Arti cial Evolution: A Continuing SAGA 1 Artificial Evolution

19 Pages·2006·0.2 MB·English

Arti(cid:1)cial Evolution(cid:2) A Continuing SAGA
Inman Harvey
Centre for the Study of Evolution
Centre for Computational Neuroscience and Robotics
School of Cognitive and Computing Sciences
University of Sussex
Brighton BN(cid:1) (cid:2)QH(cid:3) UK
inmanh(cid:1)cogs(cid:2)susx(cid:2)ac(cid:2)uk
Abstract
I start with a basic tutorial on Arti(cid:1)cial Evolution(cid:2) and then
show the simplest possible way of implementing this with the Micro(cid:3)
bial Genetic Algorithm(cid:4) Ithendiscuss someshortcomingsin manyof
thebasic assumptionsofthe orthodoxGenetic Algorithm (cid:5)GA(cid:6)com(cid:3)
munity(cid:2) and give a rather di(cid:7)erent perspective(cid:4) The basic principles
of SAGA (cid:5)Species Adaptation GAs(cid:6) will be outlined(cid:2) and the con(cid:3)
cept of Neutral Networks(cid:2) pathways of level (cid:1)tness through a (cid:1)tness
landscape will be introduced(cid:4) A practical example will demonstrate
the relevance of this(cid:4)
(cid:1) Arti(cid:2)cial Evolution
Every day we come across sophisticated(cid:1) highly(cid:2)tuned machinery that is
far far more complex than human designers could begin to imagine de(cid:2)
signing by standard techniques(cid:3) I am referring to the animals (cid:4)including
other humans(cid:5)(cid:1) plants and other organisms that we live amongst(cid:3) These
are self(cid:2)regulating(cid:1) mostly self(cid:2)repairing(cid:1) self(cid:2)sustaining machines that can
cope with changing situations in an incredibly (cid:6)exible and adaptive fash(cid:2)
ion(cid:3) Their designs are the product of billions of years of natural Darwinian
evolution(cid:3)
Proponents of Arti(cid:7)cial Evolution aim to capture and exploit the core
parts of this natural design methodology(cid:1) and use it to design arti(cid:7)cial
complexsystems to have comparable properties(cid:8) adaptive and robust robot
(cid:9)
control systems(cid:1) self(cid:2)repairing electronic circuits(cid:1) telecommunications net(cid:2)
works that grow and rearrange themselves around disruptions(cid:1) pharmaceu(cid:2)
tical drug moleculesthat match up with a range of targets(cid:3) We do not have
the resources of billions of years of experimentationon one or more planets
that Natural Evolution has had(cid:1) so we must be as e(cid:10)cient as possible(cid:1) and
learn the crucial tricks that Nature can show us(cid:3)
The context of evolution is a population (cid:4)of organisms(cid:1) objects(cid:1) agents
(cid:3)(cid:3)(cid:3)(cid:5) that survive for a limited time (cid:4)usually(cid:5) and then die(cid:3) Some pro(cid:2)
duce o(cid:11)spring for succeeding generations(cid:1) the (cid:12)(cid:7)tter(cid:13) ones tend to produce
more than the less (cid:7)t(cid:3) Over many generations(cid:1) the make(cid:2)up of the popula(cid:2)
tion changes(cid:3) Without the need for any individual to change(cid:1) the (cid:12)species(cid:13)
changes(cid:1) in some sense adapts to the prevailing conditions(cid:3) There are three
basic requirements for Darwinian evolution by Natural Selection(cid:8)
(cid:9)(cid:3) Heredity(cid:8) O(cid:11)spring are (cid:4)roughly(cid:5) identical to their parents (cid:3)(cid:3)(cid:3)
(cid:14)(cid:3) Variation(cid:8) (cid:3)(cid:3)(cid:3)except that they are not exactly the same
(cid:15)(cid:3) Selection(cid:8) The (cid:12)(cid:7)tter(cid:13) ones are more likely to have more o(cid:11)spring
than the (cid:12)un(cid:7)t(cid:13) ones
Variation is usually random and undirected(cid:1) whereas Selection is usu(cid:2)
ally non(cid:2)random and in somesense directed(cid:3) In the natural world(cid:1) direction
does not imply a conscious director(cid:3) Rather(cid:1) it re(cid:6)ects the fact that those
organisms that are not as well designed for their particular ecological niche
as their conspeci(cid:7)cs will be less likely to survive and have o(cid:11)spring(cid:16) the
others thereby automatically qualify as (cid:12)(cid:7)tter(cid:13) for that particular niche (cid:17)
whatever that nichemightbe(cid:3) If antelopes are often chased by lions(cid:1) then it
is reasonable to talk of Selection providing a selective pressure for a popu(cid:2)
lation of antelope to increase their speed over successive generations(cid:1) other
things being equal(cid:3)
In Arti(cid:7)cial Evolution(cid:1) unlike Natural Evolution(cid:1) the human experi(cid:2)
menter decides what is going to count as (cid:12)(cid:7)t(cid:13)(cid:1) in what direction Selection
should alter the population over generations(cid:3) In this sense it resembles
agricultural practice(cid:1)where for thousands of years farmershavebeen select(cid:2)
ing the cows that produce more milk(cid:1) the crops that produce more grain(cid:1)
and breeding from them for future generations(cid:3) Even without necessar(cid:2)
ily understanding the genetic details(cid:1) the manipulation of DNA underlying
the process(cid:1) farmers have long implicitly understood the basic principles
of Heredity(cid:1) Variation and Selection su(cid:10)ciently well to improve their crops
over the centuries(cid:3)
(cid:14)
(cid:3) DNA
Aswe now know (cid:4)butDarwin didnot(cid:5)(cid:1) a core mechanismunderlyingHered(cid:2)
ity and Variation is the DNA that we (cid:4)and other organisms(cid:5) inherit from
our parents and pass on to our o(cid:11)spring(cid:3) DNA is often treated as though it
is a (cid:12)blueprint(cid:13)(cid:1)or a set of instructions setting out how an organism will de(cid:2)
velop from an initial single cell(cid:3) Many biologists would say that this view of
DNA is in important respects misleading(cid:16) however(cid:1) in Arti(cid:7)cial Evolution(cid:1)
wherewecanpickand choosethose biologicalideasthat suitusregardlessof
whether they give the whole biological picture(cid:1) we typically do indeed take
this simplisticview of Arti(cid:7)cial DNA as a blueprint(cid:3) The crucial aspects of
DNA that we borrow for our own purposes are(cid:8)
(cid:9)(cid:3) DNA can be treated as a meaningless string of symbols (cid:17) Cs Gs As
and Ts in humans(cid:1) perhaps (cid:18)s and (cid:9)s in a Genetic Algorithm (cid:4)GA(cid:5)
(cid:17) that are just mindlessly copied to provide Heredity(cid:16) perhaps with
occasional copying errors to provide Variation(cid:3)
(cid:14)(cid:3) The genotype(cid:1) the full sum of DNA that an organism inherits(cid:1) has a
crucial role in determining the phenotype(cid:1) the form and the physical
and behavioural traits of an organism(cid:3)
So to give a simple illustration of Arti(cid:7)cial Evolution applied to (cid:7)nding
a good design for a paper glider(cid:1) one could invent a set of symbols that
speci(cid:7)ed how a piece of paper(cid:1) initially square(cid:1) is folded(cid:3) For example(cid:1) A
could mean (cid:12)fold the paper towards you about a vertical line through the
middle(cid:13)(cid:16)B could mean (cid:12)fold the paper away from you about a diagonal line
from NE to SW(cid:13)(cid:3) An appropriate set of such symbols could cover all the
possible standard folding moves(cid:1) and any particular list of such symbols(cid:1)
e(cid:3)g(cid:3) GABKJNPD(cid:1) can be used in each of the two ways listed above(cid:8) (cid:7)rstly(cid:1)
as a string ofsymbolsthat canbe mindlesslycopiedand passed on(cid:1) secondly
as a blueprint detailing the successive folds that turn a plain sheet of paper
into some folded object(cid:3)
The person who wants to design a paper glider using arti(cid:7)cial evolution
would then start with perhaps (cid:15)(cid:18) sheets of paper(cid:1) and write on each piece a
random sequence of the symbols(cid:3) Then she would take each piece of paper
in turn(cid:1) interpret the symbol string(cid:1) the arti(cid:7)cial DNA(cid:1) as instructions to
fold the paper(cid:1) and see what shape results(cid:3) The next step is to open a
window high up in a building(cid:1) and throw all (cid:15)(cid:18) folded shapes out of the
window(cid:3)
She would then go outside and see how the di(cid:11)erent shapes have fallen
to the ground below the window(cid:3) Some may have fallen straight down(cid:1)
(cid:15)
some may have accidentally been caught by some wind(cid:1) some shapes may
have possibly glided a metre or two(cid:3) This is where Selection comes in(cid:1) and
the ones that have not travelled far are discarded while the one that went
furthest are chosen to form the parents for the next generation(cid:3) A new set
of (cid:15)(cid:18) sheets of paper is prepared(cid:1) and strings of symbols(cid:1) of arti(cid:7)cial DNA(cid:1)
are copied onto them based on the surviving parents from the previous
generation(cid:3) This can be done in a variety of ways(cid:1) any of which are likely
to work(cid:3)
The simplest option might be the asexual one(cid:1) in which perhaps the
best (cid:19)(cid:18)(cid:20) of the previous generation each have (cid:14) o(cid:11)spring(cid:1) who inherit their
single parent(cid:13)s DNA with some small probability of a mutation altering(cid:1)
deleting or adding a symbol(cid:3) Alternatively(cid:1) a form of sexual reproduction
can be used(cid:1) wherein the parents are brought together in pairs(cid:1) and their
o(cid:11)spring inherit some DNA from each parent(cid:1) again with the possibility of
further mutations(cid:3) As long as the method chosen maintains the population
of the next generation at the samesize as the sameas the initialgeneration(cid:1)
and obeys the rules for Heredity and Variation(cid:1) then the stage is set for a
further round of Selection on the new generation(cid:3) Continuing this over
many successive generations should result in increasingly successful paper
gliders that (cid:6)y further and further out of the window(cid:3)
You can change the problem to that of designing real aircraft wings(cid:1)
or control systems for robots(cid:16) and you can change the set of symbols to a
new set specifying the curvatures and thicknesses of parts of a wing(cid:1) or the
type and connectivity of arti(cid:7)cial neurons in an arti(cid:7)cial neural net(cid:3) Then
the underlying methodologyof Arti(cid:7)cialEvolution willbasicallyremainthe
same(cid:1) except that the Selective process(cid:1) the evaluation of the (cid:7)tnesses of
di(cid:11)erent membersof the population(cid:1) is likelyto be far more expensive than
throwing paper gliders out of the window(cid:3)
When you change to a di(cid:11)erent problem(cid:1) you have to create a new
and appropriate method for interpreting strings of symbols(cid:1) the artic(cid:7)cial
DNA(cid:1) as potential solutions to the problem(cid:3) For some probelms it may be
appropriate to use real(cid:2)valued numbers as symbols in the DNA(cid:1) in whicch
case there is a potentially in(cid:7)nite range of values at such a locus on the
genotype(cid:3) In the work discussed from here on(cid:1) however(cid:1) it is explicitluy
assumed that(cid:1) as in natural DNA(cid:1) there is only a limited range of symbols(cid:1)
quite possibly limited to the binary range of (cid:18) and (cid:9)(cid:3)
(cid:21)
(cid:4) The Microbial Genetic Algorithm
There are many varieties of Evolutionary Algorithms(cid:1) many di(cid:11)erent ways
to implement(cid:1)for problemsolving(cid:1) the threemainrequirementsof Heredity(cid:1)
Variation and Selection(cid:3) I shall now describe one little known but e(cid:11)ective
method(cid:1) that is so simpleto implementthat the core of the program can be
reduced to a single line of code(cid:3) I call it the Microbial Genetic Algorithm
because it is loosely based on the way microbes can exchange genetic mate(cid:2)
rial(cid:1)DNA(cid:1)(cid:12)horizontally(cid:13)betweendi(cid:11)erentlivingmembersof thepopulation
as an alternative to (cid:12)vertically(cid:13) from one generation to the following one(cid:3)
There are three particular tricks used here that are subtlely di(cid:11)erent
from the basic algorithm described above in the paper gliders example(cid:3)
The (cid:7)rst is the use of a (cid:12)Steady State(cid:13) method rather than a (cid:12)Generational(cid:13)
method(cid:3) Instead of accumulating a complete new generation of o(cid:11)spring(cid:1)
and then discarding the older generation and replacing it wholesale by the
new(cid:1) it is very reasonable to just generate a single new o(cid:11)spring at a time(cid:16)
then (cid:4)inorder to maintainthe population sizeconstant(cid:5) choose one member
of the population to die and be replaced by the new one(cid:3) The Selection
criterion will be satis(cid:7)ed by either biasing the choice of parent(cid:4)s(cid:5) for the
new o(cid:11)spring towards the (cid:7)tter members(cid:1) or biasing the choice of which is
to die towards the less (cid:7)t(cid:3) There are at least two advantages of the Steady
State method over the generational method(cid:8) it is usually much easier to
implement(cid:1)anditallowsfore(cid:10)cientparallelimplementationswhereitisnot
actually necessary to keep the evaluations of all membersof the population
in step with each other(cid:3) Despite the fact that the generational method is
usually the (cid:7)rst to be discussed in the textbooks(cid:1) these advantages mean
that many serious users of evolutionary algorithms favour the Steady State
method(cid:3)
The second trick is to use a rank(cid:2)based method of selection(cid:1) and in
particular tournament selection(cid:3) The textbooks generally present (cid:12)(cid:7)tness(cid:2)
proportionate(cid:13) selection (cid:4)where for instance if one member has twice the
(cid:7)tness of another member of the population it can expect twice as many
o(cid:11)spring(cid:5) as the main method used in GAs(cid:3) This is probably for historical
reasons(cid:1) and because the formal analysis of GAs is mathematically easier
when using this method(cid:3) However(cid:1) professional practitioners are far more
likely to use a rank(cid:2)based selection method(cid:1) where the expected number of
o(cid:11)spring of any member is based on (cid:4)in the simplest case(cid:1) linearly propor(cid:2)
tionate to(cid:5) its ranking in the population(cid:3) To give a simple example with a
population of size (cid:19)(cid:1) they can be ranked in order on the basis of their (cid:7)tness
and then allocated an expected number of o(cid:11)spring in this ratio(cid:8) (cid:21)(cid:22)(cid:14) (cid:15)(cid:22)(cid:14)
(cid:14)(cid:22)(cid:14) (cid:9)(cid:22)(cid:14) (cid:18)(cid:22)(cid:14)(cid:3) In this fashion the top(cid:2)ranking member will have twice the
(cid:19)
COMPARE W
PICK
L
n ranked
o
ati
ul
op RECOMBINE
p W unchanged
. . . . .
. . . . . W W
REPLACE
L MUTATE L
L mutated L infected
Figure (cid:9)(cid:8) A single tournament in the Microbial Genetic Algorithm(cid:1)
expected number of o(cid:11)spring of the middle(cid:2)rankingmember(cid:1)irrespectiveof
whether it is (cid:9)(cid:18)(cid:18) times (cid:7)tter or only (cid:9)(cid:20) (cid:7)tter(cid:3)
A cheap and cheerful method of implementing this type of rank(cid:2)based
selection(cid:1) particularly appropriate for the Steady State case(cid:1) is to pick out
(cid:14) members of the population at random and compare their (cid:7)tnesses in a
(cid:12)Tournament(cid:13)(cid:3) Then picking the winner to be a parent (cid:4)or alternatively(cid:1)
picking the loser to be the individual that dies to make way for a new
o(cid:11)spring(cid:5) gives exactly the same expected selection bias as described in the
previous paragraph(cid:3) There are at leastthree advantages of thisTournament
Selection method over the orthodox (cid:7)tness proportionate selection method(cid:8)
it is usually much easier to implement(cid:1) it avoids many scaling problems of
the standard method(cid:1) and it implements a form of elitism for free(cid:3) Elitism
in this context means that the currently (cid:7)ttest member of the population
will always remain preserved unchanged(cid:3)
Now we build on these two tricks by moving on to the third trick of the
Microbial GA(cid:3) It is perfectly acceptable to operate a GA by picking two
members at random to be parents and generate a new o(cid:11)spring(cid:16) and then
pick a further two members at random(cid:1) and using Tournament Selection
choose theloser to dieand be replacedbythe newone(cid:3) It mayseeminitially
strange to have no bias towards choosing (cid:7)tter membersas parents(cid:1) but the
bias in choosing who is to die is what satis(cid:7)es the criterion of Selection(cid:3)
The trick here is to combine all this into one operation(cid:3)
So the Microbial method is to pick just two members of the population
at random(cid:1) who will be parents of the new o(cid:11)spring(cid:16) and the least (cid:7)t of
the two parents is chosen as the one to die and be replaced(cid:3) I have used so
far the conventional language of (cid:12)parent(cid:13)(cid:1) (cid:12)o(cid:11)spring(cid:13) and (cid:12)die(cid:13)(cid:1) but in fact
this is equivalent to horizontal transmission of genetic material from the
(cid:23)
(cid:12)Winner(cid:13) of the tournament to the (cid:12)Loser(cid:13)(cid:3) The Winner remains unchanged
in the population(cid:1) and the Loser receives copies of some genetic material
(cid:4)not necessarily restricted to (cid:19)(cid:18)(cid:20)(cid:5) from the Winner(cid:1) with the opportunity
for further mutations also(cid:3)
The Microbial Genetic Algorithm is illustrated in the diagram(cid:1) where
the population of genotypes of (cid:12)arti(cid:7)cial DNA(cid:13) is represented by the set of
lines on the left(cid:3) Initially these will each be a random string of symbols(cid:1)
for instance a random binary string(cid:1) and there will be some method for
translating any such string into a trial solution for the design problembeing
tackled(cid:3) This is where the human designer has to be creative in matching
the genotype(cid:2)to(cid:2)phenotype translation to the requirementsof the task(cid:3) But
then(cid:1) provided that there is a suitable method for testing and scoring any
such potential solution(cid:1) giving it a (cid:12)(cid:7)tness(cid:13)(cid:1) all the rest of the work can be
left to the algorithm(cid:3) Two strings are picked out at random(cid:1) and evaluated
to see which is the Winner and which the Loser (cid:4)W and L on the diagram(cid:5)(cid:3)
Then with some probability each locus (cid:4)genotype position(cid:5) of the Winner
may be copied over the corresponding locus of the Loser(cid:1) followed by a
separate mutation process of changing at random some small proportion of
the Loser loci(cid:3) The two strings are re(cid:2)inserted into the population (cid:17) in fact
the Winner is unchanged(cid:3)
ThisMicrobialGAobeysthe(cid:15)rulesofHeredity(cid:1)VariationandSelection(cid:1)
is e(cid:11)ective(cid:1)yet is so simplethat it can be reduced to a single line of code(cid:3) If
we assume that(cid:1) in C(cid:1) the genotypes are in a binary array gene(cid:2)POP(cid:3)(cid:2)LEN(cid:3)(cid:1)
th
i
and that the function eval(cid:4)i(cid:5) returns the (cid:7)tness of the member of the
population(cid:1) the one(cid:2)liner goes something like this(cid:8)(cid:2)
for (cid:1)t(cid:2)(cid:3)(cid:4)t(cid:5)END(cid:4)t(cid:6)(cid:6)(cid:7)
for (cid:1)W(cid:2)(cid:1)eval(cid:1)a(cid:2)POP(cid:8)rand(cid:1)(cid:7)(cid:7)(cid:9)eval(cid:1)b(cid:2)POP(cid:8)rand(cid:1)(cid:7)(cid:7)(cid:10)a(cid:11)b(cid:7)(cid:12)
L(cid:2)(cid:1)W(cid:2)(cid:2)a(cid:10)b(cid:11)a(cid:7)(cid:12)i(cid:2)(cid:3)(cid:4)i(cid:5)LEN(cid:4)i(cid:6)(cid:6)(cid:7)
if (cid:1)(cid:1)r(cid:2)rand(cid:1)(cid:7)(cid:7)(cid:5)REC(cid:6)MUT(cid:7)
gene(cid:13)L(cid:14)(cid:13)i(cid:14)(cid:2)(cid:1)r(cid:5)REC (cid:10) gene(cid:13)W(cid:14)(cid:13)i(cid:14) (cid:11) gene(cid:13)L(cid:14)(cid:13)i(cid:14)(cid:15)(cid:16)(cid:17)(cid:7)(cid:4)
(cid:5) Searching through Fitness Landscapes
Evolutionary algorithms(cid:1) including the Microbial GA(cid:1) can be thought of as
search methods in a high(cid:2)dimensional search space(cid:3) Turning back to the
paper glider folding example(cid:1) if there are (cid:24) possible folding instructions(cid:1)
(cid:1)(cid:2)
and a succession of (cid:14)(cid:19) folds(cid:1) then there are (cid:24) possible versions of folding
a glider(cid:3) Only a tiny proportion of these will have any sort of (cid:6)ying ability(cid:1)
(cid:1)(cid:2)
and an even smaller proportion will (cid:6)y properly(cid:3) If one considers all the (cid:24)
(cid:25)
designs as spread out overa landscape(cid:1) with similardesigns (cid:4)di(cid:11)eringbysay
just one fold(cid:5) nearby to each other(cid:1) then one can imaginethe search process
as searching across this landscape(cid:3) Now treat the (cid:12)(cid:7)tness(cid:13) of each possible
designasthe(cid:12)height(cid:13)ofthecorresponding positioninthislandscape(cid:1)and we
have a hilly (cid:7)tness landscape where the peaks represent our goal(cid:3) Typically
the majority of this landscape will be foothills of negligible height(cid:1) but it is
reasonable to expect that the higher mountains form connected ranges that
are the areas on which the search should be focused(cid:3)
There are many possible strategies for searching such (cid:7)tness landscapes(cid:1)
including Simulated Annealing(cid:1) Hill(cid:2)Climbing(cid:1) Tabu Search(cid:3) Since the
search spaces are to big to search exhaustively(cid:1) then all search methods in(cid:2)
volve sampling in turn successive points(cid:1) checking their (cid:7)tnesses and using
this knowledge to guide the continuation of the search from what has been
explored so far(cid:3) The distinctive feature of evolutionary approaches such as
genetic algorithms is the use of a population of search points(cid:1) searching in
parallel although not independently(cid:3)
(cid:6) Conventional Genetic Algorithm Assump(cid:7)
tions
If you read the GeneticAlgorithmtextbooks(cid:1) you will(cid:7)nd (cid:4)explicitlyor im(cid:2)
plicitly(cid:5)a numberof assumptions as to what makestheGA work e(cid:11)ectively(cid:3)
One of the major worries is that of getting stuck on a local optimum in a
(cid:7)tness landscape(cid:16) indeed this is the reason that most people are sceptical
about simple Hill(cid:2)Climbing methods(cid:3)
It is generally assumed that GAs make a good e(cid:11)ort to avoid getting
trapped on such local optima through two properties(cid:3) Firstly(cid:1) by starting
with an initial randomly spread population(cid:1) there is more chance that the
foothills to many di(cid:11)erent ranges will be encountered(cid:3) The parallel popu(cid:2)
lation search will be eventually won by those climbing the mountain range
that turns out to be the highest of those seen(cid:1) and there is less chance of
being trapped in one of the lower ranges(cid:3)
Secondly(cid:1) when there is recombinationbetween di(cid:11)erent membersof the
population(cid:1) this means that the searches are not truly independent(cid:3) Even
if two di(cid:11)erent membersare in e(cid:11)ect trapped on separate foothills (cid:4)or local
optima(cid:5)(cid:1) then their o(cid:11)spring will(cid:1) through recombination(cid:1) occupy a new
point on the (cid:7)tness landscape somewhere that is in e(cid:11)ect in(cid:2)between these
foothills(cid:3) Hence such an o(cid:11)spring could escape from the local traps that
each of its parents might be in(cid:3)
From these ideas (cid:6)ow some further assumptions(cid:1) widespread in the GA
(cid:24)
literature(cid:1) that I shall argue are completely misleading(cid:3) One major(cid:1) and
mistaken(cid:1) worry is about (cid:12)premature convergence(cid:13)(cid:3) If you follow the above
intuitions about how a single member of the population may get trapped
in a local optimum(cid:1) then you need a widely varied population to avoid this
problem(cid:3) Once all the variation in the population has disappeared over
time(cid:1) so that it is in e(cid:11)ect multiple copies of the same individual(cid:1) then
it can get stuck on a local optimum however big the population of clones
is(cid:3) Unless new variation is injected into the population(cid:1) then this genetic
convergence will happen(cid:16) and if it happens before the global optimum has
been found(cid:1) then this is the disaster of so(cid:2)called (cid:12)premature convergence(cid:13)(cid:3) I
shall give a di(cid:11)erent picture below(cid:3)
The GA textbooks usually present a theorem derived by John Holland(cid:1)
the architect of GAs(cid:1) called the Schema Theorem(cid:3) This proves that under
speci(cid:7)c limitedcircumstances the (cid:12)useful parts(cid:13) of genotypes in the popula(cid:2)
tion will grow exponentially as the GA produces the next generation from
the current one(cid:3) Although formally correct(cid:1) it is usually misinterpreted as
if this exponential growth continues unchecked over successive generations(cid:1)
whereas in fact it is only valid for a single generation(cid:16) the calculations of
(cid:7)tnesses within the population have to be done afresh each time(cid:3) So al(cid:2)
though the Schema Theorem is formally correct(cid:1) pragmatically it is useless
and irrelevant(cid:3)
The Schema Theorem is associated with a commonlyheld dogma in the
GA community(cid:1) that recombination(cid:1) the mixing and matching of various
parts of the genotype from di(cid:11)erent parents to produce the o(cid:11)spring(cid:1) is the
driving force of evolutionary search(cid:3) This feeds back to the worries about
prematureconvergencespelledoutabove(cid:3) Thereisanalternativeviewpoint(cid:1)
however(cid:3) Those who advocate the evolutionary methods of Evolutionary
Programming (cid:4)or EP(cid:5) tend to emphasise the role of mutation rather than
recombination(cid:1) and for slightly di(cid:11)erent reasons so do I here(cid:3)
(cid:8) SAGA(cid:9) Species Adaptation Genetic Algo(cid:7)
rithms
In the natural world(cid:1) of course(cid:1) evolving populations are genetically highly
converged(cid:3) If this was not so(cid:1) then the task of the Human Genome Project(cid:1)
assembling the genotype of a typical human being(cid:1) would be pointless(cid:3) The
geneticdi(cid:11)erencesbetweentwo humanbeings (cid:4)or twomembersof anyother
species(cid:5) are of course signi(cid:7)cant(cid:3) They lie behind the subtle di(cid:11)erences of
human form and behaviour(cid:1) of eye colour and temperament(cid:16)they allow the
possibility of DNA identi(cid:7)cation(cid:3) But these di(cid:11)erences are tiny compared
(cid:26)
to the similarities(cid:1) to what makes an identi(cid:7)able and coherent species(cid:3)
Each and every species on this planet probably shares a common origin
some (cid:21) billion years ago(cid:3) From this origin of life(cid:1) variations have branched
out with many such branches terminating(cid:1) as species become extinct(cid:3) But
if we imagine following the historical trace of a currently(cid:2)existing species(cid:1)
such as humans(cid:1) we will(cid:7)nd that for some (cid:21) billionyears therehas been the
phylogeneticpathwayofapopulation changingfromasinglecelltothecom(cid:2)
plex creatures we are today(cid:3) At every point in this history(cid:1) this population
would havebeen geneticallyveryconverged(cid:1) the genetic di(cid:11)erencesbetween
individuals would have been minimal compared to their similarities(cid:3)
In thought experiment at least(cid:1) we could imagine this historical trace
representedby a single individualfrom each generation(cid:1) displaying our phy(cid:2)
logenetic history(cid:3) This history would be one of long(cid:2)term change almost
entirely through mutation(cid:16) the interesting possible exceptions being when
transfer of geneticmaterialbetweenspecies mayoccasionally bring together
branches of the Tree of Life after they have previously bifurcated(cid:3) So apart
from such exceptions(cid:1) all the accumulateddesign of a present day organism
has come through the occasional lucky mutations that have been incremen(cid:2)
tally incorporated(cid:3) Whatever the role of recombinationmight be in natural
evolution (cid:17) and the jury is still out on this question (cid:17) it is mutation that
is the driving force(cid:3)
With this in mind(cid:1) some ten years ago I started to develop a framework
using similarideas for long(cid:2)term arti(cid:7)cial evolution(cid:1) for the incrementalde(cid:2)
sign methodology needed for such tasks as Evolutionary Robotics(cid:3) This
I call SAGA(cid:1) or Species Adaptation Genetic Algorithms(cid:1) as a genetically
converged population(cid:1) in e(cid:11)ect a species(cid:1) is involved(cid:3) The early stages of
SAGA (cid:4)Harvey(cid:1) (cid:9)(cid:26)(cid:26)(cid:14)(cid:16) Harvey(cid:1) (cid:9)(cid:26)(cid:26)(cid:15)(cid:5) were based on the realisation that if
long(cid:2)term evolution meant that genotype lengths were initially relatively
small (cid:4)for encoding e(cid:3)g(cid:3) relatively simple robot control systems(cid:5) and then
slowly increased in length over generations to accommodate more complex
designs as evolution progressed(cid:1) then it was inevitable that the popula(cid:2)
tion would be genetically converged throughout(cid:3) But later it came to be
recognised that actually even with genotype lengths remaining constant(cid:1) in
practice an evolving population is genetically converged in any case(cid:3) So it
has turned out that SAGA ideas are far more widely applicable than their
original domain(cid:3)
(cid:9)(cid:18)