EVOLUTION OF GENOMES WITH THEIR GENOMIC
IN GENETIC ALGORITHMS
Alexander V. Spirov
1, 2, *
, Alexander B. Kazansky
, Alexey S. Kadyrov
Juan J. Merelo
and Vladimir F.
The Sechenov Institute of Evolut
ionary Physiology and Biochemistry, 44 Thorez Ave., St. Petersburg, 194223,
Dept. of Applied Mathematics and Statistics, The State University of New York at Stony Brook, Stony Brook NY
Departamento de Arquitectura y Tecnología de C
, University of Granada, Granada, Spain
Dept. of Applied Math and Statistics, The University at Stony Brook, Stony Brook NY
Email: firstname.lastname@example.org; v:631
Algorithms (GA) and Genetic Programming were inspired by classic Darwinian ideas
However modern evolutionary biology is far beyond classic Darwinism. The application of
other algorithms and
modern biological ideas may substantially improve t
performance of Evolutionary Computations (EC).
Macroevolutionary mechanisms based on t
he mobile selfish
transposons are good candidates
breakthrough. The processes in the world of
transposons, living on a substratum of genome
s of whole
communities, are thought to be the main source of evolution creativity.
In this communication we propose a strategy of construction of a new scheme
for EC exploiting the
most essential aspects of co
evolution of the
ic parasites. We named this strategy as
Our approach exploits implicitly hybrid character of
ionary mechanisms discovered b
y modern evolutionary biology, where global search combined with loc
one, as well as
random mutagenesis combined with targeted one
We apply our approach
to one of known benchmark
the ant problem
. We found that our
enhancement of GA technique by the artificial
transposons obviously increase the efficacy of searc
hing of the
navigation algorithm. We in
vestigate in details
activity as example of
Many areas of evolutionary computation, especially genetic algorithms (GA), and genetic programmi
e inspired by ideas from
evolutionary biology. However
modern evolutionary biology has since advanced
considerably, revealing that
Darwinian evolution (microevolution) apparently is a particular case of essentially
more complicated mechanisms of macroevolu
. Many branches of modern evolution
ary computation research
evolution of mechanisms, such as functional programs, neural networks, decision trees, cellular automata,
systems, finite state automata. For these d
seems more appropria
an inspirational model tha
n classic set of Darwinian algorithms [Cf. Altenberg, 1994
Luke et al., 1999
; Lee and
Antonsson, 2001; Lones and Tyrrell, 2001
This stimulates us to select, formalize and apply to EC some new evo
simulate the creative, heuristic and self
organizing character of (biological) evolution [Spirov, 1996a;
1996b; Spirov and Samsonova, 1997; Spirov and Kadyrov, 1998; Spirov et al., 1998; Spirov and Kazansky,
02a; 2002b; 2002c].
We concentrate on mechanisms of
ic Engineering, whose key acto
. The basic idea
can be outlined as follows:
of every organism has got
very special mecha
nisms of genomic rear
d in the period
of evolutionary crisis;
The mechanisms cause multiple systemic rearrangement of gen
omes in a few generations
The mobile selfish genetic elements (synonymous or related terms are jumpin
g genes, selfi
transposons and retroelements
[Makalowski, 1995; 2200; Lozovskaya, 1995; Hurst
) are good
candidates for this breakthrough
. Many biologists speculate that proces
ses in the world of transposons
, living on
a substratum of genomes of th
e whole biological communities, are the main source of macroevolution creativity
here are several gro
of genomic parasites.
Transposons form the most sophisticated one.
now recognized that a si
gnificant portion of the genome of any eukaryote is composed of 'selfish' or 'parasitic'
genetic elements, which gain a transmission advantage relative to other components of an individual's genome,
but are either neutral or detrimental to the organism's f
Arguments have been
made that the structure of eukaryotic genomes, including the abundance of transposons, repetit
ive DNA and
introns, provide high
[Shapiro, 2000; 2002]
It has been estimated that typically 98%
of the DNA in higher organisms is neither translated into
proteins nor involved in gene regulation, that it is simply ``junk'' DNA.
The bulk of the junk DNA is
repeats comprised of DNA elements that are able to move (or transpose) throughout
These mobile DNA elements are sometimes termed "selfish DNA," since they do not appear to directly benefit
the host. Th
between different parts of a genome in order to propagate
the first sight,
this is usually to the detriment of their host.
hey do appear to benefit
the host organism
by providing genomic rearrangement
ermit the evolution of new genetic networks
Transposons are ubiquitous and may comprise up to 45% of
an organism's genome
Makalowski, 1995; 2200; Hurst
DNA of transposon origin can be recognized by their
palindrome endings flanked by short non
reversed repeated sequences resulting from insertion after staggered
any transposons have a unique DNA site, which acts as a forwarding address, directing the transposon to
a complementary DNA site in its host genome.
There are usually multiple copies of any given DNA site in the
host genome and
transposon will attach the p
roper site in
Transposons may grow be acquiring
mechanism involves the placement of two transposons into close proximity so that
they act as a single large transposon incorporating the intervening code.
Some data was
obtained recently which evidence that transposable elements are a major source of
genetic change, including the creation of novel genes, the alteration of gene functions, and the genesis of major
genomic rearrangements [
Fadool et al., 1998; Hurst
Lozovskaya, 1995; Makalowski, 1995;
]. The long coexistence of transposable elements in the genome is expected to be accompanied by host
. In this connection, speci
al interest is attracted by
known examples of both compe
and cooperative strategies
in populations of transposons. That is why trans
mutators. Besides, transposon
s can be considered as evolutionary “SOS
crew”, cooperatively acting
“in emergency”, at host’s
genomic stress [McClintock, 1984; Lozovskaya, 1995].
Modern evolutionary biology and evolutionary genetics (
a lot of knowledge
about very complicated mechanisms of genome rearrangements governed by transposons [
et al., 1998;
Brosius, 1991; Hurst
Werren, 2001; King, 199?; Makalowski, 1995; 2200; Lozovskaya, 1995; Shapiro, 2000;
2002]. From EC point of view the most sophisticated of these mechanisms can be treated as local evolutionary
search. First of all
/ recombinational hot spots
caused by transposons.
It is very promising
to include the world of selfish elements in the basic frames of Evolutionary Computations (EC) and to use the
objects/procedures for maintaining and manipulation of the parasites as a
new prospective branch of EC.
article we study in details co
artificial transposons with their hosts for GA version of the ant
Biologically Inspired EC
There is a feeling that the field of EC is getting more
inspired with the latest achievements in biology, trying to
make the evolutionary algorithms more effective. These attempts have been termed
algorithms or even “genetic” algorithms (quotes intended). Many other techniques take
n from biology,
such as transposition, host
parasite interaction and gene
regulatory networks have also been applied to
evolutionary computation. There is no uniform nomenclature, however, and sometimes the same terms are
applied to different methods, or t
he other way round.
These techniques can be divided broadly into three groups:
These methods are based on the co
evolution of two different populations, one
of them acting as “parasite”, and the other acting as “host”; the parasites
usually encode a version the problem
domain, and the hosts
the solution to the problem [Hillis, 1990; Potter and De Jong, 1994; 1995; De Jong
and Potter, 1995; Olsson, 1996; 2001]. They have been used mainly to evolve sorting networks; but similar
approaches have been used, for instance, for evolving players of the
game. In this case, the approach is
not significantly different from other co
evolutionary approaches, in which solutions and instances of a problem
are sometimes known as “bacterial” algorithms [Harvey, 1996, Nawa et
al., 1996; Simoes and Costa, 2001]. The basic idea of both approaches is to make intra
that is, crossover of a chromosome with another part of itse
lf, or else asymmetric crossover, in which a donor
chromosome transfers part of its genetic material to an acceptor chromosome. In some cases, these operators
seem to be better than classical genetic algorithms for combinatorial optimization problems, and
also in the case
of a fuzzy rule base. Similar transposition operators have also been used in other contexts, mainly in
combinatorial optimization problems.
Other biological approaches
Luke et al. [Luke et al., 1999] use a method similar to genetic regul
networks to evolve finite state automata that represent a language grammar; this kind of objects cannot be easily
represented using serial, bitstring, genetic algorithms. Burke et al. [Burke et al., 1998] try to make the
evolutionary process closer t
o its real molecular genetics base, by having a 4
letter genetic alphabet, transduction
processes, and variable
length genetic algorithms. In both cases, it is not a general
purpose techniques; they only
draw some elements from biology to solve problems th
at would be difficult to solve in other cases.
So far, it has not been found in the literature a technique that is general enough to be applied to a wide
range of problems, and that, in some cases, is able to yield as good or better results than evolutiona
In this paper we try to outline such an approach, and apply it to one of known benchmark problems
ant’s trail test [
Jefferson et al., 1991; Koza, 1992
In this article we propose general strategy of construction of a new scheme
essential sides of genomes
ic parasites co
evolution. We named this strategy as
level Evolving World
. In the next part
we give the definition of the strategy.
One of the key features of the
is very special local search performed by populations of artificial transposons. After description of the
we demonstrate the efficacy of a new approach on the example of John Muir ant’s trail test.
Key Characters of Natura
l Transposons as In
Mobile (transposable) elements encode the ability to move to new positions in the genome and can therefore
These genomic parasites li
ve on a substratum of gene pool of the whole biological
They are th
e autonomous selfish or parasitic codes
evolve with their hosts.
transmissible horizontally (from one host to another) and vertically (from the host
ancestor to the descendants).
act as intelligent and sophisticated mutator
s for the host codes
different types of mutations when they transpose themselves. These mechanisms
based both on enzymes
transposon own genes and host genes.
Class I transposable elements transpose through an RNA in
termediate. After the element is transcribed,
the RNA copy is converted into DNA, frequently as a result of reverse transcriptase activity encoded in the
element itself. This DNA copy now reinserts in the genome at another location. Transposition of class
elements involves DNA excision and homologous repair. Each class II element encodes a transposase, which
excises the element from the chromosome. The point of excision is repaired using the sequence of homologue or
sister chromatid as a template, which
creates a duplicate of the transposable element. The excised copy is free to
insert at another site within the genome.
Different mechanisms of transposon activity caus
e different types of mutations:
random insertions. The insertion of transposons (
by above sketched mechanisms) is
random but targeted. Certain regions of the host DNA are favored for insertion; these are referred
to as hot spots and tend to be specific to a transposon or its family. The insertional specificity based on fa
encoded by transposon genes.
spots. Transposable elements serve as recombinational hot
allowing the exchange of genetic material between unrelated chromosome
sequences [Makalowski, 1995]
Because they are so abundant, th
ey can mediate large scale chromosome restructurings by means of homologous
recombination between similar transposable elements at distant locations.
spots. For instance, two enzymes key to generating the immune system's
riety of antibodies are relics of an ancient transposon. A great deal of this variability is due to the
way antibody genes are assembled: by joining three separate sequences (denoted V, J, and D), each of which
comes in many variants, into a single antibod
y gene. The enzymes that do this assembly, Rag1 and Rag2, work
just like enzymes transpos
ases that mobilize transposons [Agrawal
et al., 1998]
. The transposases recognize the
ends of the transposon and cut it out of a chromosome. That freed
up piece of DNA
, with the transposase still
attached, can loop around itself and move to a new place in the genome. That's just what Rag1 and
2, which act
together in a complex, do.
Rearrangements of host genetic networks. In addition to moving themselves, all type
transposable elements occasionally move or rearrange neighboring DNA sequences of the host genome.
Transposons “strew” the genome different regulatory sequences. By so doing, transposons can re
genetic networks [
ransposons may capture genes and move them wholesale to new
parts of the genome. They make possible DNA shuffling that can place genes in new regulatory contexts and,
possibly, new roles. But what is more, when two transposable elements recognized by the
integrate into neighboring chromosomal sites, the DNA between them can become subject to transposition.
Because this provides a particularly effective pathway for the duplication and movement of exons, these
elements can help to
It has been estimated that 80% of spontaneous mutations are caused by transposons. Repeated sequences,
resulting from the activity of mobile elements, range from dozens to millions in numbers of copies per genome.
evolved with their host genome as result of selection, favoring transposons, which
introduce useful variation through gene rearrangement. In this manner, "smart" genetic operators evolved.
It is likely, that transposons to r
epresent the highly
coevolved “genetic operators”
. The possession of
smart genetic operators must have contributed to the explosive diversification of higher organisms providing
them with the capacity for natural genetic engineering.
In designing artificial evolution, it woul
d be wo
rthwhile to introduce such genom
ic parasites, in order to
facilitate the sharing of the code that they bring about.
The artificial transposons act as intelligent and sophisticated mutators. They can generate arbitrary
procedures of manipulations wit
h hosts’ chromosomes. In general, these operators can be the unitary, binary or
plural ones. Each host has got the mutators of its own. In the simplest case the transposons are the only source of
the host’s mutations.
If artificial transposon founds hopefu
l mutation strategy, then both host and parasite will get chance for
reproduction. Virtually we have co
evolution of hosts and their intelligent mutators
level Evolving World
We propose a new approach exploiting some aspects of co
ion of the hosts and their genomic parasites.
The key feature of the approach is the usage of artificial transposons. Two
level Evolving World consists of
basic level of hosts and upper level of transposons multiplying on a substratum of the host genomes.
artificial transposons are codes served by their own operators of reproduction, mutation and transmission.
Parasites and parasite ensembles always accompany biological evolution. Tom Ray simulated this
process in his
]. Parasites tend
with time to reduce their organization for the safe of host’s
resources. In a result, they acquire the possibility of fast (essentially faster then hosts) multiplication and
horizontal and vertical transmission. As a general result, they can evolve drasti
cally faster then hosts (influenza
virus is a sound example).
There are examples of evolvable virtual worlds such as Swarm, Creatures, Network Tierra [Daniels,
1999; Cliff and Grand, 1999; Ray, 2001]. In the course of evolution the worlds of
that type can
and host co
evolving worlds, i.e. they can become the two
leveled. It is the question of time and such
worlds’ complexity. In less complex virtual worlds similar splitting could be realized “by hand”, as in the case of
of computer viruses.
Parasites are so common that hosts soon co
evolve immunity to them. Then eventually the parasites co
evolve strategies to circumvent that immunity. Then eventually the hosts co
evolve defenses to repel them again,
and so on. This is
evolutionary Arms Race.
A special kind of parasite is genomic parasite living in the host genome. This special kind of co
evolution is the arms race between genomic parasites and their hosts.
Genomic parasites are the main source of host mutagenesis. If
the parasite founds a good strategy for
desirable host mutations, both the host and the parasite will get a chance for reproduction. The parasite rides a
new turn of evolution on the transformed host.
We assume that the simplest realization of the two
r evolving worlds would be as follows:
world is GA
like system (standard GA in the simplest case). The manifold of hosts’
rings is the environment for parasitic codes
. In the simplest case these GAs don’t have any
of their own;
arasites are the LISP
like programs, manipulating with the hosts’ strings. (For our applications
programs must include
performing the search of
s in the host strings).
live in hosts, they
are transmitted vertically (when host reproduces) and horizontally (from
one host to another, as infection or computer virus
the transposition operator
Analogously with their biological prototype, we can define artific
ial transposon as marked block of code in
host's chromosome. The code block marked as artificial transposon still functionally belongs to host. It is still the
part of host code. However this code block is transmittable now from host to host and able to mu
tate and growth
according different rules than remaining parts of host’s code.
The way to distinguish transposon code from other code depends from problem. In case of ant problem
we use strict definition. Special routine scan each chromosome in population
to find appropriate code blocks. In
the case of Royal Road functions we don’t use any
search routines, but we introduce in initial
population initial transposons
, 2002a; 2002b
To mark the beginning and the end of th
e transposon's code block, we could use special ''signaling``
sequences or signaling symbols in the host's chromosome. But we found more convenient to use double
chromosomes. The main string (binary and non
binary) is used for codes, while additiona
l one (binary)
marks. The possibility to use such chromosomes there is, for instance, in C++ library
Evolving Objects (EO)
et al., 2001
Let mark will be 1 and the absence of it
0. The block (cluster) of marks (.
transposon elements from the host's ones. In other word, instead to mark the beginning and the end of a
transposon, we mark all its elements in a sequence.
The main string contain
ing the host's and transposon's code blocks can be binary, symbolic, fl
point or other. In the case of binary main string transposon looks as follows:
The additional string 1111111100000000...
The main string 11111111********...
where * is either 0
We used such scheme for evaluations the performance of our artificial transposons approach relative to
standard GA on a class of Royal Road fitness functions
, 2002a; 2002b
In the case of ant problem treated in this article w
e can represent our artificial transposon as follows:
The additional string 1 1 1 . . . 1 1 1 0 0 0 0
The main string s
. . .s
* * * *
Here the main string is symbolic one; S
is one of symbols (R, L, F, N, #); R, L, F, N are the symbols of
navigational commands for animate
ant and # is turning
point referring at one of previous positions
string. R means turn left, L
urn left, F means one step forward, N
Mutagenesis Caused by Artificial Transposons
As in the case of biological prototype, artificial transposons act as sophisticated high
level mutators acting
dependently on the transposon own code and on the tr
(surrounding host's code).
different examples of known mechanisms of transposon
caused mutagenesis we can test several schemes of
tificial transposons activity
. Some of these schemes have been testing by other authors also i
nspired by modern
evolutionary ideas [
Burke et al., 1998; Luke et al., 1999; Simoes and Costa, 2001;
Pereira and Costa, 200?;
Our approach is different from others because we exploit co
evolution of hosts
transposons based on the
genomic parasites popu
Mutational Hot Spots
One of the most general and simple
of transposon action as mutators is
random point mutagenesis of the
sequence covered by transposon, coupled with transmission of the transposon. Apparently it would be an
xample of local search distributed through host population via transmission. We tested this general scheme on
two benchmark problem
Royal Road functions and the ant problem and found substantial improvement of
evolutionary search comparing with standard
GA. These results will be published else
Apart from this
scheme of mutagenesis we investigated some more, which we describe here.
Let we define as array
the transposon own code with it's nearest surrounding. For instance, the
the Royal Roads
where * is either 0 or 1.
Hence, in the case of our Royal Roads tests, the context includes only one host’s element, following the
most right element of transposon
, 2002a; 2002b
l scheme of transposon action is:
S' = F (S).
Concrete view of the
function depends on
the concrete problem.
In case of Royal Road tests
described in [
, 2002a; 2002b
we used such simple
definition of F function:
if S: 111...111
then S': 111...1110
if S: 111...1110
then S': 111...1110
function gives flip
flop mutation of the first host's element
following the most right
element of transposon.
In other words,
mutational hot spot.
In the case of ant problem,
is defined as follows:
1 1 1 . . . 1 1 1
. . . s
S': 1 1 1 . . . 1 1
. . . s
1 1 1 . . .
. . . s
S': 1 1 1 . . . 1 1
. . . s
symbol in the transposon's code;
N is NOP and # is internal cycle reference (turning point).
The F function substitutes the NOP element of the transposon code by
, for instance,
the fifth element of the
transposon, counted in order, while if the transposon ends on the internal cycle refer
ence, this element is
substituted by the fifth element of the transposon, counted backward from the end.
The Growth of Artificial Transposon
It is known that transposons tend to duplicate themselves and form clusters in host's chromosomes. We simulate
s feature as outgrowth of our transposon by one element in a time. Of course, it is not the only way to simulate
multiplication and spreading transposons in host's chromosomes, but this concrete
scheme works well in our
applications. More precisely, it mim
ics known feature of real transposons to grow by including more genes.
Namely, time by time, an artificial transposon adds one more element to it's edge:
where * is appropriate element of the main string.
Depending on application, the new
recruited transposon element may be arbitrary one (say 0 or 1 in our Royal
, 2002a; 2002b
) or it must have pred
etermined values, as in the case of our
version of ant problem.
The artificial ant problem is the simulation of an ant navigation aimed at
passing through the labeled trail
(nicknamed “The John Muir Trail” in the UCLA experiment [Jefferson
et al., 1991]).
The problem has been
repeatedly used as a benchmark problem [Jefferson et al. 1992; Koza, 1992; Lee and Wong
1997; Harries and Smith, 1997; Luke and Spector, 1997; Ito et al., 1998, Kuscu, 1998].
Jefferson et al.,
], the artificial ant has to path the John Muir trail placed in a grid world. The ant’s task is to pass through the
labeled cells one by one (the more the better) for the limited time period.
The ants are simple finite
or an artificial ne
which can move along the grid world and test their immediate surroundings. The trail
starts off quite easy to follow, and gradually gets more difficult, as the turns become more unpredictable and gaps
Each black (labeled) cell
is numbered sequentially, from the 1
which is settled directly next to
the starting cell, through to the 89
, the last cell. The ant’s task is to follow this trail and move across each black
cell in sequence.
Therefore, the successful ant’s program must
be quite sophisticated.
Artificial ant problem for two variants of trail (the “Santa Fe” and the “Los Altos”) is well tested and
discussed in publications. In both cases the trail has been carefully designed in such a way that it would be easy
to navigate at start but as ant proceeds through the trail, gaps and unexpected turns emerges progressively. By
the end of trail there are more gaps then labeled cells. But at the beginning, the successful tactic is very simple
only to pick up trail and
to move forward. A little further, the ant will need to learn the trick of turning to the
right with the trail. Some next moment they will need to learn the secret of turning occasionally left, and so on.
So, ant is progressively self
learning and perfect
ing algorithm of search in a course of passing it through.
The ant stands on a single cell and directed to the north, south, east, or west. It is capable of sensing the
state of the cell directly in front of it. In each time step, the ant must take one of
four actions. It may turn left,
turn right, move forward one step, or stand still. (When an ant steps on to a black cell, the cell turns white.) After
the ant performs its action, it shifts to a new state. Only the internal state of the ant and the state
of the cell in
front of the ant are used as inputs to the decision table which determines (a) the ant’s action and (b) the state it
will assume in the next time step. The decision table itself is coded as the ant’s genotype (Fig. 1B). The ant’s
score is th
e number of cells passed by the ant for the fixed time period.
METHODS AND APPROACH
While the ant test was implemented at least in two different C++ l
ibraries [Zongker and Punch, 199
we gave preference to the Peter Brennan’s version [Brennan, 1994].
his “ANT program” was designed in such a
to isolate, as far as possible, the components of the genetic algorithm from the trail
experiment and the ant representation. This is a deliberate decision intended to foster an easy transition fo
GA code itself, out of the ANT application, and into whatever application may find a use for the GA. The
development of this program as
example of the MGE
approach was the aim of magisterial thesis of one of us
The program consi
sts of three major subroutines:
subroutine, the each ant in the population is run against the John Muir Trail. Each ant’s
score is recorded.
subroutine, statistics are generated for
the previous Expose run. Each ant’s score is
compared to the maximum score attained in the population. One of two selection strategies is employed to
choose a given ant for reproduction. If the user has selected a
strategy, the fraction of ants
the highest scores are marked for reproduction. If the user has selected a
strategy, an ant with a
higher score has a greater chance of being marked, although there is a chance that even the highest
may not be marked.
subroutine, the genes of ants which are not marked for reproduction are overwritten
by copies of those which are marked, and then crossover and mutation are applied.
f Mobile Genetic Elements
Mobile genetic eleme
nts (MGEs) are akin to computer viruses. They are the autonomous programs, which are
transmissible horizontally (viz., from one site to another one on the same or another chromosome) or vertically
(from the ancestor to the descendants in the reproduction p
rocess). These autonomous parasitic programs
cooperate with the host genetic programs, thus realizing process of self
the only aim, which can be
associated with that activity. We developed some new operators which are the computer program pro
performing processes of replication, mutation and invasion of
s into specific sites on chromosomes, as
well as interactions of
with the chromosome (interrelations of parasite
It is appropriate here to make some
concerning the terminology. MGE
technique comprises the
procedures for initialization of mobile genetic elements and procedures for operating with the
Hereinafter in remaining
mobile elements will be referred to as “
”, whereas the procedures,
ith them will be termed as “MGE
operators”. There are only two types of operators. The one
operator is an analogue of point mutation and the two
place (binary) operator realizing the procedure of
from one chromosome (host) to another chromosome (another host).
Let us recall (see the previous sections) that the ant binary string
chromosome is coding a state transition table
of finite state automation. Altogether
there are 32 finite states of automation, ranging f
#0 up to
Fig. 1B). All operators start reading and interpreting the table beginning from the
#0. For example,
#0 determines one of the four actions or instructions (FWD
“to the right”, LFT
left” or NOP
nothing”) and the number of the next state, depending on binary input value (0 or 1). This
finite state automation can be represented as a state transition diagram and interpreted as a decisi
on tree but, as
far as references to already passed by states are permissible, that tree can have loops.
We will take into consideration that half of the decision tree which corresponds zero binary input value,
i.e. when ant see white (empty) square in fr
ont of it. Namely this part of ant’s transition state governs ant’s
search of black
squares. In so doing, we reduce ant’s genome to symbolic string
and substantially simplify
following treatment of the problem. This is an example of such symbolic
here L is LFT, R is RGT, F is FWD and #0 is
point referring at the first element of the
navigation program encoded by this
is optimal for classic
It is remarkable, that
s are really
variable length ones, but the maximum length is 32
ts. For instance, this string
is shorter but equivalent to the previous one.
For further consideration it is essential that two abovementioned
examples of symbolic string
as navigation program for our trail also, but up to 64
. Hence we can treat these programs as
building blocks for search of more sophisticated ant’s navigation algorithms.
If we use two
string implementation, then it seems perspective
for following search to mark this
sequence of symbols as a transposon.
Namely we could imagine such
additional string 1 1 1 1 1
0 0 0 0
The main string
R L L F #0
* * * *
Generally speaking, in accordance with all what we know about transposons activity in rearrangement
of host genomes, we treat it as mutational / recombinational hot spots. Besides, one of the very special features
s is that they are jumping hot spots. Apparently there are
implement these features in
ns. In this article
pay attention to that transposon features which allow us to treat it as kind
of generator and multiplicator / dis
tributor of building blocks. In such a way artificial transposon activity is
example of local search in limits of global GA search. Namely, initial population of artificial transposons
disseminate and mutate short code blocks till them find the first
building block. The transposon caring and
covered this b
uilding block (for example as it is
the case of abovementioned
selective advantage, spread
and become dominant in host population.
In the long run another tran
ind one more
or better building block and will get selective advantage, etc.
Obviously the simplest way to perform such local search would be the
general scheme o random point
mutagenesis of transposon sequence coupled with the transposon horiz
ontal transmission, as mentioned in
Mutagenesis Caused by Artificial Transposons
udy in details
populational dynamics of
as sophisticated mutators we decide
transposon variability. T
achieve this we use
definition of transposon
For all tests discussed in this article w
use this concrete
is the sequence of symbols
, having the following properties:
sequence should include symbol
s which number lie
in the range between minimum and maximum
should not contain NOP elements and internal circles;
should be finished up with command NOP or with a reference to the initial state. The
transitions cycle will be executed until o
nly white squares remain ahead of the ant.
If the fitting
is a cycle, it will be referred to as a
. But, if the fitting
finishes up with NOP, we will name it the
. The exampl
es of mature and
s are given on Fig. 2
usage of such sort of transposon definition drastically restricts transposon’s search space and
monitoring of transposon population dynamics.
By usage of the definition we exploit very
of transposon sequences manifold, but this small part contains solutions we looking for.
this restriction is one of some (or many) others.
We tested it and found appropriate for our purposes. What’s
more, the usage of the tran
to mark the transposon section
transposon have definition.
operators scan the predetermined quota of chromosomes in population. Successively decoding
chromosome record, this operator is seeking for
nces, which are identified as
operator provides the transmission of the
from an ant to another one, thus
realizing the reproduction procedure of this
in gene pool of the host (ant) popul
ation. This procedure
performs the following operations.
First, a pair of ants is chosen at random. Then, the chromosome of any of them is scanned in search of
. If the
is found, it is replicated in the partner chromosome, irrespec
tively of initial
record character in that chromosome. The chromosome scanning starts from the zero line (state#0) and goes on
as far as the first
is met. If no
is met, scanning finishes up only when the chromosome
record ends. So, sc
anning ceases irrespectively of the remaining chromosome un
scanned part content.
operator is a sort of point mutation, realized under particular conditions
. This is what we call an
. In detail,
the operator acts in such a way. If it finds
in the predetermined length range, and the action NOP completes this
, then this instruction
is substituted for the one of the three other actions (FWD, RGT or LFT). Specifically, this NOP is
the action from the fifth element of the
, counted in order. But, if the found
is completed by
the reference to the one of the elements inside
(internal cycle), then we have the following. The action
of this elemen
t is substituted for the action of the fifth element, counted backward from the end, the reference
being substituted for found at random reference to the element outside of the
The following peculiarity should be marked here.
The reference from t
he last symbol
to the first one
(i.e., by definition, a mature
proper) is processing with the mutator using the same rules. In other
words, the mutator breaks the cycle, thus destroying
So, the action of an intelligent mutator resul
ts in accumulation in the population of large length
s. Point mutations are needed for their maturation. In a result, these new mature
get chance of spreading in host population.
We should emphasize, that the two
perator operate only with mature
The test trail, used in this work is illustrated in Fig. 3. It can be seen that up to the 64
element our trail coincide
one, but the next part of the trail includes chaotically scatt
ered elements of high complexity.
Being trained on much simpler preceding trail part, the ant is not prepared to surmount the subsequent,
complicated sector (biologists would say that the ant is not pre
adapted to new conditions it faced with in this
r). More specifically, problems arise at attempts to get over gaps between the 64
and the 65
, or the 67
and the 68
s Really Accelerates
The preliminary computer experiments showed that it is not
possible to construct trail, which ants could not
come through for the real feasible computer time. The accelerating effect of
is especially noticeable
for small populations, when the probability of the effective navigation algorithm finding by
crossover and mutation operators is low.
On this basis, the following experiments were carried out on populations of 100 ants. The choice of
such a small population is also explained by our aim to carry out a comprehensive analysis of
dynamics. Such an analysis is not feasible for large populations of ants because of great number of
For example, thousands of
appear in a population of only 100 ants for 1000 generations.
Besides limiting value of ant po
pulation abundance, the following parameters were fixed in all test and
control runs: the maximum number of generations (330) and the part of population to reproduce (15%). The
of reproduction was used when the copies of chromosomes wit
h score exceeding the average
value replace all chromosomes having score less then average. The anal
ysis of preliminary runs showed
experimental results concerned and the inferences made are not sensitive to the variation of these three
, i.e. the parameters are not critical in this case.
With the aim of demonstrating of the MGE
technique efficiency we performed 100 independent runs of
the program, 5000 generations each. The results of test and control runs (population with
correspondingly) were compared in several series with the different values of standard
mutation parameters. Everywhere in this section we will accept that the effective navigation algorithm should
overcome the level of maximum score i
n 64 for 330 time steps. Different populations reached different
maximum scores (65, 67, 69, 72, 74, 76, 78, 79, 80, 81) for 5000 generations. But the best result was the score
81, reached for 330 generations.
ts of program runs with the MGE
tor and without it are illustrated in Fig. 4. It ca
, that MGE
technique obviously increases the probability of finding of effective navigation algorithm for
small populations and for a little number of generations.
As it is evident from
the graphs on Fig. 4, the mean and the
in experiment and
in control are growing, to a first approximation, linear in time. But the increment of growth in experiment with
is substantially higher, than in control.
be suggested that MGE
operators raise ant variability mainly in nonspecific manner thus
supplementing mutation effect of standard operators. But, this suggestion is not substantiated by the detailed
analysis of mutation process (see below). We carried out
control runs with the frequency values of standard
mutations, which are two and ten times higher than in control series given in Fig. 4. Hence, the high level of
does not raise the efficiency
of the navigation algorithm
it decreases this
(the results are not shown graphically).
No values of mutations and crossover parameters taken from the wide spectrum of combinations had a
pronounced effect on evoluti
onary search efficiency, if MGE
operators were disabled.
following combinations of crossover and mutation rates were tested: 0.0001 and 0.01, 0.0 and 0.04, 0.0001 and
0.08, 0.001 and 0.04, correspondingly; the results are not shown graphically).
Analysis of Transposon
population dynamics analysis was studied for host population of 100 ants, the number of
generations to the end of experiment being limited by 500. These limitations were non
critical for the
experiment. At the same time, they made possible th
e graphical representation of the results, because the number
of new abundant
forms in every run did not exceed the value of 200.
Every generation of computer population in 100 ants produces new
offspring, consisting of
tens of new
mutant forms. We accounted for only forms with abundance, exceeding minimal threshold in 10
individuals. So, for the first 500 steps of artificial evolution we had the order of 100
150 new forms.
We performed a comparative analysis of dynamics of the 2
5 ant populations which were succeeded to
found for the determined number of generations an effective navigation algorithm with the 25 unlucky ant
populations, which could not elaborate such an algorithm. Some regularities in the dynamics of ant and
populations were revealed. These regularities are illustrated in Fig. 5 and summarized as follows.
1) As a rule, only one form of
is dominating in the population at a moment; tens of new
forms appear in every host’s generation and disapp
ear as maximum, in a several generations.
2) From time to time, the current dominating form is displaced by the other one. In a large number of
generations the former dominating form can rehabilitate itself (at least, some cases were observed).
3) As a
3 (less often,
6, sometimes, up to 10) dominant forms have an opportunity to change
each other in population for the chosen period of time (the first 500 generations).
4) From time to time, an explosion of abundance of subdominant forms does oc
cur, which can last for
10 generations. Eventually, these subdominant forms can give 2
3 population explosions. One of such
explosions can finish up with the conversion of subdominant form into a dominating one.
These regularities are inherent
equally to the dynamics of stagnant ant populations and to the high
evolvable populations, which found an effective navigation algorithm for the period being studied. It turned out,
that dynamics of stagnant
populations demonstrate the same fo
ur properties as the populations,
succeeded in finding an effective navigation algorithm. The moments of finding of that algorithm correlates with
dominant forms changes.
Comparison of the dynamics of learning of ant population with the dynamics of
populations revealed apparent “coincidence” of the moment of change of
dominant form with the
moment of finding of the first effective navigation algorithm (Fig. 5). Just after this moment, mean population
score steeply rises up to the next
plateau. The process lasts for several generations. This local S
of the mean score growth correlate with curves of population size dynamics of dominant
the old form, then the new one) (Fig.5). It should be emphasize
d that this is only a correlation, not a functional
relationship. However, the existence of direct functional relationship between the code of a new
dominant form and the code of an effective navigation algorithm is still should be proved.
s Have More Pronounced Effect on the Rate of Ant
It was mentioned in the section “Methods and
Approach”, that by default, MGE
operator is working only with
s of length, which lie in the range from 5 to 11. In all exp
eriments, illustrated in the Figs. 3
admissible sizes of
lie in the range from 5 to 11. Analyzing
population dynamics, we
revealed, that very soon, over some tens generations, all
reach the upper length threshold
s of length 12 and more appear in the population. MGE
operator recognizes these large
s but leave them intact, i.e. it does not apply to them the mutation procedure. This is explained by the
fact, that the one
erator causes mutation not only in the
s, close to
transposons by the
definition (See “MGE
operators” section), but in the mature
as well. Selection pressure cause
surprisingly fast elimination of all
of length less than 11
(irrespectively, mature or immature it is)
and an accumulation of
s of length 12 and more (MGE
operator does not act on the latter).
We investigated also the behavior of an ant population, having
s of lager lengths. It became
revealed regularity viz., domination of
of maximum length is valid for all its sizes up to
32 (this is a physical limit).
Moreover, it turned out, that
with higher upper size threshold have more pronounced effect
on the rate of ant
training. The averaged score dynamics, being taken from the previous experiments (see Fig. 3)
was compared with the score dynamics, obtained in the experiment with the same parameters but one
length threshold which was made equal to
32 (Fig. 6).
The analysis of
population dynamics has shown that observed general features of dynamics
s are the same for both cases
with high upper size threshold and
one. In a several gene
of maximum possible length are coming to domination. As may be
inferred from the diagram (Fig. 6),
of length 32 are more effective mutators, than
length 11. So, the larger
, the “wiser” is it as a
mutator. We cannot give any simple explanation of
this effect so far.
Transmission of Transposon
s Is Necessary For Their
Effective Mutation Effect
s are transmitted vertically (from ancestors to descendants),
host, that have a
superiority in reproduction success is rapidly spreading in the population and gives new forms. But this process
per se is insufficient for the effective acceleration
of ant learning. Two
from one ant to another is a necessary for rising of ant training ability. In
Fig. 7 we illustrate the results of comparing of the test, presented in Fig.3, with the similar test, in which
cy of applying of two
was reduced by the factor of 10 and accounted 5%. This
parameter determines the proportion of population, which is subjected
to the action the two
in a generation. In all previous experiments, presented in this article, this quota accou
The obvious lowering of ant learning abilities with the decreasing of frequency of the two
operator application is evident from the diagram. Disabling of the operator lowers the efficacy further and makes
it almost equal to the
control (case without
lations Adapts to the Selective
In contrast to external, rigidly predetermined operator of mutation for classical GA, wise mutators co
with their host. It turned out, that the maxim
um length of
is the critical parameter, controlling fitting
of the host to parasite.
Small sized ant populations are predisposed to noticeable fluctuations, what makes them inappropriate
for our analysis. That is why, in this section we presen
t the results of computer experiments with the more
abundant ant population of 1000 individuals. The large population is more stable, so, the fine peculiarities of
dynamics are obvious (Fig. 8).
The analysis of all computer experiments, carried
out and presented in previous sections gave us
possible to propose the following model of the
role in the ant population dynamics.
In accordance to our model,
the population of hosts (i.e., ants) to a selective
for short period of evolutionary time (as a maximum
some tens of generations). So, as can be
seen from the diagram 8, the quotas of population, subjected to the action
place and two
operator accounts 17% and 48% correspondingly, over 40
50 generations. For this short period of time ant
population is able to adapt to the
selection pressure at the expense of loosing of short
with length of less than 11.
The problem of programming an artificial ant to fo
llow the Santa Fe trail has been repeatedly used as a
benchmark problem in GP [Koza, 1992; Lee and Wong
1995; Chellapilla, 1997; Harries and Smith, 1997; Luke
and Spector, 1997; Ito et al., 1998, Kuscu, 1998]. Recently Langdon and Poli have shown that per
several techniques is not much better than the best performance obtainable using uniform random search
[Langdon and Poli, 1998].
to these authors, the search space is large and forms a Karst landscape
containing many false peaks and m
any plateaus riven with deep valleys. The problem fitness landscape is
difficult for hill climbers and the problem is also difficult for Genetic Algorithms as it contains multiple levels of
There are many techniques capable of finding solutions
to the ant problem (GA, GP, simulated
) and although these have different performance the best typically only do marginally
better than the best performance that could be obtained with random search [Langdon and Poli, 1998]. That i
why the ant problem may be indicative of real
problem spaces and so be worthy of further study.
Forms Are the Components of the Effective
The results of careful analysis of organization of several t
ens of dominant
13 elements in
, taken from those ant populations, which coped with the navigation task, can be summarized as follows.
1) By the definition, the
program begins and ends with the zero state, i.e., it is a lo
executed over and over until the ant will meet the black cell. Typical examples of
corresponding ant movement trajectories are given in Table 1.
fold execution of the
program produces in most cases the closed
i.e., the ant will return to the starting position. The examples of these closed trajectories are given in Table 1. As
a rule, the closed contour is located in domains the size of 4
4 or 5
5 cells. Some cases of
countered which provide ant movement back and forth along the polygonal path (See Table 1).
3) As a rule, the
program is beginning to work not from the zero state but from the Nth state,
which is specific to every
, not beginning with
the initial, zero state. This transition into the Nth state
takes place as soon as the ant (host of the
) runs against the white cell.
4) Start the
program from the Nth state provides the execution of the simplest navigation
necessary for overcoming the simplest gaps, arranged in the first half of the trail (“looking around”,
then one step ahead, “looking around” again and so forth). This algorithm provides the successful passage of trail
up to the 64
majority of program
s guarantee overcoming of the element of high complexity
between the 64
and the 65
cells (See Table 1).
s are not suitable for the navigation programs. In that case the chromosome
elements, arranged in
free domain take control over navigation.
The detailed analysis of the organization of dominant
forms in populations, which are
succeeded in finding of the effective navigation programs, showed, that the
lves become the
components of these programs. Namely, the case in point is about the part of navigation program that is used for
effective “snuffing around” in situation, when ant faces with a wide gap.
In other words, transposons in our experiments reall
y found, cover and transmit host’s building blocks.
Mutators Have a Search Space Confining Effect
The Muir’s Trail search space has rugged geometry due to specific and discrete character of the problem. That is
why, the gradient methods are not effec
tive here. Moreover, this ant navigation problem is classified as a GA
hard problem, especially if trail is not designed specially for ant population training. The efficiency of
in the role of intelligent mutators can be measured by their searc
h space domain confining ability.
Therefore, the selec
tion criteria inserted into MGE
operators had to increase the probability of the effective
navigation algorithm finding on the element of high complexity. We proposed, that quasi
sions without NOP (“no operation” instruction) and without internal cycles (in conditions, when an ant
have white elements ahead of it) will be picked up by selection and used for universal navigation algorithms
A comparison of mutation frequ
encies in experiment and control with the according learning rates
confirm multiple reduction of evaluation numbers, needed for reaching of the same required learning in
. Mutation frequencies for basic experiments (Fig.3) in co
ntrol accounts: crossover
rate + mutation rate = 0.0001+0.04 P/bit/generation; MGE1 and MGE2 operators add in average 0.0027 and
0.0075 P/bit/generation accordingly. In other words,
transposons in average add
to value 0.041 about 0.012
is addition brings to multiple acceleration of ant population learning! Hence, according to
fig. 5, up to the end of the experiment (4622 time
step) the control set gives max score 6.47, whereas in the test
set this value is attained already on the 451 tim
step, i.e. 10 times sooner.
And what is more, though the ant test is now accepted as a classical one, its implementation in the form
of finite state automata is far from optimum. Firstly, the 32 states are obviously too much for the classical trails.
s redundancy brings to enormous extension of search space dimensionality. Secondly, the possibility to
generate various action sequences in the situation, when the ant faces with the black cell is redundant as well. It
is clear that the “step forward” is t
he only adequate action in this situation. Thirdly, multiple internal cycles,
essentially increasing the size of search space are hardly needed. At last, the action NOP is absolutely useless.
Apparently, the most simple and effective method of this navigat
ion problem solving would be using
the symbol strings, composed of combinations of three possible actions (FWD, RGT, and LFT) in the situation,
when the ant faces with t
he white cell. Applying the MGE
approach to the ant problem, we just perform such a
rch space size reduction. In so doing, we deal only with the “white half” of search space which is formed by
all sequences of actions, executed while the ant has white cells in front of it. Besides we escape internal loops,
and exclude the NOP action. We s
that mechanism explains the MGE
approach effect i.e., ten
increase of evolutionary search rate. The additional
contributory factor for the MGE
technique efficiency raising
is inclusion of transposition procedure, application frequency of which
being made high in compare to the other
It is become common place that hybrid optimization approaches are more effective instrument for heuristic
search then solo techniques. I
n this regard it is remarkable that complicated mechanisms are thought to be the
main power of macroevolution has evident hybrid character.
In this paper we demonstrated that the targeted
mutagenesis of transposon sequence coupled with the transposon horiz
ontal transmission qualitatively improve
the GA search performance. High rate of the transmission is crucial for such improvement. As we mentioned
before, recent years some authors have been using several new algorithms for EC improvement owing from fresh
findings and ideas of modern evolutionary biology. For our approach is essential “populational ecological” as
well as co
evolutionary aspects of interactions jumping selfish mutators with chromosomes
evolutionary formation of the world of gen
omic parasites with own competition and cooperation and own
communication we suppose have very promising perspectives. In this regard, our long term goal is to find
conditions and rules of genomes
genomic parasites co
evolution. It seems quite reasonable
that in the long run
of evolution genomes
parasites interaction forms kind of natural
. The usage of this meta
language for genome rearrangements could explain fascinating efficacy of
evolution that still beyond complete rational explanation.
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found building blocks: the tests with royal road
functions, The 6th World Multiconference on
Systemics, Cybernetics and
Informatics, SCI2002, July 14
18, Orlando, Florida.
Zongker, D. and Punch,
B., (1955), lil
Figure 1. (A). The John Mu
ir Trail (According to Brennan, 1994). Some “milestone” squares are numbered. The trail itself is
a series of black squares on a 32x32 white toroidal (i.e., wraparound) grid. Each black cell is numbered sequentially, from t
to the 89
(B). An exam
ple of organization of an ant as finite state automata. There are 32 states at all. Each state determines
two alternate actions, depending on input signal. The input signal is what an ant sees before him. If the cell before him is
black then the input is 1
, in opposite case the input is 0. Each of alternative actions includes one of four possible movements
(FWD, RGT, LFT or NOP) and transition to the next state. (See text for further details.)
additional string 1 1 1 1 1 1
0 0 0 0
The main str
L F F L L #0
* * * *
additional string 1 1 1 1 1
0 0 0 0
The main string
F F L N
* * * *
Mature and immature transposons.
A. Here is an example of mature
is a closed five
element cycle of states transitions (0, 17, 13, 21,
9, and again, 0).
B. The state table corresponding to the transposon (A).
. Here is an example of immature
. It dif
fers from the previous one
by the presence o
f procedure NOP in the last,
this sequence is not
D. The state table corresponding to the transposon (C).
Ant trail used in our computer experiments. The trail itself is a series of squares on a 32x32 white
idal grid. Each cell is numbered sequentially, from the 1
to the 89
The first two gaps of the higher
complexity are between 64
Figure 4. Numerical experiments, demonstrating statistically certain increasing of the G
A efficiency due to the effect of
operators. A comparison of the mean and the best
generation score dynamics (MGE
operator being activated) with
operator is disabled). The score values are averaged over 100 runs in both cases.
ize of population = 100; the number of generations = 5000; the
size varies from 5 to 11; crossover
rate (P/bit)/generation = 0.0001; mutation rate (P/bit)/generation = 0.04;
are the best
generation scores and
mean scores for the te
are the best
generation scores and
are the mean scores for the control runs.
Figure 5. An example of mobile genetic elements size population dynamics inside gene pool of the host (ant) population (the
first 500 generations). T
he curve of maximum score dynamics for ant population is given at the top of the diagram (marked
off with squares; the additional score scale is given on the left of the diagram). The moment of finding of the first effecti
navigation algorithm and the mo
ment of changing of dominant form of
are marked off with the edges of arrows
(see details in the text).
Figure 6. Comparison of ant populations learning abilities in dependence on
length. The curves of
maximum and mean score dyna
mics (the parameters of
size lies in the range of 5
32), averaged over
100 computer runs are compared with the corresponding curves, presented on fig.3, where parameter of
size lies between 5 and 11. The values of all other p
arameters are the same as in the
caption to Fig. 3.
are the best
generation scores and
are the mean scores for the runs for large
are the best
generation scores and
are the mean scores for the runs from the Fig. 3.
ure 7. The influence of decreasing of frequen
cy of applying of two
operator on the ant learning
abilities. The other parameters are the same as in the previous experiments (see caption to Fig. 3).
are the best
generation scores and
e mean scores for the test runs from the Fig. 3;
are the best
are the mean scores for the runs with disable MGE
Figure 8. The dynamics of quotas (in %) of individuals in ant population, subjected to the act
operators (MGE 1 and MGE 2, correspondingly).
Table 1. Examples of ant’ paths determined by
is turn right,
is turn left,