Non-linear regression using Genetic Programming
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The objective of this example is to find back the following non-linear equation: y=4*sin(3*x)+x*x/10
Here is a good 1 minute run with seed 2, obtained with the (regression.ez code).
If you don't have an NVIDIA GPGPU card on your machine, please compile with:
$ easena ./regression.ez -gp ; make
and launched with:
$ ./regression --nbCPUThreads 20
If you have a multi-core CPU, EASEA parallelizes will parallelize over several threads using OpenMP. In order to use up to 20 threads (depending on the number of cores of your CPU), you can launch the program with:
$ ./regression --nbCPUThreads 20
If you have a machine with ann NVIDIA GPGPU card, make sure that the NVIDIA CUDA development environment is correctly installed (obtainable for free on the NVIDIA website) and compile with:
$ easena ./regression.ez -cuda_gp ; make
You can launch with the same line:
$ ./regression --nbCPUThreads 20
collet@biplan:~/regression$ easena ./regression.ez -gp ; make ;./regression --nbCPUThreads 20 --plotStats 0 --seed 2
EASENA version: 2.19 (RE)
Compiled with GP template
CONGRATULATIONS !!!
Target file(s) generation succeeded without warnings.
You can now type "make" to compile your project.
g++ -fopenmp -O2 -g -Wall -fmessage-length=0 -I/biolo/easea/easea//libeasea/include -I/usr/local/cuda/common/inc/ -I/usr/local/cuda/include/ -c -o regression.o regression.cpp
g++ -fopenmp -O2 -g -Wall -fmessage-length=0 -I/biolo/easea/easea//libeasea/include -I/usr/local/cuda/common/inc/ -I/usr/local/cuda/include/ -c -o regressionIndividual.o regressionIndividual.cpp
g++ -o regression regression.o regressionIndividual.o -g /biolo/easea/easea//libeasea//libeasea.a -lpthread -fopenmp
------------------------------------------------------------------------------------------------
|GENER.| ELAPSED | PLANNED | ACTUAL |BEST INDIVIDUAL| AVG | WORST | STAND |
|NUMBER| TIME | EVALUATION NB | EVALUATION NB | FITNESS |FITNESS|FITNESS| DEV |
------------------------------------------------------------------------------------------------
0 0.074s 50000 48604 3.476540039e+03 1.5e+04 1.2e+06 2.5e+08
1 0.348s 100000 97721 2.629287354e+03 4.0e+03 3.6e+02 1.2e+04
2 0.663s 150000 146667 2.627041016e+03 3.6e+03 2.0e+02 1.7e+04
3 1.004s 200000 195655 2.598434570e+03 3.5e+03 1.4e+02 8.5e+03
4 1.449s 250000 244934 2.597528564e+03 3.4e+03 3.0e+02 7.8e+03
5 2.075s 300000 294291 2.412631348e+03 3.1e+03 4.5e+02 2.5e+04
6 2.628s 350000 343754 2.256219971e+03 2.9e+03 4.7e+02 3.0e+04
7 3.356s 400000 393360 1.988074951e+03 2.7e+03 2.8e+02 8.1e+03
8 4.265s 450000 443077 1.972303467e+03 2.6e+03 1.5e+02 4.9e+03
9 5.178s 500000 492790 1.603686401e+03 2.6e+03 1.8e+02 5.9e+03
10 6.108s 550000 542498 1.317219116e+03 2.5e+03 2.4e+02 7.3e+03
11 6.995s 600000 592211 1.603133087e+02 2.4e+03 3.2e+02 1.5e+04
12 7.852s 650000 641891 1.603133087e+02 2.2e+03 3.6e+02 1.0e+04
13 8.809s 700000 691607 1.327802887e+02 2.0e+03 4.1e+02 1.5e+04
14 9.806s 750000 741346 8.705255127e+01 1.8e+03 4.8e+02 1.5e+04
15 10.866s 800000 791084 7.755667114e+01 1.5e+03 5.4e+02 1.0e+04
16 11.848s 850000 840789 8.454118729e+00 1.2e+03 7.3e+02 1.5e+04
17 12.857s 900000 890480 8.454118729e+00 9.6e+02 8.1e+02 1.5e+04
18 14.025s 950000 940150 8.454118729e+00 7.4e+02 8.1e+02 1.5e+04
19 15.204s 1000000 989832 6.428004265e+00 5.5e+02 7.8e+02 1.1e+04
20 16.360s 1050000 1039494 6.253423691e+00 4.3e+02 7.7e+02 3.9e+04
21 17.519s 1100000 1089163 6.253423691e+00 3.6e+02 7.5e+02 1.5e+04
22 18.666s 1150000 1138833 6.231546402e+00 3.1e+02 7.4e+02 1.5e+04
23 19.824s 1200000 1188477 6.231546402e+00 2.9e+02 7.6e+02 1.5e+04
24 20.880s 1250000 1238179 6.231546402e+00 2.8e+02 8.0e+02 1.6e+04
25 21.847s 1300000 1287843 6.230583191e+00 2.8e+02 8.3e+02 1.6e+04
26 22.852s 1350000 1337423 6.230583191e+00 2.6e+02 8.0e+02 1.9e+04
27 23.923s 1400000 1387031 6.230583191e+00 2.4e+02 7.7e+02 1.5e+04
28 25.038s 1450000 1436694 6.230583191e+00 2.3e+02 7.4e+02 1.5e+04
29 26.115s 1500000 1486339 6.230583191e+00 2.3e+02 7.4e+02 1.7e+04
30 27.165s 1550000 1535970 1.726973772e+00 2.3e+02 7.4e+02 1.4e+04
31 28.218s 1600000 1585632 1.726973772e+00 2.4e+02 7.4e+02 1.5e+04
32 29.239s 1650000 1635278 1.726973772e+00 2.3e+02 7.5e+02 2.2e+04
33 30.265s 1700000 1684903 1.726973772e+00 2.4e+02 7.5e+02 1.8e+04
34 31.286s 1750000 1734602 1.716903687e+00 2.4e+02 7.5e+02 1.5e+04
35 32.302s 1800000 1784250 1.716903687e+00 2.6e+02 7.9e+02 1.6e+04
36 33.335s 1850000 1833942 1.704545975e+00 2.7e+02 8.2e+02 2.2e+04
37 34.422s 1900000 1883652 1.136579871e+00 2.4e+02 7.7e+02 1.3e+04
38 35.510s 1950000 1933347 1.136579871e+00 2.3e+02 7.7e+02 2.1e+04
39 36.628s 2000000 1983073 1.121906757e+00 2.3e+02 7.6e+02 2.0e+04
40 37.740s 2050000 2032784 1.121906757e+00 2.3e+02 7.7e+02 3.0e+04
41 38.842s 2100000 2082499 1.121906757e+00 2.2e+02 7.5e+02 2.5e+04
42 39.940s 2150000 2132195 1.114099026e+00 2.2e+02 8.0e+02 6.1e+04
43 41.037s 2200000 2181887 1.114099026e+00 2.2e+02 7.6e+02 2.1e+04
44 42.178s 2250000 2231600 1.114099026e+00 2.2e+02 7.4e+02 1.6e+04
45 43.340s 2300000 2281319 1.114099026e+00 2.2e+02 7.4e+02 1.9e+04
46 44.489s 2350000 2331011 1.114099026e+00 2.2e+02 7.5e+02 2.1e+04
47 45.593s 2400000 2380697 1.114099026e+00 2.2e+02 7.4e+02 1.5e+04
48 46.736s 2450000 2430423 1.114099026e+00 2.2e+02 7.6e+02 3.6e+04
49 47.903s 2500000 2480129 1.114099026e+00 2.1e+02 7.3e+02 1.5e+04
50 49.079s 2550000 2529836 1.114099026e+00 2.2e+02 7.4e+02 2.0e+04
51 50.260s 2600000 2579537 1.114099026e+00 2.2e+02 7.5e+02 2.0e+04
52 51.449s 2650000 2629255 2.936421037e-01 2.2e+02 7.4e+02 3.1e+04
53 52.645s 2700000 2678981 2.936421037e-01 2.2e+02 7.5e+02 2.0e+04
54 53.861s 2750000 2728678 2.936421037e-01 2.2e+02 7.8e+02 3.6e+04
55 55.088s 2800000 2778398 2.936421037e-01 2.2e+02 7.4e+02 1.5e+04
56 56.319s 2850000 2828100 2.936421037e-01 2.2e+02 7.5e+02 2.1e+04
57 57.481s 2900000 2877787 2.936421037e-01 2.2e+02 7.5e+02 3.0e+04
58 58.653s 2950000 2927521 2.936421037e-01 2.2e+02 7.3e+02 1.5e+04
59 59.855s 3000000 2977250 2.936421037e-01 2.2e+02 7.5e+02 3.0e+04
60 61.075s 3050000 3026988 2.936421037e-01 2.2e+02 7.5e+02 1.5e+04
Time Over
Time Limit was 60 seconds
EASEA LOG [INFO]: Seed: 2
EASEA LOG [INFO]: Best fitness: 0.293642
EASEA LOG [INFO]: Elapsed time: 61.0758
Now serializing individual (((sin((x)/(0.333335)))*(((0.632737)/(0.175179))+((0.322471)/(0.831035))))+((((0.857195)*(0.361795))
*((x)*(x)))*(0.322471)))
----------
y=(((sin((x)/(0.333335)))*(((0.632737)/(0.175179))+((0.322471)/(0.831035))))+((((0.857195)*(0.361795))*((x)*(x)))*(0.322471)))
----------
collet@biplan:~/regression$
Simplifying the expression of the found function (using any online function simplifier yields:
y=3.99998 * sin(2.99998 * x)+0.10000 * x^2
If we assume that (due to rounding errors) 3.99998 is the same as 4 and that 2.99998 is the same as 3, the found function is the same as the original function:
y=4*sin(3*x)+x*x/10
This can be seen if we print the found function in black over the original function in red: 
Please note that this function is not polynomial, and even though it has a periodic component, it cannot be found using a Fourier transfrom (due to the added parabola).
It will be of course difficult to find more difficult functions, but this example shows the potential of Genetic Programming for non-linear regression.