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gen-river-readme.txt Mar 29 1998 971 bytes
gen-river.zip Mar 29 1998 10565 bytes
gen-salesman-readme.txt Mar 29 1998 908 bytes
gen-salesman.zip Mar 29 1998 15714 bytes
gentech-readme-de.txt Mar 29 1998 12161 bytes
gentech-readme.txt Apr 2 16:49 10568 bytes
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The Genetic Algorythm
======================
This genetic algorythm tries to implement, as far as I understand,
the original written one by nature.
The documentation is still almost done in the german language, sorry.
If there are volunters who wants to participate,
e.g. for translation, porting to the Java[tm] language,
you are wellcome !
This package contains the sources for:
jaulibs.zip - my general purpose c++ tookit ;-)
this package was created in
the pre STL age ..
gentech.zip - _the_ genetic OO module
gen-river.zip - an implementation of
the riverproblem.
gen-salesman.zip - an implementation of
the traveler-salesman problem.
1.) The Genetic Algorythm
==========================
The genetic algorythm
is designed and implemented in C++ with complete virtual classes.
1.1) The Basic Principle
========================
Nature defines and constructs lifeforms with its genome.
The genome is coded by it's chromosomes.
A chromosome is a chain of nucleotides, the elements of the chomosomes.
In nature these nukleotides a represented with the following four bases:
Adenin (A), Guanin (G), Cytosin (C) und Thymin (T).
The different sequences of these nucleotides, bases, on the chromosome,
does code the genome[2].
The nature optimizes it's lifeforms with different methods.
One of these methods is the sexual reproduction, so called mating.
While mating, the genome of the mating partners are mixed,
this is called "crossing over" [1,2,3,6].
The result of the mix is the genome of the partners child(s).
E.g.:
Father : A G C T A G | A G G G T C | A C T A G
Mother : A A C T C G | A G C G T G | T C T A C
------------------------------------------------------
1st Child: A G C T A G | A G C G T G | A C T A G
2nd Child: A A C T C G | A G G G T C | T C T A C
Besides the "normal" crossing over (homologous or symetric crossing over[2]),
asymetric crossing over exists[2].
Within the asymetric crossing over, at least in the version
of this genetic algorythm, one child contains the whole
genome of both parents.
So a growing (length) of the chromosomes is possible !
During the reproduction process so called mutations are possible.
This mutations modifies the sequence of chromosomes with the
following possible ways:
Mutation : Nucleotides are changed randomized.
In the nature, e.g. by radioactive radiation[1,2,3,4,6].
Inversion : A segment of a chromosome is transfered in reversed
order (last in - first out) [2,6].
E.g.: A G T A | A G C A T | C A G T ==>
A G T A | T A C G A | C A G T .
Translocation : A segment of a chromosome is transfered
to a different position to the destination (progeny). [6]
E.g.: A G T A | A G C A T | C A G T ==>
A G | A G C A T | T A C A G T .
On chromosomes the genome is stored.
The logical whit (minimal part) of this genome is called gene.
The gene represents a segment of a chromosome, but the definition
of this noun is not that sharp since this documentation was written
in March 1994.
A chromosome, e.g. with a length of 10 000 bases, contains
not only usable (usefull) information.
So useless information is also within the chromosomes.
The chromosome's genes are often fractional.
The segments of genes/chromosomes with usefull information
are called exons[2].
The segments of genes/chromosomes with useless/junk information
are called introns[2].
The fractional genes/chromosomes are spliced (splicing[2]),
before they are transfered and used for the working process,
e.g. the production of protein.
The results of splicing is the usefull meaning information,
non fractional extrons.
So the working process receives just the
(you can call this compressed) usefull information.
Using this generation process, the nature is able to create
new life forces (creatures).
With or without purpose, well, this is a philisophical or
theological matter.
The natural environment defines the viability of it's
creatures.
Darwin's thesis says, that only the best of a population
can prevail, so called "Survival of the Fittest".
This natural selection prefers consequently the best of a
generation. These "best" are able to reproduce itself
more often (than the "worse"),
so they can take care of a better condition of it's progeny.
The next generation is thus more optimized as its predecessor
(may be). So it is possible, that a population creates it's
next optimized version.
This natural evolution principle, describes with
crossing over(symetrical and asymetrical),
mutations, splicing and selection,
is the role model for this genetic algorythm.
Well, I think that I can think, so it may works ;-)
1.2) The Genetic Algorythm
=============================
Under the terms of the natural principle of evolution
a problem should be solved.
The following steps are necessary:
a.) Creation of a random starting population
b.) Setting the normal fitness [0..1]
to the spliced genome using a given fitness function.
This fitness function is problem-orientaded,
and must be define for each problem.
c.) Select the parents according the best fitness
(Survival of the Fittest).
d.) Reproducing using the selekted parents with
crossing over(s).
e.) Drop the not well conditioned members of the population,
to make the population's size finite.
f.) Mutate if necessary (statistically)
g.) continue at point b.)
This look will be terminated, if the choosen target fitness is reached,
or is a choosen number of non optimized generations in a row.
The selection (c) of the parents occurs with the roulette system.
The better individuals receives higher propability as the worse
individuals of the generation.
The probability, that parents are composed outta individuals with a better
fitness is most probably.
But it is not impossible, that parents are composed outta
individuals, which fitness may be worse at the current time.
Herewith it is avoided, that currently questionable worse solutions
are rejected.[1,3,4,6]
The decease within the population can be regulated in two ways.
One way is to create a complete new generation[4], which replaces
the parents generation.
in this case, the birth rate equals one.
The other way is to use a lower birth rate, e.g. 0.6.
In this case 60 percent new individuals are created,
whereby their parents must die.
Because bigamously relationships are allowed for both methods,
after the decease of the parents as much individuals with a worse
fitness must die, as the population's maximum is not exceeded.
1.2.1 Implementation Details
=============================
This nature analogical principle is declared in the file
'GENTECH.H', and defined in the file 'GENTECH.CPP'.
The class 'Chromosom' contains the nukleotides of one chromosome
and u.a. the methods for splicing and mutations.
For details, please have a look at the file 'GENTECH.H'.
The class 'Chromosomen' (many chromosomes -> population)
contains the methods for selection, crossing over and the
whole evolution process.
The fitness method within the class 'Chromosomen'
is a virtuale one.
The user, who want's to define the problem,
must define this one regarding his problem.
It must return a normal floating value within [0..1].
1.2.2 The Encoding of the Problem
=================================
'How do I encode the problem within the chromosomes' ?
Is the basic question, and it's answer the problem's solution.
For example: In the riverproblem (see 1.3.1 below),
the combination of the boat crew must be encoded.
Christian Mueller implemented an encoding which only results in
possible valid crew combinations.
In this case, one nucleotide has the following range of values within [0..4]:
0 : 1 Monk
1 : 2 Monks
2 : 1 Cannibal
3 : 2 Cannibal2
4 : 1 Monk und 1 Cannibal
An encoded (solution) chromosome of this kind, supplies the alternating
boat crew from shore-a to shore b and vice versa.
The implementations of the game itself is contained within the files
'RIVER.[H|CPP]' using the class 'RiverGame'.
The chromosomes encoding of this game is contained within the files
'RIVERGEN.H[CPP]'.
Here you find the class 'RiverProblem' as an derivation of
the class 'Chromosomen'.
1.3) Example Applications
=========================
1.3.1) The Riverproblem
=======================
The riverproblem is that monks and canibals must cross the river in
an way, so that the canibal number is never greater as the monk number
on both riversides - except only canibals exist on one riverside.
The boat is able to transport up to two persons, but one person as the minimum.
1.3.2) The Traveler-Salesman problem
=====================================
The salesman-problem is that the salesman must travel to many towns in
an way, so that he takes the shortest way.
The difference to the river-problem (see river.gen) is that the
solution is not clear ... meaning that the shortest way is unknown.
1.4) Installation / Compilation
================================
you can compile the code with GNU-C++ V >= 2.7.2
under linux with ´make -f makefile.linux´,
or under Cygnus-Gnu-Win32-B19 with ´make -f makefile.cygwin32b19´.
Bibliographie :
================
[1] Holland, John H. : Genetische Algorithmen,
Spektrum der Wissenschaft, September 1992, S.44-51
[2] Chambon, Pierre : Gestueckelte Gene - ein Informations-Mosaik,
Spektrum der Wissenschaft, Juli 1981, S.104-117
[3] Dewdney, A.K. : Genetische Algorithmen,
Computer-Kurzweil, Spektrum-der-Wissenschaft-Verlagsgesellschaft
1988, ISBN 3-922508-50-2, S.68-72
[4] Weckwerth, Guido : Zeugende Zahlen,
MC, Oktober 1993, S.54-58, Januar 1994, S.72-75
[5] Schader, Kuhlins : Programmieren in C++,
Springer-Verlag Heidelberg 1993, ISBN 3-540-56524-8
[6] Schoeneburg, Eberhard : Genetische Algorithmen und Evolutionsstrategien
Addison-Wesley 1994, ISBN 3-89319-495-2
We do wish much fun in natural reproduction method of resolution ;-)
Authors:
Christian Mueller and Sven Goethel
Sven Goethel, Bielefeld den 11.3.1994 (last changes)
Sven Goethel, Bielefeld den 1.4.2001 (translation to english)