GA Exercise - Adaptive Landscape

The Adaptive Landscape shown earlier is actually the function: 
z = -( abs(sin(x))+abs(sin(2*x))+abs(sin(3*x))+abs(sin(5*x)) ) 
    -( abs(sin(y))+abs(sin(2*y))+abs(sin(3*y))+abs(sin(5*y)) )
over the range x = 2 to 4, y = 0.5 to 2.

It was drawn by the following commands in gnuplot on UNIX: 


# gnuplot commands to plot a nice mountainous 3-d surface
set nocontour
set surface
set hidden3d

# fine granularity:
set isosamples 50

splot [2:4] [0.5:2] -( abs(sin(x))+abs(sin(2*x))+abs(sin(3*x))+abs(sin(5*x)) ) -( abs(sin(y))+abs(sin(2*y))+abs(sin(3*y))+abs(sin(5*y)) )

gnuplot is easy to use. Type "gnuplot", then it gives you a command line.
Type   plot sin(x)   just as a demo.
Type   help   for help topics.

Exercise

  1. Evolve values of x and y that maximise this function over this interval.
  2. Note all fitnesses (z) are negative! You are searching for the least negative fitness.
  3. Do in your own time.
  4. Any programming language.

  5. Demonstrate, using gnuplot or any other plotting program, your population climbing the mountain, generation after generation.
  6. Population size should be 30.
  7. In gnuplot, see   plot file with points   (in   help plot) for how to plot a lot of x,y,z points stored in a file (to plot the individuals on the mountain).

To be handed up:

  1. Tidy, bound printout of full working code, commented, in any language.
    (Hint: Colour printout in landscape mode is normally the best way to print out code.)
  2. Pictures of the landscape, with the 30 individuals climbing on it, generation after generation until they are reasonably converged on the highest peak.
  3. To print from gnuplot, plot into a postscript file, then print it. See   set terminal postscript   and   set output file   (in   help set).