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Newsgroups: comp.ai.genetic,comp.answers,news.answers
Path: bloom-beacon.mit.edu!hookup!news.moneng.mei.com!howland.reston.ans.net!EU.net!uknet!cf-cm!cf.cm.ac.uk!David.Beasley
From: David.Beasley@cf.cm.ac.uk (David Beasley)
Subject: FAQ: comp.ai.genetic part 6/6 (A Guide to Frequently Asked Questions)
Message-ID: <part6_764003894@cm.cf.ac.uk>
Followup-To: comp.ai.genetic
Summary: This is part 6 of a <trilogy> entitled "The Hitch-Hiker's Guide to
Evolutionary Computation". A periodically published list of
Frequently Asked Questions (and their answers) about Evolutionary
Algorithms, Life and Everything. It should be read by anyone who
whishes to post to the comp.ai.genetic newsgroup, preferably *before*
posting.
Originator: David.Beasley@cf.cm.ac.uk (David Beasley)
Sender: David.Beasley@cf.cm.ac.uk (David Beasley)
Organization: University of Wales College of Cardiff, Cardiff, WALES, UK.
References: <part5_764003894@cm.cf.ac.uk>
Date: Fri, 18 Mar 94 15:21:45 GMT
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Xref: bloom-beacon.mit.edu comp.ai.genetic:2509 comp.answers:4209 news.answers:16515
Archive-name: ai-faq/genetic/part6
Last-Modified: 3/20/94
Issue: 2.1
TABLE OF CONTENTS OF PART 6
Q21: What are Gray codes, and why are they used?
Q22: What test data is available?
Q42: What is Life all about?
Q42b: Is there a FAQ to this group?
Q98: Are there any patents on EAs?
Q99: A Glossary on EAs?
----------------------------------------------------------------------
Subject: Q21: What are Gray codes, and why are they used?
The correct spelling is "Gray"---not "gray", "Grey", or "grey"---
since Gray codes are named after the Frank Gray who patented their
use for shaft encoders in 1953 [1]. Gray codes actually have a
longer history, and the inquisitive reader may want to look up the
August, 1972, issue of Scientific American, which contains two
articles of interest: one on the origin of binary codes [2], and
another by Martin Gardner on some entertaining aspects of Gray
codes [3]. Other references containing descriptions of Gray codes
and more modern, non-GA, applications include the second edition of
Numerical Recipes [4], Horowitz and Hill [5], Kozen [6], and
Reingold [7].
A Gray code represents each number in the sequence of integers
{0...2^N-1} as a binary string of length N in an order such that
adjacent integers have Gray code representations that differ in only
one bit position. Marching through the integer sequence therefore
requires flipping just one bit at a time. Some call this defining
property of Gray codes the "adjacency property" [8].
Example (N=3): The binary coding of {0...7} is {000, 001, 010, 011,
100, 101, 110, 111}, while one Gray coding is {000, 001, 011, 010,
110, 111, 101, 100}. In essence, a Gray code takes a binary sequence
and shuffles it to form some new sequence with the adjacency
property. There exist, therefore, multiple Gray codings or any
given N. The example shown here belongs to a class of Gray codes
that goes by the fancy name "binary-reflected Gray codes". These are
the most commonly seen Gray codes, and one simple scheme for
generationg such a Gray code sequence says, "start with all bits zero
and successively flip the right-most bit that produces a new string."
Hollstien [9] investigated the use of GAs for optimizing functions of
two variables and claimed that a Gray code representation worked
slightly better than the binary representation. He attrributed this
difference to the adjacency property of Gray codes. Notice in the
above example that the step from three to four requires the flipping
of all the bits in the binary representation. In general, adjacent
integers in the binary representaion often lie many bit flips apart.
This fact makes it less likely that a MUTATION operator can effect
small changes for a binary-coded INDIVIDUAL.
A Gray code representation seems to improve a MUTATION operator's
chances of making incremental improvements, and a close examination
suggests why. In a binary-coded string of length N, a single
mutation in the most significant bit (MSB) alters the number by
2^(N-1). In a Gray-coded string, fewer mutations lead to a change
this large. The user of Gray codes does, however, pay a price for
this feature: those "fewer mutations" lead to much larger changes.
In the Gray code illustrated above, for example, a single mutation of
the left-most bit changes a zero to a seven and vice-versa, while the
largest change a single mutation can make to a corresponding binary-
coded INDIVIDUAL is always four. One might still view this aspect of
Gray codes with some favor: most mutations will make only small
changes, while the occasional mutation that effects a truly big
change may initiate EXPLORATION of an entirely new region in the
space of CHROMOSOMEs.
The algorithm for converting between the binary-reflected Gray code
described above and the standard binary code turns out to be
surprisingly simple to state. First label the bits of a binary-coded
string B[i], where larger i's represent more significant bits, and
similarly label the corresponding Gray-coded string G[i]. We convert
one to the other as follows: Copy the most significant bit. Then
for each smaller i do either G[i] = XOR(B[i+1], B[i])---to convert
binary to Gray---or B[i] = XOR(B[i+1], G[i])---to convert Gray to
binary.
One may easily implement the above algorithm in C. Imagine you do
something like
typedef unsigned short ALLELE;
and then use type "allele" for each bit in your CHROMOSOME, then the
following two functions will convert between binary and Gray code
representations. You must pass them the address of the high-order
bits for each of the two strings as well as the length of each
string. (See the comment statements for examples.) NB: These
functions assume a chromosome arranged as shown in the following
illustration.
index: C[9] C[0]
*-----------------------------------------------------------*
Char C: | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 |
*-----------------------------------------------------------*
^^^^^ ^^^^^
high-order bit low-order bit
C CODE
/* Gray <==> binary conversion routines */
/* written by Dan T. Abell, 7 October 1993 */
/* please send any comments or suggestions */
/* to dabell@quark.umd.edu */
void gray_to_binary (Cg, Cb, n)
/* convert chromosome of length n from */
/* Gray code to binary representation */
allele *Cg,*Cb;
int n;
{
int j;
*Cb = *Cg; /* copy the high-order bit */
for (j = 0; j < n; j++) {
Cb--; Cg--; /* for the remaining bits */
*Cb= *(Cb+1)^*Cg; /* do the appropriate XOR */
}
}
void binary_to_gray(Cb, Cg, n)
/* convert chromosome of length n from */
/* binary to Gray code representation */
allele *Cb, *Cg;
int n;
{
int j;
*Cg = *Cb; /* copy the high-order bit */
for (j = 0; j < n; j++) {
Cg--; Cb--; /* for the remaining bits */
*Cg= *(Cb+1)^*Cb; /* do the appropriate XOR */
}
}
References
[1] F. Gray, "Pulse Code Communication", U. S. Patent 2 632 058,
March 17, 1953.
[2] F. G. Heath, "Origins of the Binary Code", Scientific American
v.227,n.2 (August, 1972) p.76.
[3] Martin Gardner, "Mathematical Games", Scientific American
v.227,n.2 (August, 1972) p.106.
[4] William H. Press, et al., Numerical Recipes in C, Second Edition
(Cambridge University Press, 1992).
[5] Paul Horowitz and Winfield Hill, The Art of Electronics, Second
Edition (Cambridge University Press, 1989).
[6] Dexter Kozen, The Design and Analysis of Algorithms (Springer-
Verlag, New York, NY, 1992).
[7] Edward M. Reingold, et al., Combinatorial Algorithms (Prentice
Hall, Englewood Cliffs, NJ, 1977).
[8] David E. Goldberg, GENETIC ALGORITHMs in Search, OPTIMIZATION,
and Machine Learning (Addison-Wesley, Reading, MA, 1989).
[9] R. B. Hollstien, Artificial Genetic Adaptation in Computer
Control Systems (PhD thesis, University of Michigan, 1971).
------------------------------
Subject: Q22: What test data is available?
TSP DATA
There is a TSP library (TSPLIB) available which has many solved and
semi-solved TSPs and different variants. The library is maintained by
Gerhard Reinelt <reinelt@ares.iwr.Uni-Heidelberg.de>. It is available
from various FTP sites, including: softlib.cs.rice.edu:/pub/
OTHER DATA
Information about test problems for any of the problem areas listed
below can be obtained by emailing o.rlibrary@ic.ac.uk with the body
of the email message being just the word info
Problem areas: Assignment problem, Crew scheduling, Data envelopment
analysis, Generalised assignment problem, Integer programming, Linear
programming, Location problems, Multiple knapsack problem, Quadratic
assignment problem, Resource constrained shortest path, Scheduling
(flow shop, job shop, open shop), Set covering, Set partitioning,
Steiner problems, TRAVELLING SALESMAN PROBLEM, Two-dimensional
cutting problems, Vehicle routing problems
------------------------------
Subject: Q42: What is Life all about?
42
References
Adams, D. (1979) "The Hitch Hiker's Guide to the Galaxy", London: Pan
Books.
Adams, D. (1980) "The Restaurant at the End of the Universe", London:
Pan Books.
Adams, D. (1982) "Life, the Universe and Everything", London: Pan
Books.
Adams, D. (1984) "So long, and thanks for all the Fish", London: Pan
Books.
Adams, D. (1992) "Mostly Harmless", London: Heinemann.
------------------------------
Subject: Q42b: Is there a FAQ to this group?
Yes.
------------------------------
Subject: Q98: Are there any patents on EAs?
Process patents have been issued both for the Bucket Brigade
Algorithm (BBA) in CLASSIFIER SYSTEMs: U.S. patent #[..] (to John
Holland) and for GP: U.S. patent #4,935,877 (to John Koza).
This FAQ does not attempt to provide legal advice. However, use of
the Lisp code in the book [KOZA92] is freely licensed for academic
use. Although those wishing to make commercial use of any process
should obviously consult any patent holders in question, it is pretty
clear that it's not in anyone's best interests to stifle GA/GP
research and/or development. Commercial licenses much like those used
for CAD software can presumably be obtained for the use of these
processes where necessary.
Jarmo Alander's massive bibliography of GAs (see Q10.8) includes a
(probably) complete list of all currently know patents. There is
also a periodic posting on comp.ai.neural-nets by Gregory Aharonian
<srctran@world.std.com> about patents on Artificial Neural Networks
(ANNs).
------------------------------
Subject: Q99: A Glossary on EAs?
1/5 SUCCESS RULE:
Derived by I. Rechenberg, the suggestion that when Gaussian
MUTATIONs are applied to real-valued vectors in searching for
the minimum of a function, a rule-of-thumb to attain good rates
of error convergence is to adapt the STANDARD DEVIATION of
mutations to generate one superior solution out of every five
attempts.
A
ADAPTIVE BEHAVIOUR:
"...underlying mechanisms that allow animals, and potentially,
ROBOTs to adapt and survive in uncertain environments" --- Meyer
& Wilson (1991), [SAB90]
AI: See ARTIFICIAL INTELLIGENCE.
ALIFE:
See ARTIFICIAL LIFE.
ALLELE:
(biol) Each GENE is able to occupy only a particular region of a
CHROMOSOME, it's locus. At any given locus there may exist, in
the POPULATION, alternative forms of the gene. These alternative
are called alleles of one another.
(EC) The value of a GENE. Hence, for a binary representation,
each gene may have an ALLELE of 0 or 1.
ARTIFICIAL INTELLIGENCE:
"...the study of how to make computers do things at which, at
the moment, people are better" --- Elaine Rich (1988)
ARTIFICIAL LIFE:
Term coined by Christopher G. Langton for his 1987 [ALIFEI]
conference. In the preface of the proceedings he defines ALIFE
as "...the study of simple computer generated hypothetical life
forms, i.e. life-as-it-could-be."
B
BUILDING BLOCK:
(EC) A small, tightly clustered group of GENEs which have co-
evolved in such a way that their introduction into any
CHROMOSOME will be likely to give increased FITNESS to that
chromosome.
The "building block hypothesis" [GOLD89] states that GAs find
solutions by first finding as many BUILDING BLOCKs as possible,
and then combining them together to give the highest FITNESS.
C
CENTRAL DOGMA:
(biol) The dogma that nucleic acids act as templates for the
synthesis of proteins, but never the reverse. More generally,
the dogma that GENEs exert an influence over the form of a body,
but the form of a body is never translated back into genetic
code: acquired characteristics are not inherited. cf LAMARCKISM.
(GA) The dogma that the behaviour of the algorithm must be
analysed using the SCHEMA THEOREM.
(life in general) The dogma that this all is useful in a way.
"You guys have a dogma. A certain irrational set of believes.
Well, here's my irrational set of beliefs. Something that
works."
--- Rodney A. Brooks, [LEVY92]
CFS: See CLASSIFIER SYSTEM.
CHROMOSOME:
(biol) One of the chains of DNA found in cells. CHROMOSOMEs
contain GENEs, each encoded as a subsection of the DNA chain.
Chromosomes are usually present in all cells in an organism,
even though only a minority of them will be active in any one
cell.
(EC) A datastructure which holds a `string' of task parameters,
or GENEs. This may be stored, for example, as a binary bit-
string, or an array of integers.
CLASSIFIER SYSTEM:
A system which takes a (set of) inputs, and produces a (set of)
outputs which indicate some classification of the inputs. An
example might take inputs from sensors in a chemical plant, and
classify them in terms of: 'running ok', 'needs more water',
'needs less water', 'emergency'. See Q1.4 for more information.
COMBINATORIAL OPTIMIZATION:
Some tasks involve combining a set of entities in a specific way
(e.g. the task of building a house). A general combinatorial
task involves deciding (a) the specifications of those entities
(e.g. what size, shape, material to make the bricks from), and
(b) the way in which those entities are brought together (e.g.
the number of bricks, and their relative positions). If the
resulting combination of entities can in some way be given a
FITNESS score, then COMBINATORIAL OPTIMIZATION is the task of
designing a set of entities, and deciding how they must be
configured, so as to give maximum fitness. cf ORDER-BASED
PROBLEM.
COMMA STRATEGY:
Notation originally proposed in EVOLUTION STRATEGIEs, when a
POPULATION of "mu" PARENTs generates "lambda" OFFSPRING and the
mu parents are discarded, leving only the lambda INDIVIDUALs to
compete directly. Such a process is written as a (mu,lambda)
search. The process of only competing offspring then is a
"comma strategy." cf. PLUS STRATEGY.
CONVERGED:
A GENE is said to have CONVERGED when 95% of the CHROMOSOMEs in
the POPULATION all contain the same ALLELE for that gene. In
some circumstances, a population can be said to have converged
when all genes have converged. (However, this is not true of
populations containing multiple SPECIES, for example.)
Most people use "convergence" fairly loosely, to mean "the GA
has stopped finding new, better solutions". Of course, if you
wait long enough, the GA will *eventually* find a better
solution (unless you have already found the global optimum).
What people really mean is "I'm not willing to wait for the GA
to find a new, better solution, because I've already waited
longer than I wanted to and it hasn't improved in ages."
CONVERGENCE VELOCITY:
The rate of error reduction.
COOPERATION:
The behavior of two or more INDIVIDUALs acting to increase the
gains of all participating individuals.
CROSSOVER:
(EC) A REPRODUCTION OPERATOR which forms a new CHROMOSOME by
combining parts of each of two `parent' chromosomes. The
simplest form is single-point CROSSOVER, in which an arbitrary
point in the chromosome is picked. All the information from
PARENT A is copied from the start up to the crossover point,
then all the information from parent B is copied from the
crossover point to the end of the chromosome. The new chromosome
thus gets the head of one parent's chromosome combined with the
tail of the other. Variations exist which use more than one
crossover point, or combine information from parents in other
ways.
(biol) A complicated process whereby CHROMOSOMEs, while
engaged in the production of GAMETEs, exchange portions of
genetic material. The result is that an almost infinite variety
of gametes may be produced. Subsequently, during sexual
REPRODUCTION, male and female gametes (i.e. sperm and ova) fuse
to produce a new cell with a complete set of DIPLOID
CHROMOSOMEs.
In [HOLLAND92] the sentence "When sperm and ova fuse, matching
CHROMOSOMEs line up with one another and then cross over partway
along their length, thus swapping genetic material" is thus
wrong, since these two activities occur in different parts of
the life cycle. [eds note: If sexual REPRODUCTION (the Real
Thing) worked like in GAs, then Holland would be right, but as
we all know, it's not the case. We just encountered a
Freudian slip of a Grandmaster. BTW: even the German
translation of this article has this "bug", although it's
well-hidden by the translator.]
CS: See CLASSIFIER SYSTEM.
D
DARWINISM:
(biol) Theory of EVOLUTION, proposed by Darwin, that evolution
comes about through random variation of heritable
characteristics, coupled with natural SELECTION (survival of the
fittest). A physical mechanism for this, in terms of GENEs and
CHROMOSOMEs, was discovered many years later. cf LAMARCKISM.
(EC) Theory which inspired all branches of EC.
DECEPTION:
The condition where the combination of good BUILDING BLOCKs
leads to reduced FITNESS, rather than increased fitness.
Proposed by [GOLD89] as a reason for the failure of GAs on many
tasks.
DIPLOID CHROMOSOME:
(biol) A CHROMOSOME which consists of a pair of homologous
chromosomes, i.e. two chromosomes containing the same GENEs in
the same sequence. In sexually reproducing SPECIES, the genes
in one of the chromosomes will have been inherited from the
father's GAMETE (sperm), while the genes in the other chromosome
are from the mother's gamete (ovum).
DNA: (biol) Deoxyribonucleic Acid, a double stranded macromolecule of
helical structure (comparable to a spiral staircase). Both
single strands are linear, unbranched nucleic acid molecules
build up from alternating deoxyribose (sugar) and phosphate
molecules. Each deoxyribose part is coupled to a nucleotide
base, which is responsible for establishing the connection to
the other strand of the DNA. The 4 nucleotide bases Adenine
(A), Thymine (T), Cytosine (C) and Guanine (G) are the alphabet
of the genetic information. The sequences of these bases in the
DNA molecule determines the building plan of any organism. [eds
note: suggested reading: James D. Watson (1968) "The Double
Helix", London: Weidenfeld and Nicholson]
(literature) Douglas Noel Adams, contemporary Science Fiction
comedy writer. Published "The Hitch-Hiker's Guide to the Galaxy"
when he was 25 years old, which made him one of the currently
most successful British authors. [eds note: interestingly
Watson was also 25 years old, when he discovered the DNA; both
events are probably not interconnected; you might also want to
look at: Neil Gaiman's (1987) "DON'T PANIC -- The Official
Hitch-Hiker's Guide to the Galaxy companion", and of course get
your hands on the wholly remarkable FAQ in alt.fan.douglas-
adams]
DNS: (biol) Desoxyribonukleinsaeure, German for DNA.
(comp) The Domain Name System, a distributed database system for
translating computer names (e.g. lumpi.informatik.uni-
dortmund.de) into numeric Internet, i.e. IP-addresses
(129.217.36.140) and vice-versa. DNS allows you to hook into
the net without remembering long lists of numeric references,
unless your system administrator has incorrectly set-up your
site's system.
E
EC: See EVOLUTIONARY COMPUTATION.
ENCORE:
The EvolutioNary Computation REpository Network. An network of
anonymous FTP sites holding all manner of interesting things
related to EC. The default "EClair" node is at the Santa Fe
Institute: alife.santafe.edu:/pub/USER-AREA/EC/ mirror sites
include The Chinese University of Hong Kong:
ftp.cs.cuhk.hk:/pub/EC/ Other nodes are planned. See Q15.3 for
more information.
ENVIRONMENT:
(biol) That which surrounds an organism. Can be 'physical'
(abiotic), or biotic. In both, the organism occupies a NICHE
which influences its FITNESS within the total ENVIRONMENT. A
biotic environment may present frequency-dependent fitness
functions within a POPULATION, that is, the fitness of an
organism's behaviour may depend upon how many others are also
doing it. Over several GENERATIONs, biotic environments may
foster co-evolution, in which fitness is determined with
SELECTION partly by other SPECIES.
EP: See EVOLUTIONARY PROGRAMMING.
EPISTASIS:
(biol) A "masking" or "switching" effect among GENEs. A biology
textbook says: "A gene is said to be epistatic when its presence
suppresses the effect of a gene at another locus. Epistatic
genes are sometimes called inhibiting genes because of their
effect on other genes which are described as hypostatic."
(EC) When EC researchers use the term EPISTASIS, they are
generally referring to any kind of strong interaction among
GENEs, not just masking effects. A possible definition is:
EPISTASIS is the interaction between different GENEs in a
CHROMOSOME. It is the extent to which the contribution to
FITNESS of one gene depends on the values of other genes.
Problems with little or no EPISTASIS are trivial to solve
(hillclimbing is sufficient). But highly epistatic problems are
difficult to solve, even for GAs. High epistasis means that
BUILDING BLOCKs cannot form, and there will be DECEPTION.
ES: See EVOLUTION STRATEGY.
ESS: See EVOLUTIONARILY STABLE STRATEGY.
EVOLUTION:
That process of change which is assured given a reproductive
POPULATION in which there are (1) varieties of INDIVIDUALs, with
some varieties being (2) heritable, of which some varieties (3)
differ in FITNESS (reproductive success).
"Don't assume that all people who accept EVOLUTION are atheists"
--- Talk.origin FAQ
EVOLUTION STRATEGIE:
EVOLUTION STRATEGY:
A type of evolutionary algorithm developed in the early 1960s in
Germany. It employs real-coded parameters, and in its original
form, it relied on MUTATION as the search operator, and a
POPULATION size of one. Since then it has evolved to share many
features with GENETIC ALGORITHMs. See Q1.3 for more
information.
EVOLUTIONARILY STABLE STRATEGY:
A strategy that does well in a POPULATION dominated by the same
strategy. (cf Maynard Smith, 1974)
EVOLUTIONARY COMPUTATION:
Encompasses methods of simulating EVOLUTION on a computer. The
term is relatively new and represents an effort bring together
researchers who have been working in closely related fields but
following different paradigms. The field is now seen as
including research in GENETIC ALGORITHMs, EVOLUTION STRATEGIEs,
EVOLUTIONARY PROGRAMMING, ARTIFICIAL LIFE, and so forth. For a
good overview see the editorial introduction to Vol. 1, No. 1 of
"Evolutionary Computation" (MIT Press, 1993). That, along with
the papers in the issue, should give you a good idea of
representative research.
EVOLUTIONARY PROGRAMMING:
An evolutionay algorithm developed in the mid 1960s. It is a
stochastic OPTIMIZATION strategy, which is similar to GENETIC
ALGORITHMs, but dispenses with both "genomic" representations
and with CROSSOVER as a REPRODUCTION OPERATOR. See Q1.2 for
more information.
EVOLUTIONARY SYSTEMS:
A process or system which employs the evolutionary dynamics of
REPRODUCTION, MUTATION, competition and SELECTION. The specific
forms of these processes are irrelevant to a system being
described as "evolutionary."
EXPECTANCY:
Or expected value. Pertaining to a random variable X, for a
continuous random variable, the expected value is:
E(X) = INTEGRAL(-inf, inf) [X f(X) dX].
The discrete expectation takes a similar form using a summation
instead of an integral.
EXPLOITATION:
When traversing a SEARCH SPACE, EXPLOITATION is the process of
using information gathered from previously visited points in the
search space to determine which places might be profitable to
visit next. An example is hillclimbing, which investigates
adjacent points in the search space, and moves in the direction
giving the greatest increase in FITNESS. Exploitation
techniques are good at finding local maxima.
EXPLORATION:
The process of visiting entirely new regions of a SEARCH SPACE,
to see if anything promising may be found there. Unlike
EXPLOITATION, EXPLORATION involves leaps into the unknown.
Problems which have many local maxima can sometimes only be
solved by this sort of random search.
F
FAQ: Frequently Asked Questions. See definition given near the top of
part 1.
FITNESS:
(biol) Loosely: adaptedness. Often measured as, and sometimes
equated to, relative reproductive success. Also proportional to
expected time to extinction. "The fit are those who fit their
existing ENVIRONMENTs and whose descendants will fit future
environments." (J. Thoday, "A Century of Darwin", 1959).
Accidents of history are relevant.
(EC) A value assigned to an INDIVIDUAL which reflects how well
the INDIVIDUAL solves the task in hand. A "fitness function" is
used to map a CHROMOSOME to a FITNESS value.
FUNCTION OPTIMIZATION:
For a function which takes a set of N input parameters, and
returns a single output value, F, FUNCTION OPTIMIZATION is the
task of finding the set(s) of parameters which produce the
maximum (or minimum) value of F. Function OPTIMIZATION is a type
of VALUE-BASED PROBLEM.
FTP: File Transfer Protocol. A system which allows the retrieval of
files stored on a remote computer. Basic FTP requires a password
before access can be gained to the remote computer. Anonymous
FTP does not require a special password: after giving
"anonymous" as the user name, any password will do (typically,
you give your email address at this point). Files available by
FTP are specified as <ftp-site-name>:<the-complete-filename> See
Q15.5.
FUNCTION SET:
(GP) The set of operators used in GP. These functions label the
internal (non-leaf) points of the parse trees that represent the
programs in the POPULATION. An example FUNCTION SET might be
{+, -, *}.
G
GA: See GENETIC ALGORITHM.
GAME THEORY:
A mathematical theory originally developed for human games, and
generalized to human economics and military strategy, and to
EVOLUTION in the theory of EVOLUTIONARILY STABLE STRATEGY. GAME
THEORY comes into it's own wherever the optimum policy is not
fixed, but depends upon the policy which is statistically most
likely to be adopted by opponents.
GAMETE:
(biol) Cells which carry genetic information from their PARENTs
for the purposes of sexual REPRODUCTION. In animals, male
GAMETEs are called sperm, female gametes are called ova. Gametes
have HAPLOID CHROMOSOMEs.
GAUSSIAN DISTRIBUTION:
See NORMALLY DISTRIBUTED.
GENE:
(EC) A subsection of a CHROMOSOME which (usually) encodes the
value of a single parameter.
(biol) A unit of heredity. May be defined in different ways for
different purposes. Molecular biologists sometimes use it in a
more abstract sense. Following Williams (cf Q10.7) `any
hereditary information for which there is a favorable or
unfavorable SELECTION bias equal to several or many times its
rate of endogenous change.' cf CHROMOSOME.
GENE-POOL:
The whole set of GENEs in a breeding POPULATION. The metaphor
on which the term is based de-emphasizes the undeniable fact
that genes actually go about in discrete bodies, and emphasizes
the idea of genes flowing about the world like a liquid.
"Everybody out of the GENE-POOL, now!"
--- Author prefers to be anonymous
GENERATION:
(EC) An iteration of the measurement of FITNESS and the creation
of a new POPULATION by means of REPRODUCTION OPERATORs.
GENETIC ALGORITHM:
A type of EVOLUTIONARY COMPUTATION devised by John Holland
[HOLLAND92]. A model of machine learning that uses a
genetic/evolutionary metaphor. Implementations typically use
fixed-length character strings to represent their genetic
information, together with a POPULATION of INDIVIDUALs which
undergo CROSSOVER and MUTATION in order to find interesting
regions of the SEARCH SPACE. See Q1.1 for more information.
GENETIC DRIFT:
Changes in gene/allele frequencies in a POPULATION over many
GENERATIONs, resulting from chance rather than SELECTION.
Occurs most rapidly in small populations. Can lead to some
ALLELEs becoming `extinct', thus reducing the genetic
variability in the population.
GENETIC PROGRAMMING:
GENETIC ALGORITHMs applied to programs. GENETIC PROGRAMMING is
more expressive than fixed-length character string GAs, though
GAs are likely to be more efficient for some classes of
problems. See Q1.5 for more information.
GENETIC OPERATOR:
A search operator acting on a coding structure that is analogous
to a GENOTYPE of an organism (e.g. a CHROMOSOME).
GENOTYPE:
The genetic composition of an organism: the information
contained in the GENOME.
GENOME:
The entire collection of GENEs (and hence CHROMOSOMEs) possessed
by an organism.
GLOBAL OPTIMIZATION:
The process by which a search is made for the extremum (or
extrema) of a functional which, in EVOLUTIONARY COMPUTATION,
corresponds to the FITNESS or error function that is used to
assess the PERFORMANCE of any INDIVIDUAL.
GP: See GENETIC PROGRAMMING.
H
HAPLOID CHROMOSOME:
(biol) A CHROMOSOME consisting of a single sequence of GENEs.
These are found in GAMETEs. cf DIPLOID CHROMOSOME.
In EC, it is usual for CHROMOSOMEs to be haploid.
HARD SELECTION:
SELECTION acts on competing INDIVIDUALs. When only the best
available individuals are retained for generating future
progeny, this is termed "hard selection." In contrast, "soft
selection" offers a probabilistic mechanism for maitaining
individuals to be PARENTs of future progeny despite possessing
relatively poorer objective values.
I
INDIVIDUAL:
A single member of a POPULATION. In EC, each INDIVIDUAL
contains a CHROMOSOME (or, more generally, a GENOME) which
represents a possible solution to the task being tackled, i.e. a
single point in the SEARCH SPACE. Other information is usually
also stored in each individual, e.g. its FITNESS.
INVERSION:
(EC) A REORDERING operator which works by selecting two cut
points in a CHROMOSOME, and reversing the order of all the GENEs
between those two points.
L
LAMARCKISM:
Theory of EVOLUTION which preceded Darwin's. Lamarck believed
that evolution came about through the inheritance of acquired
characteristics. That is, the skills or physical features which
an INDIVIDUAL acquires during its lifetime can be passed on to
its OFFSPRING. Although Lamarckian inheritance does not take
place in nature, the idea has been usefully applied by some in
EC. cf DARWINISM.
LCS: See LEARNING CLASSIFIER SYSTEM.
LEARNING CLASSIFIER SYSTEM:
A CLASSIFIER SYSTEM which "learns" how to classify its inputs.
This often involves "showing" the system many examples of input
patterns, and their corresponding correct outputs. See Q1.4 for
more information.
M
MIGRATION:
The transfer of (the GENEs of) an INDIVIDUAL from one SUB-
POPULATION to another.
MOBOT:
MOBile ROBOT. cf ROBOT.
MUTATION:
(EC) a REPRODUCTION OPERATOR which forms a new CHROMOSOME by
making (usually small) alterations to the values of GENEs in a
copy of a single, PARENT chromosome.
N
NICHE:
(biol) In natural ecosystems, there are many different ways in
which animals may survive (grazing, hunting, on the ground, in
trees, etc.), and each survival strategy is called an
"ecological niche." SPECIES which occupy different NICHEs (e.g.
one eating plants, the other eating insects) may coexist side by
side without competition, in a stable way. But if two species
occupying the same niche are brought into the same area, there
will be competition, and eventually the weaker of the two
species will be made (locally) extinct. Hence diversity of
species depends on them occupying a diversity of niches (or on
geographical separation).
(EC) In EC, we often want to maintain diversity in the
POPULATION. Sometimes a FITNESS function may be known to be
multimodal, and we want to locate all the peaks. We may consider
each peak in the fitness function as analogous to a NICHE. By
applying techniques such as fitness sharing (Goldberg &
Richardson, [ICGA87]), the population can be prevented from
converging on a single peak, and instead stable SUB-POPULATIONs
form at each peak. This is analogous to different SPECIES
occupying different niches. See also SPECIES, SPECIATION.
NORMALLY DISTRIBUTED:
A random variable is NORMALLY DISTRIBUTED if its density
function is described as
f(x) = 1/sqrt(2*pi*sqr(sigma)) * exp(-0.5*(x-mu)*(x-
mu)/sqr(sigma))
where mu is the mean of the random variable x and sigma is the
STANDARD DEVIATION.
O
OBJECT VARIABLES:
Parameters that are directly involved in assessing the relative
worth of an INDIVIDUAL.
OFFSPRING:
An INDIVIDUAL generated by any process of REPRODUCTION.
OPTIMIZATION:
The process of iteratively improving the solution to a problem
with respect to a specified objective function.
ORDER-BASED PROBLEM:
A problem where the solution must be specified in terms of an
arrangement (e.g. a linear ordering) of specific items, e.g.
TRAVELLING SALESMAN PROBLEM, computer process scheduling.
ORDER-BASED PROBLEMs are a class of COMBINATORIAL OPTIMIZATION
problems in which the entities to be combined are already
determined. cf VALUE-BASED PROBLEM.
ONTOGENESIS:
Refers to a single organism, and means the life span of an
organism from it's birth to death. cf PHYLOGENESIS.
P
PANMICTIC POPULATION:
(EC, biol) A mixed POPULATION. A population in which any
INDIVIDUAL may be mated with any other individual with a
probability which depends only on FITNESS. Most conventional
evolutionary algorithms have PANMICTIC POPULATIONs.
The opposite is a POPULATION divided into groups known as SUB-
POPULATIONs, where INDIVIDUALs may only mate with others in the
same sub-population. cf SPECIATION.
PARENT:
An INDIVIDUAL which takes part in REPRODUCTION to generate one
or more other individuals, known as OFFSPRING, or children.
PERFORMANCE:
cf FITNESS.
PHENOTYPE:
The expressed traits of an INDIVIDUAL.
PHYLOGENESIS:
Refers to a POPULATION of organisms. The life span of a
POPULATION of organisms from pre-historic times until today. cf
ONTOGENESIS.
PLUS STRATEGY:
Notation originally proposed in EVOLUTION STRATEGIEs, when a
POPULATION of "mu" PARENTs generates "lambda" OFFSPRING and all
mu and lambda INDIVIDUALs compete directly, the process is
written as a (mu+lambda) search. The process of competing all
parents and offspring then is a "plus strategy." cf. COMMA
STRATEGY.
POPULATION:
A group of INDIVIDUALs which may interact together, for example
by mating, producing OFFSPRING, etc. Typical POPULATION sizes in
EC range from 1 (for certain EVOLUTION STRATEGIEs)
to many thousands (for GENETIC PROGRAMMING). cf SUB-
POPULATION.
R
RECOMBINATION:
cf CROSSOVER.
REORDERING:
(EC) A REORDERING operator is a REPRODUCTION OPERATOR which
changes the order of GENEs in a CHROMOSOME, with the hope of
bringing related genes closer together, thereby facilitating the
production of BUILDING BLOCKs. cf INVERSION.
REPRODUCTION:
(biol, EC) The creation of a new INDIVIDUAL from two PARENTs
(sexual REPRODUCTION). Asexual reproduction is the creation of
a new individual from a single parent.
REPRODUCTION OPERATOR:
(EC) A mechanism which influences the way in which genetic
information is passed on from PARENT(s) to OFFSPRING during
REPRODUCTION. REPRODUCTION OPERATORs fall into three broad
categories: CROSSOVER, MUTATION and REORDERING operators.
REQUISITE VARIETY:
In GENETIC ALGORITHMs, when the POPULATION fails to have a
"requisite variety" CROSSOVER will no longer be a useful search
operator because it will have a propensity to simply regenerate
the PARENTs.
ROBOT:
"The Encyclopedia Galactica defines a ROBOT as a mechanical
apparatus designed to do the work of man. The marketing division
of the Sirius Cybernetics Corporation defines a robot as `Your
Plastic Pal Who's Fun To Be With'."
--- Douglas Adams (1979)
S
SAFIER:
An EVOLUTIONARY COMPUTATION FTP Repository, now defunct.
Superceeded by ENCORE.
SCHEMA:
A pattern of GENE values in a CHROMOSOME, which may include
`dont care' states. Thus in a binary chromosome, each SCHEMA
(plural schemata) can be specified by a string of the same
length as the chromosome, with each character one of {0, 1, #}.
A particular chromosome is said to `contain' a particular schema
if it matches the schema (e.g. chromosome 01101 matches schema
#1#0#).
The `order' of a SCHEMA is the number of non-dont-care positions
specified, while the `defining length' is the distance between
the furthest two non-dont-care positions. Thus #1#0# is of order
2 and defining length 3.
SCHEMA THEOREM:
Theorem devised by Holland [HOLLAND92] to explain the behaviour
of GAs. In essence, it says that a GA gives exponentially
increasing reproductive trials to above average schemata.
Because each CHROMOSOME contains a great many schemata, the rate
of SCHEMA processing in the POPULATION is very high, leading to
a phenomenon known as implicit parallelism. This gives a GA with
a population of size N a speedup by a factor of N cubed,
compared to a random search.
SEARCH SPACE:
If the solution to a task can be represented by a set of N real-
valued parameters, then the job of finding this solution can be
thought of as a search in an N-dimensional space. This is
referred to simply as the SEARCH SPACE. More generally, if the
solution to a task can be represented using a representation
scheme, R, then the search space is the set of all possible
configurations which may be represented in R.
SEARCH OPERATORS:
Processes used to generate new INDIVIDUALs to be evaluated.
SEARCH OPERATORS in GENETIC ALGORITHMs are typically based on
CROSSOVER and point MUTATION. Search operators in EVOLUTION
STRATEGIEs and EVOLUTIONARY PROGRAMMING typically follow from
the representation of a solution and often involve Gaussian or
lognormal perturbations when applied to real-valued vectors.
SELECTION:
The process by which some INDIVIDUALs in a POPULATION are chosen
for REPRODUCTION, typically on the basis of favoring individuals
with higher FITNESS.
SELF-ADAPTATION:
The inclusion of a mechanism not only to evolve the OBJECT
VARIABLES of a solution, but simultaneously to evolve
information on how each solution will generate new OFFSPRING.
SIMULATION:
The act of modeling a natural process.
SOFT SELECTION:
The mechanism which allows inferior INDIVIDUALs in a POPULATION
a non-zero probability of surviving into future GENERATIONs.
See HARD SELECTION.
SPECIATION:
(biol) The process whereby a new SPECIES comes about. The most
common cause of SPECIATION is that of geographical isolation. If
a SUB-POPULATION of a single species is separated geographically
from the main POPULATION for a sufficiently long time, their
GENEs will diverge (either due to differences in SELECTION
pressures in different locations, or simply due to GENETIC
DRIFT). Eventually, genetic differences will be so great that
members of the sub-population must be considered as belonging to
a different (and new) species.
SPECIATION is very important in evolutionary biology. Small SUB-
POPULATIONs can evolve much more rapidly than a large POPULATION
(because genetic changes don't take long to become fixed in the
population). Sometimes, this EVOLUTION will produce superior
INDIVIDUALs which can outcompete, and eventually replace the
SPECIES of the original, main population.
(EC) Techniques analogous to geographical isolation are used in
a number of GAs. Typically, the POPULATION is divided into SUB-
POPULATIONs, and INDIVIDUALs are only allowed to mate with
others in the same sub-population. (A small amount of MIGRATION
is performed.)
This produces many SUB-POPULATIONs which differ in their
characteristics, and may be referred to as different "species".
This technique can be useful for finding multiple solutions to a
problem, or simply maintaining diversity in the SEARCH SPACE.
Most biology/genetics textbooks contain information on
SPECIATION. A more detailed account can be found in "Genetics,
Speciation and the Founder Principle", L.V. Giddings, K.Y.
Kaneshiro and W.W. Anderson (Eds.), Oxford University Press
1989.
SPECIES:
(biol) There is no universally-agreed firm definition of a
SPECIES. A species may be roughly defined as a collection of
living creatures, having similar characteristics, which can
breed together to produce viable OFFSPRING similar to their
PARENTs. Members of one species occupy the same ecological
NICHE. (Members of different species may occupy the same, or
different niches.)
(EC) In EC the definition of "species" is less clear, since
generally it is always possible for a pair INDIVIDUALs to breed
together. It is probably safest to use this term only in the
context of algorithms which employ explicit SPECIATION
mechanisms.
(biol) The existence of different SPECIES allows different
ecological NICHEs to be exploited. Furthermore, the existence of
a variety of different species itself creates new niches, thus
allowing room for further species. Thus nature bootstraps itself
into almost limitless complexity and diversity.
Conversely, the domination of one, or a small number of SPECIES
reduces the number of viable NICHEs, leads to a decline in
diversity, and a reduction in the ability to cope with new
situations.
"Give any one species too much rope, and they'll fuck it up"
--- Roger Waters, "Amused to Death", 1992
STANDARD DEVIATION:
A measurement for the spread of a set of data; a measurement for
the variation of a random variable.
STATISTICS:
Descriptive measures of data; a field of mathematics that uses
probability theory to gain insight into systems' behavior.
STEPSIZE:
Typically, the average distance in the appropriate space between
a PARENT and its OFFSPRING.
STRATEGY VARIABLE:
Evolvable parameters that relate the distribution of OFFSPRING
from a PARENT.
SUB-POPULATION:
A POPULATION may be sub-divided into groups, known as SUB-
POPULATIONs, where INDIVIDUALs may only mate with others in the
same group. (This technique might be chosen for parallel
processors). Such sub-divisions may markedly influence the
evolutionary dynamics of a population (e.g. Wright's 'shifting
balance' model). Sub-populations may be defined by various
MIGRATION constraints: islands with limited arbitrary migration;
stepping-stones with migration to neighboring islands;
isolation-by-distance in which each individual mates only with
near neighbors. cf PANMICTIC POPULATION, SPECIATION.
SUMMERSCHOOL:
(USA) One of the most interesting things in the US educational
system: class work during the summer break.
T
TERMINAL SET:
(GP) The set of terminal (leaf) nodes in the parse trees
representing the programs in the POPULATION. A terminal might
be a variable, such as X, a constant value, such as 42, (cf Q42)
or a function taking no arguments, such as (move-north).
TRAVELLING SALESMAN PROBLEM:
The travelling salesperson has the task of visiting a number of
clients, located in different cities. The problem to solve is:
in what order should the cities be visited in order to minimise
the total distance travelled (including returning home)? This is
a classical example of an ORDER-BASED PROBLEM.
TSP: See TRAVELLING SALESMAN PROBLEM.
U
USENET:
"Usenet is like a herd of performing elephants with diarrhea --
massive, difficult to redirect, awe-inspiring, entertaining, and
a source of mind-boggling amounts of excrement when you least
expect it."
--- Gene Spafford (1992)
V
VALUE-BASED PROBLEM:
A problem where the solution must be specified in terms of a set
of real-valued parameters. FUNCTION OPTIMIZATION problems are
of this type. cf SEARCH SPACE, ORDER-BASED PROBLEM.
VECTOR OPTIMIZATION:
Typically, an OPTIMIZATION problem wherein multiple objectives
must be satisfied.
Z
ZEN NAVIGATION:
A methodology with tremendous propensity to get lost during a
hike from A to B. ZEN NAVIGATION simply consists in finding
something that looks as if it knew where it is going to and
follow it. The results are more often surprising than
successful, but it's usually being worth for the sake of the few
occasions when it is both.
Sometimes ZEN NAVIGATION is referred to as "doing scientific
research," where A is a state of mind being considered as pre-
PhD, and B (usually a different) state of mind, known as post-
PhD. While your time spent in state C, somewhere inbetween A and
B, is usually referred to as "being a nobody."
ACKNOWLEDGMENTS
Finally, credit where credit is due. I'd like to thank all the people
who helped in assembling this guide, and their patience with my
"variations on English grammar". In the order I received their
contributions, thanks to:
Contributors,
Lutz Prechelt (University of Karlsruhe) the comp.ai.neural-nets
FAQmeister, for letting me strip several ideas from "his" FAQ.
Ritesh "peace" Bansal (CMU) for lots of comments and references.
David Beasley (University of Wales) for a valuable list of
publications (Q12), and many further additions. David Corne, Peter
Ross, and Hsiao-Lan Fang (University of Edinburgh) for their
TIMETABLING and JSSP entries. Mark Kantrowitz (CMU) for mocking
about this-and-that, and being a "mostly valuable" source concerning
FAQ maintenance; parts of A11 have been stripped from "his" ai-
faq/part4 FAQ; Mark also contributed the less verbose ARCHIVE SERVER
infos. The texts of Q1.1, Q1.5, Q98 and some entries of Q99 are
courtesy by James Rice (Stanford University), stripped from his
genetic-programming FAQ (Q15). Jonathan I. Kamens (MIT) provided
infos on how-to-hook-into the USENET FAQ system. Una Smith (Yale
University) contributed the better parts of the Internet resources
guide (Q15.5). Daniel Polani (Gutenberg University, Mainz)
"contributed" the Alife II Video proceedings info. Jim McCoy
(University of Texas) reminded me of the GP archive he maintains
(Q20). Ron Goldthwaite (UC Davis) added definitions of Environment,
Evolution, Fitness, and Population to the glossary, and some thoughts
why Biologists should take note of EC (Q3). Joachim Geidel
(University of Karlsruhe) sent a diff of the current "navy server"
contents and the software survey, pointing to "missing links" (Q20).
Richard Dawkins "Glossary" section of "The extended phenotype" served
for many new entries, too numerous to mention here (Q99). Mark Davis
(New Mexico State University) wrote the part on Evolutionary
Programming (Q1.2). Dan Abell (University of Maryland) contributed
the section on efficient greycoding (Q21). Walter Harms (University
of Oldenburg) commented on introductory EC literature. Lieutenant
Colonel J.S. Robertson (USMA, West Point), for providing a home for
this subversive posting on their FTP server
euler.math.usma.edu/pub/misc/GA Rosie O'Neill for suggesting the PhD
thesis entry (Q10.11). Charlie Pearce (University of Nottingham) for
critical remarks concerning "tables"; well, here they are! J.
Ribeiro Filho (University College London) for the pointer to the IEEE
Computer GA Software Survey; the PeGAsuS description (Q20) was
stripped from it. Paul Harrald for the entry on game playing (Q2).
Reviewers,
Robert Elliott Smith (The University of Alabama) reviewed the TCGA
infos (Q14), and Nici Schraudolph (UCSD) first unconsciously, later
consciously, provided about 97% of Q20* answers. Nicheal Lynn Cramer
(BBN) adjusted my historic view of GP genesis. David Fogel (ORINCON)
commented and helped on this-and-that (where this-and-that is closely
related to EP), and provided many missing entries for the glossary
(Q99). Kazuhiro M. Saito (MIT) and Mark D. Smucker (Iowa State)
caught my favorite typo(s). Craig W. Reynolds was the first who
solved one of the well-hidden puzzles in the FAQ, and also added some
valuable stuff. Joachim Born (TU Berlin) updated the Evolution
Machine (EM) entry and provided the pointer to the Bionics technical
report ftp site (Q14). Pattie Maes (MIT Media Lab) reviewed the
ALIFE IV additions to the list of conferences (Q12). Scott D. Yelich
(Santa Fe Institute) reviewed the SFI connectivity entry (Q15). Rick
Riolo (MERIT) reviewed the CFS-C entry (Q20). Davika Seunarine
(Acadia Univ.) for smoothing out this and that. Paul Field (Queen
Mary and Westfield College) for correcting typos, and providing
insights into the blindfold pogo-sticking nomads of the Himalayas.
and Everybody...
Last not least I'd like to thank Hans-Paul Schwefel, Thomas Baeck,
Frank Kursawe, Guenter Rudolph for their contributions, and the rest
of the Systems Analysis Research Group for wholly remarkable patience
and almost incredible unflappability during my various extravangances
and ego-trips during my time (1990-1993) with this group.
It was a tremendously worthwhile experience. Thanks!
"And all our yesterdays have lighted fools; the way to dusty death;
out, out brief candle; life's but a walking shadow; a poor player;
that struts and gets his hour upon the stage; and then is heared
no more; it is a tale; told by an idiot, full of sound an fury,
signifying nothing."
--- Shakespeare, Macbeth
EPILOGUE
"Natural selection is a mechanism for generating
an exceedingly high degree of improbability."
--- Sir Ronald Aylmer Fisher (1890-1962)
This is a GREAT quotation, it sounds like something directly out of a
turn of the century Douglas Adams: Natural selection: the original
"Infinite Improbability Drive"
--- Craig Reynolds, on reading the previous quote
"`The Babel fish,' said The Hitch Hiker's Guide to the Galaxy
quietly, `is small, yellow and leech-like, and probably the oddest
thing in the Universe. It feeds on brainwave energy received not
from his own carrier but from those around it. It absorbs all
unconscious mental frequencies from this brainwave energy to nourish
itself with. It then excretes into the mind of its carrier a
telepathic matrix formed by combining the conscious thought
frequencies with nerve signals picked up from the speech centers of
the brain which has supplied them. The practical upshot of all this
is that if you stick a Babel fish in your ear you can instantly
understand anything said to you in any form of language. The speech
patterns you actually hear decode the brainwave matrix which has been
fed into your mind by your Babel fish. `Now it is such a bizarrely
improbable coincidence than anything so mindbogglingly useful could
have evolved purely by chance that some thinkers have chosen to see
it as a final and clinching proof of the non-existence of God. `The
argument goes something like this: ``I refuse to prove that I
exist,'' says God, ``for proof denies faith, and without faith I am
nothing.'' ``But,'' says Man, ``The Babel fish is a dead giveaway
isn't it? It could not have evolved by chance. It proves you exist,
and so therefore, by your own arguments, you don't. QED.'' ``Oh
dear,'' says God, ``I hadn't thought of that,'' and promptly vanishes
in a puff of logic. ``Oh, that was easy,'' says Man, and for an
encore goes on to prove that black is white and gets himself killed
on the next zebra crossing."
--- Douglas Adams (1979)
"Well, people; I really wish this thingie to turn into a paper babel-
fish for all those young ape-descended organic life forms on this
crazy planet, who don't have any clue about what's going on in this
exciting "new" research field, called Evolutionary Computation.
However, this is just a start, I need your help to increase the
usefulness of this guide, especially its readability for natively
English speaking folks; whatever it is: I'd like to hear from
you...!"
--- The Editor
"Parents of young organic life forms should be warned, that
paper babel-fishes can be harmful, if stuck too deep into the ear."
--- Encyclopedia Galactica
------------------------------
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