SME Assignment 2-Smooth Curve Fitting Solved

Smooth Curve Fitting

Smooth curve fitting is the process of constructing a curve, or mathematical function, that approximately fits a series of data points.

In this assignment, you are given set of points and you will use the genetic algorithm to find the best coefficients to fit a curve (polynomial equation) to these points such that the distance between the polynomial and the points is minimum.

http://en.wikipedia.org/wiki/Curve_fitting

Notes on what you must implement:

• Each coefficient is a floating point between [-10, 10].
• The fitness function is the mean square error (MSE). The best individual is

  the one with the smallest fitness function because we want to minimize MSE.

• Use tournament selection.
• Use 2-point crossover.
• Use non-uniform mutation.
• Given a file of M data sets (i.e. M test cases), for each case, print and save the list of coefficients and the total error. You must write the output to a file.

Input File Structure:

• First line: M represents number of sets.
• Each set consists of: Line N D, where N is number of points and D is the

  requested polynomial degree. This is followed by N lines each one

  representing an (x, y) point.

• For example:

  1
  42
  15
  28
  3 13
  4 20
  This example has 1 test case which has 4 points, and the requested degree is 2 (a0, a1, a2).

  Output File Structure:

• Consists of M lines, each line has D+1 coefficients followed by “Error =” Total Error.
• For example, for the above case, the output might be: 1.33, 0.12, 4.09, Error = 2.1563