# Some Genetic Algorithms Results

Genetic algorithms tend to be very slow on simple functions like
sum x_i^2 (the `sphere model') in low dimensions n, where steepest descent with a gradient computed by central differences and a good good line search takes 2*n+3 function values only. Rosenbrock's function also takes thousends of function values. But some high-dimensional multimodal problems seem to be handled reasonably well.

The following is my summary of the results collected in: Some results from the Literature with Genetic Algorithms (collected by Leo Lazauskas)

3 digit accuracy was the goal to be achieved

Sphere model

n=3: 805-2152 f
n=30: only one algorithm ES1 was OK with 40000 f

Rosenbrock

n=2: 1235-12309 f
n=4: > 77000 f

Step Function

n=5: 2005 f

Gaussian Quartic

n=30: 933-5256 f

Shekel's Foxholes

n=2: 1256-5561 f

Rastrigin

n=20: 3608-6098 f
n=50: 42753 f
n=100: 45111-109072 f
n=200: 52948-309768 f
n=400: 112634-7964400 f
n=1000: 337570-574561 f

Schwefel (Sine Root)

n=10: 8699-20000 f
n=20: 10987-16100 f
n=50: 119316 f
n=100: 101458-1262228 f
n=150: 7041440 f
n=200: 241478-248000 f
n=400: 430084-699803 f
n=1000: 1067221 f

Griewank

n=10: 59520-100000 f
n=20: 26700-66000 f
n=100: 77250-361722 f
n=200: 128875-748300 f
n=400: 229750-1630000 f
n=1000: 563350 f

Ackley

n=30: 13997-19420 f
n=100: 57628-53860 f
n=200: 122347-107800 f
n=400: 262606-220820 f
n=1000: 686614-548306 f

Global Optimization Test Results
Optimization Test Problem Collection
Global Optimization