Edited NSGA-II program (MATLAB) to optimise F6 Schaffer's Function, including a real-time graphical display of the results
***Also have a look at [the much more basic genetic algorithm I coded myself](http://redd.it/1c0852)***
Here, I have attached a graphical display of the results to an already complete MATLAB implementation (downloadable here, developed by S. Mostapha Kalami Heris at K. N. Toosi University of Technology, Tehran, Iran) of Deb, et al's Improved Non-dominated Sorting Genetic algorith (NSGA-II). This type of genetic algorithm is designed with multi-objective optimization problems in mind but it also works well at optimizing single-objective problems. I have edited the objective function (cost.m) by substituting the original function (commented out) with the F6 Schaffers function (Single-objective, 2 unknown variables)
You can learn the basics of GAs really easily but this is a much more advanced variation (view more of Deb's research). If you would like to see more current Multi-Objective Evolutionary Algorithms I recommend looking at Coello Coello's Repository and also at the rest of his website.
Shaffer's F6 function is a testing function which includes many oscillations/peaks which are particularly difficult for traditional hill-climbing optimization techniques to converge to a global optimum (instead, solutions are 'trapped' at local optima). The F6 function is designed to have its peak at the origin with a value of one. Included in the download is 'f6Surfaces.m' which includes a 3D surface of the function (x-parameter, y-parameter and evaluation function values) as well as a couple of 2D plot (x-value set to equal zero (it's optimal), with y-values being plotted against 'cost', the same procedure is carried out swapping x-and-y values).
If you run 'nsga2.m' you will see 3 further plots. One is the maximum objective value vs time(s) and the other is the average of all the objective values vs time. A third plot merges the two previous ones together, with generation number displayed along the x-axis instead of time.