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Materials
Algorithms Project
Program Library
Program MAP_NEURAL_GENETIC_ALGORITHM
- Provenance of code.
- Purpose of code.
- Specification.
- Description of program's operation.
- References.
- Parameter descriptions.
- Error indicators.
- Accuracy estimate.
- Any additional information.
- Example of code
- Auxiliary routines required.
- Keywords.
- Download source code.
- Links.
Provenance of Source Code
Iqbal Shah and Thomas
Sourmail,
Phase Transformations
Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge CB2 3QZ, U.K.
E-mail:
Added to MAP: September 2002.
Purpose
An application of the genetic algorithm (GA) for reaching a solution given a fitting function. This can in theory be applied to any problem, where a database of inputs and outputs has trained a neural network.
Specification
|
Language: |
C |
|
Product form: |
Source code and executable files for UNIX/Linux machines. |
Complete program.
Description
Neural networks can be used to perform complex regression with a large number of inputs [1,2]. The resulting non-linear models can capture their interactions, but we may wish to use the neural network backwards and identify sets of input variables resulting in a desired output value. However, the large numbers of variables and the non-linear character of the model render this difficult.
The problem is that of looking for the input set (xi), which will give a desired output y, with:
with the function f being non-linear. Genetic algorithms (GAs) is one possible method of solving such a problem. Goldberg described these algorithms as “search procedures based on the mechanics of natural selection and natural genetics” [50].
Once a target output value t is selected, the GA randomly generates sets of inputs called “chromosomes”, which exist in populations:
Each chromosome Xi is composed of a set of variables {xi1… xiz} called "genes". These sets are then ranked according to a fitness factor, which describes how well they perform. In the above example, a fitness factor F could be:
where yi is the desired output for an ith
set of inputs. Those that are close to the desired output are allowed to
"breed" in order to generate another z sets of inputs, whereas the
others are eliminated. In this way, it should be possible to evolve towards the
correct set of inputs, hence demonstrating that the GA process is based on the
concept of “survival of the fittest”.
It is recommended that
Goldberg [3] is read before proceeding with this program, in order to
understand the terminology, as well as the effects and reasons for using
different operators.
MAP provides a set of data files, which can be used with the GA program for finding different sets of inputs. The ga_for_all.zip file, which can be downloaded from here, contains the following files. A working version of a GA is also included to optimise the yield strength of austenitic stainless steels as a function of composition (wt%), temperature (K) and heat treatment temperature (K) (MAP_STEEL_AUSTENITIC_YIELD):
iqbalcode.c A C program used to run the genetic algorithm (GA).
treatout.c A C program for un-normalising the output data files, but is kept within the /unnormalise subdirectory.
gareadme.txt/ gareadme.doc A manual giving further details about running and using the GA program for altering different settings to optimise the process.
nn-input Normalised inputs file (target and accuracy values for the GA).
norm_test.in This is a text file, which contains the normalised input variables initialised by the GA to be fed into the neural network.
generate44/ generate55 This is the executable file for the neural network program. generate44 runs on UNIX selntems and generate55 on the PC. It reads the normalised input data file, norm_test.in, and uses the weight files in subdirectory c. The results are written to the temporary output file _out.
nn-output_b A file which contains the normalised inputs and outputs of the GA after the program has concluded, but is kept within the /unnormalise subdirectory.
score-output A file that contains the scores of each chromosome after the program has concluded.
result A file, which contains the unnormalised values for inputs, outputs and error of each chromosome after unnormalising data in the normalised nn-output_b file.
These files must be placed in the same directory as the GA executable program and should not be changed (unless otherwise stated). As previously mentioned, a working neural network has been included. The following are concerned with the neural network files that work with the GA, but can be changed according to user requirements:
_w*f The weights files for the different models.
*.lu Files containing information for calculating the size of the error bars for the different models.
spec1.t1 An altered version of spec.t1, which is a dynamic file, created by spec.ex/spec.exe, which contains information about the module and the number of data items being supplied. It is read by the program generate44/generate55.exe.
outran.x A normalised output file that was created when developing the model. It is accessed by generate44 via spec1.t1.
MINMAX Minimum and maximum values for the wt% of each element, the temperature (K) and heat treatment temperature (K) used in the original database. (i.e. the minimum and maximum values of each column in the original database before normalisation).
The file gareadme.txt contains a manual, which provides a detailed set of instructions for downloading and running the GA program. A summary of the information in this manual is given here.
References
- D. J. C. MacKay, 1997, Mathematical Modelling of Weld Phenomena 3, eds. H. Cerjak & H.K.D.H. Bhadeshia, Inst. of Materials, London, pp 359.
- https://wol.inference.phy.cam.ac.uk/mackay/README.html David MacKay's Source_code.
- D. E. Goldberg: Genetic Algorithms in Search, Optimisation and Machine Learning. Addison Wesley (1989).
- Review of neural networks in materials science
- M.Phil. Thesis describing the model
Parameters
Input parameters
To specify the target value and accuracy desired, nn-input must be amended.
Row 1 Normalised target value
Row 2 Accuracy (in decimal e.g. 0.1 for 10%)
The normalised target value relates to a real value, according to the MINMAX file used.
To initiate the GA search, the inputs are randomly generated and placed in norm_test.in. It should be noted that each chromosome generally relates to a different steel composition, but this could change over the course of optimisation. For the current yield strength model, the composition, temperature and heat treatment temperature, totalling 19 data items, are specified:
Gene number Variable
1 Normalised Cr wt.%
2 Normalised Ni wt.%
3 Normalised Mo wt.%
4 Normalised Mn wt.%
5 Normalised Si wt.%
6 Normalised Nb wt.%
7 Normalised Ti wt.%
8 Normalised V wt.%
9 Normalised Cu wt.%
10 Normalised N wt.%
11 Normalised C wt.%
12 Normalised B wt.%
13 Normalised P wt.%
14 Normalised S wt.%
15 Normalised Co wt.%
16 Normalised Al wt.%
17 Normalised stoichometric addition ratio of Nb and Ti
18 Normalised heat treatment temperature (K)
19 Normalised test temperature (K)
Each input is normalised using the equation:
normalised value = (value - min)/(max - min) - 0.5
where the values for Min and Max are defined as follows:
|
Gene number |
Variable |
Min |
Max |
|
1 |
Cr wt.% |
15.90 |
21.06 |
|
2 |
Ni wt.% |
8.40 |
34.45 |
|
3 |
Mo wt.% |
0.00 |
2.91 |
|
4 |
Mn wt.% |
0.61 |
1.82 |
|
5 |
Si wt.% |
0.00 |
1.15 |
|
6 |
Nb wt.% |
0.00 |
0.95 |
|
7 |
Ti wt.% |
0.00 |
0.56 |
|
8 |
V wt.% |
0.00 |
0.06 |
|
9 |
Cu wt.% |
0.00 |
0.35 |
|
10 |
N wt.% |
0.00 |
0.08 |
|
11 |
C wt.% |
0.01 |
0.12 |
|
12 |
B wt.% |
0.00 |
0.02 |
|
13 |
P wt.% |
0.00 |
0.04 |
|
14 |
S wt.% |
0.00 |
0.05 |
|
15 |
Co wt.% |
0.00 |
0.54 |
|
16 |
Al wt.% |
0.00 |
0.52 |
|
17 |
Stoichometric addition ratio of Nb and Ti |
0.00 |
3.06 |
|
18 |
Heat treatment temperature (K) |
1279 |
1473 |
|
19 |
Test temperature (K) |
293 |
1273 |
Output parameters
Two output files are produced by the GA program:
nn-output_b A file which contains the normalised inputs and outputs of the GA after the program has concluded, but is kept within the /unnormalise subdirectory.
score-output A file that contains the scores of each chromosome after the program has concluded.
score-output simply prints out the scores for each chromosome.
nn-output_b contains the inputs (composition, temperature, heat treatment temperature for yield strength), prediction and (prediction + error). This is done for the best chromosomes within all populations:
Column 1-19 The normalised predicted inputs.
Column 20 The normalised predicted output
Column 21 A value for the error, which includes the experimental noise of the database, an estimation of the uncertainty in the prediction and the test error. However, this is added to the prediction value so that the MINMAX file can easily handle the value.
The normalised values for the temperatures in all columns must be un-normalised using the equation:
actual value = (normalised value + 0.5)*(max - min) + min
The C program, treatout.c, is used to translate the output files to produce the actual values of inputs and outputs which are written to result.
Error Indicators
None.
Accuracy
See:
Input parameters.
Output parameters.
Further Comments
None.
Example
1. Program text
Complete program.
2. Program data
The input file is:
0.4
0.1
3. Program results
The output file nn-output_b, which contains the normalised values for yield strength model including composition wt %, heat treatment temperature (HTT in K) and test temperature (TST in K):
|
Cr |
Ni |
Mo |
Mn |
Si |
Nb |
Ti |
V |
|
-0.50098 |
1.02233 |
0.847732 |
0.956254 |
1.071616 |
-0.45782 |
0.511222 |
-0.11883 |
|
-0.16101 |
0.256176 |
-0.03355 |
0.183018 |
0.667754 |
0.58004 |
-0.18862 |
-0.38744 |
|
-0.96214 |
0.485774 |
0.956256 |
-0.55776 |
0.768124 |
-0.01484 |
0.192882 |
0.44606 |
|
-0.54415 |
0.593968 |
0.41279 |
0.437972 |
0.003138 |
0.114784 |
-0.09118 |
0.200396 |
|
0.509944 |
0.885392 |
0.756296 |
0.02447 |
1.043348 |
-0.22878 |
0.298126 |
0.316028 |
|
-0.92847 |
0.001604 |
0.835018 |
-0.91864 |
0.415142 |
0.670886 |
-0.1629 |
0.095364 |
|
Cu |
N |
C |
B |
P |
S |
Co |
Al |
|
-0.06951 |
-0.14572 |
-0.1708 |
0.410288 |
-0.58563 |
0.81566 |
0.770394 |
0.469506 |
|
0.770666 |
-0.18601 |
-0.52197 |
0.280574 |
-0.20051 |
0.57496 |
0.061582 |
0.535408 |
|
0.590836 |
1.031872 |
-0.39492 |
0.117738 |
-0.4555 |
-0.39937 |
-0.01293 |
0.157058 |
|
-0.04015 |
0.34606 |
0.453118 |
0.162696 |
0.045304 |
0.042122 |
0.436606 |
-0.43415 |
|
-0.22158 |
0.446884 |
0.769066 |
0.596744 |
-0.61458 |
0.5797 |
0.105568 |
0.751496 |
|
1.077814 |
0.245742 |
0.827036 |
-0.28689 |
0.102666 |
-0.22555 |
-0.25317 |
0.025078 |
|
Ratio |
HTT |
TST |
Pred |
Pred +
Err |
|
||
|
-0.35223 |
0.88121 |
-0.08682 |
0.38812 |
1.503626 |
|
||
|
0.261894 |
0.853972 |
1.071118 |
-0.64601 |
0.623897 |
|
||
|
-0.10509 |
-0.33942 |
0.971052 |
-0.61658 |
1.0188 |
|
||
|
0.207308 |
-0.95481 |
0.586838 |
-0.77732 |
0.956581 |
|
||
|
0.20268 |
-0.16369 |
0.380716 |
0.047217 |
1.08183 |
|
||
|
0.573096 |
-0.18247 |
-0.57423 |
0.742344 |
1.859643 |
|
||
These are then run with treatout.c, where the normalised values are converted into the actual values for composition wt %, heat treatment temperature (K) and test temperature (K) are output to result:
|
Cr |
Ni |
Mo |
Mn |
Si |
Nb |
Ti |
V |
|
||
|
14.80976 |
10.47962 |
2.553839 |
1.308281 |
1.821103 |
0.01 |
0.04 |
0 |
|
||
|
14.80976 |
10.47962 |
4.365 |
1.308281 |
1.821103 |
0.01 |
0.04 |
0 |
|
||
|
17.52873 |
5.464738 |
1.162568 |
2.425 |
0.322959 |
0.01 |
0.04 |
0 |
|
||
|
18.48 |
21.425 |
4.365 |
1.215 |
0.575 |
0.01 |
0.04 |
0 |
|
||
|
13.58437 |
4.390227 |
4.365 |
2.425 |
1.470473 |
0.01 |
0.04 |
0 |
|
||
|
13.58437 |
4.390227 |
1.086076 |
2.425 |
1.725 |
0.01 |
0.04 |
0 |
|
||
|
18.8676 |
9.704428 |
3.859469 |
2.264457 |
0.857313 |
0.01 |
0.04 |
0 |
|
||
|
18.8676 |
9.704428 |
4.365 |
2.264457 |
0.857313 |
0.01 |
0.04 |
0 |
|
||
|
Cu |
N |
C |
B |
P |
S |
Co |
Al |
|||
|
0.17 |
0.005871 |
0.016949 |
0.00459 |
0.025 |
0.013 |
0 |
0 |
|||
|
0.17 |
0.005871 |
0.016949 |
0.00459 |
0.025 |
0.013 |
0 |
0 |
|||
|
0.17 |
0.003882 |
0.026032 |
0.007638 |
0.025 |
0.013 |
0 |
0 |
|||
|
0.17 |
0.0405 |
0.066 |
0.0075 |
0.025 |
0.013 |
0 |
0 |
|||
|
0.17 |
0.035633 |
0.02123 |
0.007806 |
0.025 |
0.013 |
0 |
0 |
|||
|
0.17 |
0.035633 |
0.02123 |
0.0075 |
0.025 |
0.013 |
0 |
0 |
|||
|
0.17 |
0.057779 |
0.031085 |
0.004425 |
0.025 |
0.013 |
0 |
0 |
|||
|
0.17 |
0.057779 |
0.031085 |
0.004425 |
0.025 |
0.013 |
0 |
0 |
|||
|
Ratio |
HTT |
TST |
Pred |
Pred +
Err |
|
|||||
|
0.880904 |
1400 |
298 |
214.0423 |
100.2677 |
|
|||||
|
0.880904 |
1400 |
298 |
214.9005 |
103.1479 |
|
|||||
|
0.699653 |
1400 |
298 |
289.0625 |
158.9392 |
|
|||||
|
1.53125 |
1400 |
298 |
392.0956 |
248.0149 |
|
|||||
|
0.138988 |
1400 |
298 |
271.873 |
126.3189 |
|
|||||
|
1.53125 |
1400 |
298 |
252.3648 |
204.8545 |
|
|||||
|
0.98207 |
1400 |
298 |
378.1229 |
205.0144 |
|
|||||
|
0.98207 |
1400 |
298 |
379.159 |
205.091 |
|
|||||
Nb. The results in the above table are for the best performing chromosomes for each population.
Auxiliary Routines
None.
Keywords
austenitic stainless steel, genetic algorithm, yield strength, neural network
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