next up previous
Next: Finding Trigonometric Identities Up: The Problem Spaces Previous: The Problem Spaces

Symbolic Regression

In the first problem we apply our system to a symbolic regression problem summarised in Table 1 [Ryan 98a]. The system is given a set of input and output pairs, and must determine the function that maps one onto the other. The particular function examined is X4 + X3 + X2 + X with the input values in the range [-1..+1]. As the target function has no constant values, only the variable X, it was decided to use only one terminal operand, i.e. X. So as not to unduly bias the system towards the correct solution, the terminal operators set consisted of more than the binary addition and multiplication operators, which alone would be sufficient to reach the target function. To determine the fitness of an individual program 20 test points were applied in the range -1 to 1, and the fitness was taken as the sum of the error.


 
Table 1: Grammatical Evolution Tableau for Symbolic Regression
Objective : Find a function of one independent
  variable and one dependent
  variable,in symbolic form that fits
  a given sample of 20 (xi, yi)
  data points, where the target
  functions is the quartic polynomial
  X4 + X3 + X2 + X
Terminal Operands: X (the independent variable)
Terminal Operators The binary operators +, *,
  $ \,-$ and, the unary operators
  Sin, Cos, Exp and Log
Fitness cases The given sample of 20 data points
  in the interval [-1, +1]
Raw Fitness The sum, taken over the 20 fitness
  cases, of the error
Standardised Fitness Same as raw fitness
Hits The number of fitness cases for
  which the error is less than 0.01
Wrapper Standard productions to generate
  C functions
Parameters M = 500, G = 51


next up previous
Next: Finding Trigonometric Identities Up: The Problem Spaces Previous: The Problem Spaces
root
1998-10-02