Jui-Ting Lee
ABSTRACT
Existing EDAs learn linkages starting from pairwise interactions. The characteristic function which indicates the relations among variables are binary. In other words, the characteristic function indicates that there exist or not interactions among variables. Empirically, it can occur that two variables should be sometimes related but sometimes not. This paper introduces a real-valued characteristic function to illustrate this property of fuzziness. We examine all the possible binary models and real-valued models on a test problem. The results show that the optimal real-valued model is better than all the binary models. This paper also proposes a crossover method which is able to utilize the real-valued information. Experiments show that the proposed crossover could reduce the number of function evaluations up to four times. Moreover, this paper proposes an effective method to find a threshold for entropy based interaction-detection metric and a method to learn real-valued models. Experiments show that the proposed crossover with the learned real-valued models works well.
- R. Etxeberria and P. Larra\Hnaga. Global optimization using bayesian networks. Proceedings of the Second Symposium on Artificial Intelligence Adaptive Systems, pages 332--339, 1999.Google Scholar
- D. E. Goldberg. Simple genetic algorithms and the minimal, deceptive problem. Genetic Algorithms and Simulated Annealing, pages 74--88, 1987.Google Scholar
- D. E. Goldberg, K. Sastry, and T. Latoza. On the supply of building blocks. In Proceedings of the Genetic and Evolutionary Computation Conference, pages 336--342. Morgan Kaufmann, 2001.Google Scholar
- G. R. Harik. Finding multiple solutions in problems of bounded difficulty. Technical Report IlliGAL Report No. 94002, University of Illinois at Urbana-Champaign, Urbana, IL, January 1994.Google Scholar
- G. R. Harik. Linkage learning via probabilistic modeling in the ecga. Technical Report IlliGAL Report No. 99010, University of Illinois at Urbana-Champaign, Urbana, IL, February 1999.Google Scholar
- M. Hutter and M. Zaffalon. Distribution of mutual information from complete and incomplete data. Computational Statistics & Data Analysis, 48(3):633--657, 2005. to appear.Google ScholarCross Ref
- G. D. Kleiter. The posterior probability of bayes nets with strong dependences. Soft Computing, 3:162--173, 1999.Google ScholarCross Ref
- M. Munetomo. Linkage identification based on epistasis measures to realize efficient genetic algorithms. In Proceedings of the Evolutionary Computation on 2002. CEC '02. Proceedings of the 2002 Congress - Volume 02, CEC '02, pages 1332--1337, Washington, DC, USA, 2002. IEEE Computer Society. Google ScholarDigital Library
- M. Munetomo and D. E. Goldberg. Identifying linkage by nonlinearity check. Technical Report IlliGAL Report No. 98012, University of Illinois at Urbana-Champaign, Urbana, IL, February 1998.Google Scholar
- M. Pelikan. Bayesian optimization algorithm: from single level to hierarchy. Doctoral dissertation,, University of Illinois at Urbana-Champaign, Champaign, IL, 2002. Google ScholarDigital Library
- M. Pelikan and D. E. Goldberg. Hierarchical bayesian optimization algorithm = bayesian optimization algorithm niching local structures. pages 525--532. Morgan Kaufmann, 2001.Google Scholar
- M. Pelikan, D. E. Goldberg, and E. Cantu-Paz. BOA: The bayesian optimization algorithm. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-1999), pages 525--532, 1999.Google Scholar
- G. C. Rota. The Number of Partitions of a Set. The American Mathematical Monthly, 71(5):498--504, 1964.Google ScholarCross Ref
- C. E. Shannon. A mathematical theory of communication. Bell system technical journal, 27, 1948.Google Scholar
- M. Tsuji, M. Munetomo, and K. Akama. Modeling dependencies of loci with string classification according to fitness differences. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2004), pages 246--257, 2004.Google ScholarCross Ref
- M. Tsuji, M. Munetomo, and K. Akama. A crossover for complex building blocks overlapping. In Proceedings of the 8th annual conference on Genetic and evolutionary computation, GECCO '06, pages 1337--1344, New York, NY, USA, 2006. ACM. Google ScholarDigital Library
- R. Watson and J. B. Pollack. Hierarchically consistent test problems for genetic algorithms. 1999.Google Scholar
- T.-L. Yu, D. E. Goldberg, K. Sastry, C. F. Lima, and M. Pelikan. Dependency structure matrix, genetic algorithms ,and effective recombination. Evolutionary Computation, vol. 17, no. 4, pp. 595--626, 2009. Google ScholarDigital Library
- T.-L. Yu, K. Sastry, and D. E. Goldberg. Linkage learning, overlapping building blocks, and systematic strategy for scalable recombination. In Proceedings of the 2005 conference on Genetic and evolutionary computation, GECCO '05, pages 1217--1224, New York, NY, USA, 2005. ACM. Google ScholarDigital Library
- T.-L. Yu, K. Sastry, D. E. Goldberg, and M. Pelikan. Population sizing for entropy-based model building in discrete estimation of distribution algorithms. In Proceedings of the 9th annual conference on Genetic and evolutionary computation, GECCO '07, pages 601--608, New York, NY, USA, 2007. ACM. Google ScholarDigital Library
Index Terms
- The essence of real-valued characteristic function for pairwise relation in linkage learning for EDAs
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