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FAQ: comp.ai.genetic part 6/6 (A Guide to Frequently Asked Questions) |
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Last-Modified: 4/12/01
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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 for
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 attributed 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+1 */
/* from Gray code Cg[0...n] */
/* to binary code Cb[0...n] */
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+1 */
/* from binary code Cb[0...n] */
/* to Gray code Cg[0...n] */
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).
[10] Albert Nijenhuis and Herbert S. Wilf, Combinatorial Algorithms,
(Academic Press, Inc., New York, San Francisco, London 1975).
------------------------------
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 . It is available
from various FTP sites, including:
softlib.cs.rice.edu/pub/tsplib/tsblib.tar
OPERATIONAL RESEARCH DATA
Information about Operational Research test problems in a wide
variety of areas can be obtained by emailing
with the body of the email message being just the word "info". The
files in OR-Library are also available via anonymous FTP from
mscmga.ms.ic.ac.uk/pub/ A WWW page is also available at URL:
http://mscmga.ms.ic.ac.uk/info.html Instructions on how to use OR-
Library can be found in the file "paper.txt", or in the article:
J.E.Beasley, "OR-Library: distributing test problems by electronic
mail", Journal of the Operational Research Society 41(11) (1990)
pp1069-1072.
The following is a list of some of the topics covered.
File Problem area
assigninfo.txt Assignment problem
deainfo.txt Data envelopment analysis
gapinfo.txt Generalised assignment problem
mipinfo.txt Integer programming
lpinfo.txt Linear programming
scpinfo.txt Set covering
sppinfo.txt Set partitioning
tspinfo.txt Travelling salesman problem
periodtspinfo.txt Period travelling salesman problem
netflowinfo.txt Network flow problem
Location:
capmstinfo.txt capacitated minimal spanning tree
capinfo.txt capacitated warehouse location
pmedinfo.txt p-median
uncapinfo.txt uncapacitated warehouse location
mknapinfo.txt Multiple knapsack problem
qapinfo.txt Quadratic assignment problem
rcspinfo.txt Resource constrained shortest path
phubinfo.txt p-hub location problem
Scheduling:
airlandinfo.txt Aircraft Landing Problem
cspinfo.txt Crew scheduling
flowshopinfo.txt flow shop
jobshopinfo.txt job shop
openshopinfo.txt open shop
tableinfo.txt timetabling problem
Steiner:
esteininfo.txt Euclidean Steiner problem
rsteininfo.txt Rectilinear Steiner problem
steininfo.txt Steiner problem in graphs
Two-dimensional cutting:
assortinfo.txt assortment problem
cgcutinfo.txt constrained guillotine
ngcutinfo.txt constrained non-guillotine
gcutinfo.txt unconstrained guillotine
Vehicle routing:
areainfo.txt fixed areas
fixedinfo.txt fixed routes
periodinfo.txt period routing
vrpinfo.txt single period
multivrpinfo.txt multiple depot vehicle routing problem
OTHER DATA
William Spears maintains a WWW page titled:
Test Functions for Evolutionary Algorithms which contians links to
various sources of test functions.
http://www.aic.nrl.navy.mil:80/~spears/functs.html
ENCORE (see Q15.3) also contains some test data. See directories
under /etc/data/
------------------------------
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 in CLASSIFIER SYSTEMs: U.S. patent #4,697,242: J.H. Holland
and A. Burks, "Adaptive computing system capable of learning and
discovery", 1985, issued Sept 29 1987; 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
about patents on Artificial Neural Networks
(ANNs).
------------------------------
Subject: Q99: A Glossary on EAs?
A very good glossary of genetics terminology can be found at
http://helios.bto.ed.ac.uk/bto/glossary
1
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, its 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."
An interesting discussion on convergence by Michael Vose can be
found in GA-Digest v8n22, available from
ftp.aic.nrl.navy.mil/pub/galist/digests/v8n22
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 which typically takes place as
follows: 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 DIPLOID cell
with a pair of chromosomes.
In [HOLLAND92] the sentence "When sperm and ova fuse, matching
chromosomes line up with one another 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. DARWINISM was
combined with the selectionism of Weismann and the genetics of
Mendel to form the Neo-Darwinian Synthesis during the
1930s-1950s by T. Dobzhansky, E. Mayr, G. Simpson, R. Fisher, S.
Wright, and others. cf LAMARCKISM.
The talk.origins FAQ contains more details (See Q10.7). Also,
the "Dictionary of Darwinism and of Evolution" (Ed. by Patrick
Tort) was published in early 1996. It contains a vast amount of
information about what Darwinism is and (perhaps more
importantly) is not. Further information from
http://www.planete.net/~ptort/darwin/evolengl.html (in various
languages).
(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:
(biol) This refers to a cell which contains two copies of each
CHROMOSOME. The copies are homologous i.e. they contain the
same GENEs in the same sequence. In many sexually reproducing
SPECIES, the genes in one of the sets of chromosomes will have
been inherited from the father's GAMETE (sperm), while the genes
in the other set of chromosomes 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
EA: See EVOLUTIONARY ALGORITHM.
EC: See EVOLUTIONARY COMPUTATION.
ELITISM:
ELITISM (or an elitist strategy) is a mechanism which is
employed in some EAs which ensures that the CHROMOSOMEs of the
most highly fit member(s) of the POPULATION are passed on to the
next GENERATION without being altered by GENETIC OPERATORs.
Using elitism ensures that the minimum FITNESS of the population
can never reduce from one generation to the next. Elitism
usually brings about a more rapid convergence of the population.
In some applications elitism improves the chances of locating an
optimal INDIVIDUAL, while in others it reduces it.
ENCORE:
The EvolutioNary Computation REpository Network. An collection
of FTP servers/World Wide Web sites holding all manner of
interesting things related to EC. 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.
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). (See the talk.origins
FAQ for discussion on this (See Q10.7).)
"Don't assume that all people who accept EVOLUTION are atheists"
--- Talk.origins 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) Or, in other words, "An
'ESS' ... is a strategy such that, if all the members of a
population adopt it, no mutant strategy can invade." (Maynard
Smith "Evolution and the Theory of Games", 1982).
EVOLUTIONARY ALGORITHM:
A algorithm designed to perform EVOLUTIONARY COMPUTATION.
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:
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