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<hr><p align="left"><small>发信人: coy (我爱美好哦), 信区: Algorithm <br>
标 题: 遗传算法（1） <br>
发信站: 武汉白云黄鹤站 (Wed May 31 21:37:03 2000), 站内信件 <br>
<br>
先前答应了人家，现在兑现，呵呵。 <br>
这一篇是说明。 <br>
COPYRIGHT NOTICE <br>
This software is copyright by Zbigniew Michalewicz. Permission is <br>
granted to copy and use the software for scientific, noncommercial <br>
purposes only. The software is provided "as is", i.e., without any <br>
warranties. <br>
GENERAL REMARKS <br>
The Genocop system aims at finding a global optimum (minimum or <br>
maximum: this is one of the input parameters) of a function; <br>
additional linear constraints (equations and inequalities) can <br>
be specified as well. <br>
This is a first version of Genocop system (version 1.0); it is meant to be <br>
a pre-release only. This version was implemented by one of my master <br>
students, Swarnalatha Swaminathan. <br>
Next versions would aim at better user interfaces <br>
and at improving usability of the system (different termination conditions, <br>
declaring integer and boolean variables, etc.). In summer 1993 I plan also <br>
to release Genocop II, which would handle nonlinear constraints as well. <br>
The system is based on the article "GENOCOP: A Genetic Algorithm for <br>
Numerical Optimization with Linear Constraints" accepted for publication <br>
in the Communications of the ACM. The paper was accepted there in <br>
April 1991 (16 months ago) and until today the editors of CACM did not <br>
schedule it in the coming issues of the journal. However, the article <br>
was incorporated (with a permission from the ACM) into one of the chapters <br>
of my new book "Genetic Algorithms + Data Structures = Evolution Programs" <br>
(Springer Verlag, August 1992). <br>
The current version of Genocop should run without changes on any BSD-UN*X <br>
system (preferably on a Sun SPARC machine). Note, however, that the <br>
system was NOT designed with portability in mind, i.e., the partability <br>
was not the main factor in the design process. <br>
HOW TO RUN THE GENOCOP SYSTEM <br>
To run the genocop system, there are four simple steps to follow: <br>
(1) prepare input file, say, "your_input", <br>
(2) incorporate the function in the eval.c file, <br>
(3) type "make", <br>
(4) type "genocop your_input your_output" ("your_output" is the name <br>
of the output file provided by you). <br>
A simple example follows. The input file of this example is the <br>
transferred file "input" you have now in your directory, the typical <br>
output is present in the file "output". The function is already <br>
incorporated in the file "eval.c". <br>
In the example we try to maximize a function of 4 variables: <br>
X[1]*sin(X[2]) + X[3]*X[3] -12.7*X[4] <br>
(NOTE: indexes of variables start from one, and not zero). <br>
Additional requirements are: <br>
one linear equality: <br>
2*X[1] + X[2] - 3.5*X[4] = 1 <br>
two linear inequalities: <br>
X[2] + X[3] <= 3.00 <br>
X[1] - 2*X[2] <= 0.00 <br>
Also: <br>
1.00 <= X1 <= 8.00 <br>
0.00 <= X2 <= 8.00 <br>
-2.10 <= X3 <= 3.10 <br>
0.00 <= X4 <= 4.40 <br>
The input file "input" is as follows (see file "input"): <br>
___________________________________________________ <br>
4 1 2 4 <br>
2.0 1.0 0.0 -3.5 1.0 <br>
0.0 1.0 1.0 0.0 3.0 <br>
1.0 -2.0 0.0 0.0 0.0 <br>
1.0 1 8.0 <br>
1.0 1 8.0 <br>
0.0 2 8.0 <br>
-2.1 3 3.1 <br>
0.0 4 4.4 <br>
70 500 <br>
4 4 4 4 4 8 <br>
0.2 <br>
1 <br>
2 <br>
0.25 <br>
10 <br>
___________________________________________________ <br>
Explanations (line by line) of the input file: <br>
4 1 2 4 <br>
These four integers have the following meaning (in order): <br>
number of variables, <br>
number of equalities, <br>
number of inequalities, <br>
number of domains specified. <br>
The next line: <br>
2.0 1.0 0.0 -3.5 1.0 <br>
represents the equation: <br>
2*X[1] + X[2] - 3.5*X[4] = 1; <br>
note, that for 4 variables you must provide 5 numbers (one for each variable <br>
and the additional one for a value of the right hand side of the equation). <br>
The next two lines: <br>
0.0 1.0 1.0 0.0 3.0 <br>
1.0 -2.0 0.0 0.0 0.0 <br>
represent two inequalities. NOTE, that all inequalities assume that <br>
left hand side is LESS OR EQUAL to the right hand side. In other words, <br>
to represent an inequality: <br>
3.1*X[2] - 4.9*X[4] >= 12.1 <br>
you have to represent it as (assuming four variables): <br>
0.0 -3.1 0.0 4.9 -12.1, i.e., <br>
-3.1*X[2] + 4.9*X[4] <= -12.1 <br>
The next four lines of the input file: <br>
1.0 1 8.0 <br>
0.0 2 8.0 <br>
-2.1 3 3.1 <br>
0.0 4 4.4 <br>
describe domains of variables (the middle - integer - number of <br>
each line serves as an index of a variable). <br>
The line: <br>
70 500 <br>
indicate the population size (70) and the total number of generations (500). <br>
The next line: <br>
4 4 4 4 4 8 <br>
provides the frequencies of 6 operators (these are integers; their total <br>
should not exceed 50% of the population size). <br>
You can leave these frequencies as a standard set for all your <br>
experiments. <br>
The final lines of the input file are: <br>
0.2 (the coeficient q for cumulative probability distribution; <br>
higher q values provide stronger selective pressure; <br>
standard value 0.2 is already relatively high for a population <br>
size 70). <br>
1 (1 is for maximization problem, 0 for minimization). <br>
2 (a parameter for non-uniform mutation; should stay as 2). <br>
0.25 (a parameter for arithmetical crossover, float between 0 and 1). <br>
10 (a parameter for simple crossover, leave it as it is). <br>
EVALUATION FUNCTION: <br>
One of the transferred files is "eval.c". For our current example, <br>
it is: <br>
_____________________________________________________ <br>
#include "thesis.h" <br>
float evaluate(X) <br>
VECTOR X; <br>
VECTOR X; <br>
{ <br>
return(X[1]*sin(X[2]) + X[3]*X[3] -12.7*X[4]); <br>
} <br>
_____________________________________________________ <br>
To provide any function, just replace return line with <br>
appropriate expression, note again that variables are: <br>
X[1], X[2], etc. <br>
If you change the function, you will have to retype "make". <br>
Now, everything is ready. Just type: <br>
% make <br>
and <br>
% genocop your_input your_ouput <br>
and (hopefully) you'll get your result. <br>
IMPORTANT REMARKS: <br>
(1) If the input file contains more than one equations, these equations <br>
must be linearly independent (this is responsibility of the user). <br>
(2) There is a line in the thesis.h file: <br>
#define TRIES 100 <br>
The variable TRIES defined the number of attempts the Genocop system <br>
tries to find a feasible point in the search space. If successful, <br>
the system will run further. If not, the Genocop will prompt you <br>
for an initial point. <br>
OUTPUT: the output file is self-explanatory. After several control <br>
lines, you get the generation number and the current best value <br>
(for generations, where there is an improvement). <br>
This is followed by the final population. <br>
FINAL NOTICE: It is quite likely that there are some bugs in the system; <br>
please, report them to zbyszek@mosaic.uncc.edu. <br>
I will try to take care of them in the next version (1.1). <br>
I hope these remarks would be sufficient to experiment with the system. <br>
Happy optimizing, <br>
Zbigniew Michalewicz <br>
****************************************************************************** <br>
* Mail: Department of Computer Science E-mail: zbyszek@mosaic.uncc.edu * <br>
* University of North Carolina Phone: (704) 547-4873 * <br>
* Charlotte, NC 28223 Fax: (704) 547-2352 * <br>
****************************************************************************** <br>
<br>
<br>
<br>
-- <br>
○ <br>
<//> <br>
／＼ <br>
FINAL NOTICE: It is quite likely that there are some bugs in the system; <br>
please, report them to zbyszek@mosaic.uncc.edu. <br>
I will try to take care of them in the next version (1.1). <br>
I hope these remarks would be sufficient to experiment with the system. <br>
Happy optimizing, <br>
Zbigniew Michalewicz <br>
****************************************************************************** <br>
* Mail: Department of Computer Science E-mail: zbyszek@mosaic.uncc.edu * <br>
* University of North Carolina Phone: (704) 547-4873 * <br>
* Charlotte, NC 28223 Fax: (704) 547-2352 * <br>
****************************************************************************** <br>
<br>
<br>
<br>
-- <br>
○ <br>
＼○／ <br>
┃ <br>
／\ <br>
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