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Simulated Annealing Programming Using Effective Subtrees

Yuichiro UEDA* , Mitsunori MIKI** and Tomoyuki HIROYASU***

(Received October 20, 2008)

Simulated Annealing Programming (SAP), an automatic programming method, is an extension method of Simulated Annealing (SA) that allows SA to handle tree structures. In this method, the point to exchange is chosen randomly, and the subtree to insert is also generated randomly. In this paper, we propose the method that finds out effective subtrees in search and that uses them to generate subtree for inserting. The proposal method can perform search more efficiently than standard SAP in Santa Fe trail problem and Symbolic Regression problem.

Key words automatic programming, program search, genetic programming, simulated annealing, effective subtrees

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* Graduate Student, Department of Knowledge Engineering and Computer Sciences, Doshisha University, Kyoto Telephone:+81-774-65-6921, Fax:+81-774-65-6716, E-mail:[email protected]

** Department of Knowledge Engineering and Computer Sciences, Doshisha University, Kyoto Telephone:+81-774-65-6930, Fax:+81-774-65-6716, E-mail:[email protected]

*** Faculty of Life and Medical Sciences, Doshisha University, Kyoto

Telephone:+81-774-65-6932, Fax:+81-774-65-6019, E-mail:[email protected]

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acceptance criterion transition

criterion of archiving an effective subtree Yes

archive an effective subtree

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end No

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probability of success

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standard SAP type B

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Number of nodes

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4

1) J. R Koza, Genetic Programming: On the Pro- gramming of Computers by Means of Natural Se- lection, MIT Press, 1992.

2) , 1 , ( ‰ , ¾ , ³!

" #y%&…(r)¿*# +³t³€‚²'

”, â

V W ! ‰"

æ , Vol.48, pp. 88–102, 2007.

3) J. R Koza, Genetic Programming II: Automatic Discovery of Reusable Programs, MIT Press, 1994.

4) T. Asai, K. Abe, S. Kawasoe, H. Arimura, H.

Sakamoto, S. Akikawa, Efficient Substruc- ture Discovery from Large Semistructured Data”, Proc. of the 2nd SIAM Intl. Conf. on Data Min- ing, pp. 158–174, 2002.

5) D.Katagiri, S. Yamada, Speedup of Evolution- ary Behavior Learning with Crossover Depend- ing on the Usage Frequency of a Node”, IEEE International Conference on Systems, Man, and Cybernetics, 1999, No. 5, pp. 601–606, 1999.

6) #$%& , â#('æ , )*

á

Æ,+ , 2001.

7) N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, Equation of State Calcu- lation by Fast Computing Machines”, Journ. of Chemical Physics, Vol. 21, pp. 1087–1092, 1953.

Fig. 3. Algorithm of Proposal Method.
Fig. 4 /¯q (a) ” Santa Fe trail î
Fig. 5. History of Program Size.

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Weighted analytic centers are used to improve the location of standing points for the Stand and Hit method of identi- fying necessary LMI constraints in semidefinite programming..

In other words, the aggressive coarsening based on generalized aggregations is balanced by massive smoothing, and the resulting method is optimal in the following sense: for

A generalization of Theorem 12.4.1 in [20] to the generalized eigenvalue problem for (A, M ) provides an upper bound for the approximation error of the smallest Ritz value in K k (x