# hw10 - HW#10 Solutions 2010 Points possible: 20 Problem 1:...

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HW#10 Solutions 2010 Points possible: 20 Problem 1: DES (not graded) The derivation of this equation is as follows: ± ² ³ ´ ² µ¶· ± ¸ ³ ¹º » ´¼´ ² µ¶· ½ ´ µ¶· ¸ ± ¾ ³ ¹º » ´¼ ¸ ´ ² µ¶· ½ ¹º » ´¼´ µ¶· ¸ ½ ´ µ¶· ¾ ¿ ± À ³ ¹º » ´¼ ÀÁ² ´ ² µ¶· ½ ¹º » ´¼ ÀÁ¸ ´ µ¶· ¸ ½ Â ½ ¹º » ´¼ ÀÁÀ ´ µ¶· À À Ã Ã ³ Ä¹º » ´¼ ÀÁÅ Æ ´ Æ µ¶· Å À ÅÇ² Problem 2: Symbolic Regression (not graded) (a) The parse tree can be represented mathematically as follows: ¹¹È ½ ¹¹ÉÊË¹Ì » Ì¼ » ¹Ì » Ì¼¼ ½ Ì¼ Í Ì Í Ì¼ Í Ì¼ ½ Ì Performing simple algebra, you can show that this is indeed Ì Î ½ Ì ¾ ½ Ì ¸ ½ Ì (b) Yes. The bottom of the parse tree (shown below) can be replaced by defining a constant ‘1’ in the terminal set.

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HW#10 Solutions 2010 Problem 3: Using Genetic Programming Software (10 points) (a) (1 points) Tableau for Symbolic Regression of X 2 /2+2X+2 Objective: Find a function of one independent variable, a constant, 2, and one dependent variable, in symbolic form, that fits a given sample of 21 (x i , y i ) data points, where the target function is the quadratic polynomial X 2 /2+2X+2 Terminal set: X, constant 2 Function set: Addition (+), subtraction (-), multiplication(*), protected division(%) Fitness cases: The given sample of 21 data points(x i , y i ), where the x i come from the interval [-1,1] Raw fitness: The sum of the absolute difference between the expected output value and the value returned by the individual on all fitness cases Standardized fitness: Equals raw fitness for this problem Hits: Number of fitness cases for which the individual produces results within minus or plus 0.1% of the expected results
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## This note was uploaded on 10/02/2011 for the course ORIE 5430 taught by Professor Shoemaker during the Fall '11 term at Cornell University (Engineering School).

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hw10 - HW#10 Solutions 2010 Points possible: 20 Problem 1:...

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