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Analytic Programming - Comparative Study

Analytic Programming - Comparative Study. Ivan Zelinka, Zuzana Opla t ková http://www.ft.utb.cz/people/zelinka Email {z elinka ,oplatkova} @ft.utb.cz Tomas Bata University in Zlin Faculty of Technology Institut of Information Technologies Mostni 5139 Zlin 760 01 Czech Republic.

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Analytic Programming - Comparative Study

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  1. Analytic Programming - Comparative Study Ivan Zelinka, Zuzana Oplatkováhttp://www.ft.utb.cz/people/zelinkaEmail {zelinka,oplatkova}@ft.utb.czTomas Bata University in ZlinFaculty of TechnologyInstitut of Information TechnologiesMostni 5139Zlin 760 01Czech Republic

  2. Main Principles of AP I C2 Sin Round e C1 Tanh Glaischer t Catalan User function FractionalPart • Set of functions and its possible arguments (terminals)Example: {Sin, Tan, e, Tanh, t,...} • Rule for construction of analytic solution from given individual • Rule for critical situations treating: • pathological functions (without arguments, self-looped...) • functions with imaginary or real part (if not expected)) • infinity in functions • „frozen“ functions (extremely long time to get its cost value - hrs...) • Rule for cost function evaluation Fcost = |DataSet – FAP(t )|

  3. Main Principles of AP - II ^/- z/x

  4. Functions generated by AP

  5. Variants of AP Analytic programming and structure of set of functions and terminals Standard (Koza) Metaevolution Nonlinear fitting +,-, *, /, x, K => only 6 elements +,-, *, /, x, rand1…rand100 => 105 elements The same like in metaevolution. Only nonlinear fitting method is used instead of EA to estimate constants K[[…]] EA is used to find general solution like is demonstrated below. Then is called other EA (can be the same) to estimate numerical values of constants K[[…]]. Result then look like

  6. Sinus “Four and Three” DE Three Four SOMA Three Four Sinus Three GA Three Four Sinus Four SA Three Four

  7. Quintic and Sextic DE QuinticSextic SOMAQuinticSextic Quintic GAQuinticSextic SAQuinticSextic Sextic

  8. Conclusions • On two types of set of functions and terminals three methods were used to estimate solution: • Standard set like in Koza’s GP • Modified set with only one universal constant K, indexed later in evolutionary process • Three methods were used to estimate solution: • Standard AP i.e. EA=>exact programm estimation • AP based on metaevolution i.e. EA=>general programm=>EA=>coefficients estimation • AP based on nonlinear fitting i.e. • EA=>general programm=>nonlinear fitting=>coefficients estimation • Numerical difficulty: • Koza : 4000 individuals, 1 400 000 – 3 000 000 cost function evaluations • AP : 60 – 150 individuals, 500 – 18 000 cost functions evaluations • Future ressearch: • Use AP for solution of different problems (mathematical physics, cybernetics,…) • Use AP for new EAs construction in metaevolutionary way

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