verlag, 2005.
[25]
M. Pelikan and D. E. Goldberg. Escaping hierarchical traps with competent genetic algorithms. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), pages 511--518, 2001.
[26]
M. Pelikan and D. E. Goldberg. A hierarchy machine: Learning to optimize from nature and humans. Complexity, 8(5):36--45, 2003.
[27]
M. Pelikan, D. E. Goldberg, and E. Cantú-Paz. BOA: The Bayesian optimization algorithm. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-99), I:525--532, 1999.
[28]
M. Pelikan, D. E. Goldberg, and F. Lobo. A survey of optimization by building and using probabilistic models. Computational Optimization and Applications, 21(1):5--20, 2002.
[29]
K. Sastry, M. Pelikan, and D. E. Goldberg. Decomposable problems, niching, and scalability of multiobjective estimation of distribution algorithms. IlliGAL Report No. 2005004, University of Illinois at Urbana-Champaign, Illinois Genetic Algorithms Laboratory, Urbana, IL, 2005.
[30]
G. Schwarz. Estimating the dimension of a model. The Annals of Statistics, 6:461--464, 1978.
[31]
D. Thierens. Analysis and design of genetic algorithms. PhD thesis, Katholieke Universiteit Leuven, Leuven, Belgium, 1995.
[32]
D. Thierens and P. A. N. Bosman. Multi-objective mixture-based iterated density estimation evolutionary algorithms. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), pages 663--670, 2001.
[33]
E. Zitzler, M. Laumanns, and L. Thiele. SPEA2: Improving the strength Pareto evolutionary algorithm. Technical Report 103, Swiss Federal Institute of Technology (ETH) Zürich, 2001.

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cover image ACM Conferences
GECCO '05: Proceedings of the 7th annual conference on Genetic and evolutionary computation
June 2005
2272 pages
ISBN:1595930108
DOI:10.1145/1068009
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Published: 25 June 2005

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Author Tags

  1. BOA
  2. NSGA-II
  3. clustering
  4. estimation of distribution algorithms
  5. genetic algorithms
  6. multiobjective optimization
  7. nondominated sorting

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