Last update 17.9.1999
Note: the following tests were performed with a previous GGP version. With default settings, the current version behaves differently because some system parameters were modified and new features were introduced.
Test case: Approximate the function sin(3.1416x)/(3.1416x) which is defined in 25 pints in the interval x=0...1 with a single basis function, represented by a full tree of depth 3. Use 25 points in the interval x=1...2 for testing the quality of the extrapolation. Use GGP default values for the system parameters. Note that only 3 fitness computations are performed for optimizing the nonlinear parameter of each individual. The parameters of the fittest individuals are optimized more than once. The number of individuals is approximately one third of the number of fitness computations. After 1800 fitness computations (600 individuals), an excellent solution is already known. The remaining computations have been done for watching what happens.
The standard GGP pool contains 100 random individuals. The GGP performance depends on the initialization. With another random initialization, the following performance is obtained:
A GGP solution is considered to be good if 1) the error of the approximation is small and 2) the ratio extrapolation error / approximation error is close to 1. The following figure shows, that a ratio very close to 1 is reached for the best solutions found here.