<s>
In	O
computer	B-General_Concept
science	I-General_Concept
and	O
operations	O
research	O
,	O
the	O
ant	B-Algorithm
colony	I-Algorithm
optimization	I-Algorithm
algorithm	I-Algorithm
(	O
ACO	O
)	O
is	O
a	O
probabilistic	O
technique	O
for	O
solving	O
computational	O
problems	O
which	O
can	O
be	O
reduced	O
to	O
finding	O
good	O
paths	O
through	O
graphs	O
.	O
</s>
<s>
Artificial	B-Algorithm
ants	I-Algorithm
stand	O
for	O
multi-agent	O
methods	O
inspired	O
by	O
the	O
behavior	O
of	O
real	O
ants	B-Application
.	O
</s>
<s>
The	O
pheromone-based	O
communication	O
of	O
biological	O
ants	B-Application
is	O
often	O
the	O
predominant	O
paradigm	O
used	O
.	O
</s>
<s>
Combinations	O
of	O
artificial	B-Algorithm
ants	I-Algorithm
and	O
local	B-Algorithm
search	I-Algorithm
algorithms	I-Algorithm
have	O
become	O
a	O
method	O
of	O
choice	O
for	O
numerous	O
optimization	O
tasks	O
involving	O
some	O
sort	O
of	O
graph	O
,	O
e.g.	O
,	O
vehicle	B-Algorithm
routing	I-Algorithm
and	O
internet	O
routing	B-Protocol
.	O
</s>
<s>
As	O
an	O
example	O
,	O
ant	B-Algorithm
colony	I-Algorithm
optimization	I-Algorithm
is	O
a	O
class	O
of	O
optimization	O
algorithms	O
modeled	O
on	O
the	O
actions	O
of	O
an	O
ant	B-Application
colony	O
.	O
</s>
<s>
Artificial	O
'	O
ants	B-Application
 '	O
(	O
e.g.	O
</s>
<s>
Real	O
ants	B-Application
lay	O
down	O
pheromones	O
directing	O
each	O
other	O
to	O
resources	O
while	O
exploring	O
their	O
environment	O
.	O
</s>
<s>
The	O
simulated	O
'	O
ants	B-Application
 '	O
similarly	O
record	O
their	O
positions	O
and	O
the	O
quality	O
of	O
their	O
solutions	O
,	O
so	O
that	O
in	O
later	O
simulation	O
iterations	B-Algorithm
more	O
ants	B-Application
locate	O
better	O
solutions	O
.	O
</s>
<s>
One	O
variation	O
on	O
this	O
approach	O
is	O
the	B-Algorithm
bees	I-Algorithm
algorithm	I-Algorithm
,	O
which	O
is	O
more	O
analogous	O
to	O
the	O
foraging	O
patterns	O
of	O
the	O
honey	O
bee	O
,	O
another	O
social	O
insect	O
.	O
</s>
<s>
This	O
algorithm	O
is	O
a	O
member	O
of	O
the	O
ant	B-Algorithm
colony	I-Algorithm
algorithms	I-Algorithm
family	O
,	O
in	O
swarm	B-Architecture
intelligence	I-Architecture
methods	O
,	O
and	O
it	O
constitutes	O
some	O
metaheuristic	B-Algorithm
optimizations	O
.	O
</s>
<s>
Initially	O
proposed	O
by	O
Marco	O
Dorigo	O
in	O
1992	O
in	O
his	O
PhD	O
thesis	O
,	O
the	O
first	O
algorithm	O
was	O
aiming	O
to	O
search	O
for	O
an	O
optimal	O
path	O
in	O
a	O
graph	O
,	O
based	O
on	O
the	O
behavior	O
of	O
ants	B-Application
seeking	O
a	O
path	O
between	O
their	O
colony	O
and	O
a	O
source	O
of	O
food	O
.	O
</s>
<s>
The	O
original	O
idea	O
has	O
since	O
diversified	O
to	O
solve	O
a	O
wider	O
class	O
of	O
numerical	O
problems	O
,	O
and	O
as	O
a	O
result	O
,	O
several	O
problems	O
have	O
emerged	O
,	O
drawing	O
on	O
various	O
aspects	O
of	O
the	O
behavior	O
of	O
ants	B-Application
.	O
</s>
<s>
In	O
the	O
natural	O
world	O
,	O
ants	B-Application
of	O
some	O
species	O
(	O
initially	O
)	O
wander	O
randomly	O
,	O
and	O
upon	O
finding	O
food	O
return	O
to	O
their	O
colony	O
while	O
laying	O
down	O
pheromone	O
trails	O
.	O
</s>
<s>
If	O
other	O
ants	B-Application
find	O
such	O
a	O
path	O
,	O
they	O
are	O
likely	O
not	O
to	O
keep	O
travelling	O
at	O
random	O
,	O
but	O
instead	O
to	O
follow	O
the	O
trail	O
,	O
returning	O
and	O
reinforcing	O
it	O
if	O
they	O
eventually	O
find	O
food	O
(	O
see	O
Ant	B-Application
communication	O
)	O
.	O
</s>
<s>
The	O
more	O
time	O
it	O
takes	O
for	O
an	O
ant	B-Application
to	O
travel	O
down	O
the	O
path	O
and	O
back	O
again	O
,	O
the	O
more	O
time	O
the	O
pheromones	O
have	O
to	O
evaporate	O
.	O
</s>
<s>
Pheromone	O
evaporation	O
also	O
has	O
the	O
advantage	O
of	O
avoiding	O
the	O
convergence	B-Algorithm
to	O
a	O
locally	O
optimal	O
solution	O
.	O
</s>
<s>
If	O
there	O
were	O
no	O
evaporation	O
at	O
all	O
,	O
the	O
paths	O
chosen	O
by	O
the	O
first	O
ants	B-Application
would	O
tend	O
to	O
be	O
excessively	O
attractive	O
to	O
the	O
following	O
ones	O
.	O
</s>
<s>
The	O
influence	O
of	O
pheromone	O
evaporation	O
in	O
real	O
ant	B-Algorithm
systems	I-Algorithm
is	O
unclear	O
,	O
but	O
it	O
is	O
very	O
important	O
in	O
artificial	O
systems	O
.	O
</s>
<s>
The	O
overall	O
result	O
is	O
that	O
when	O
one	O
ant	B-Application
finds	O
a	O
good	O
(	O
i.e.	O
,	O
short	O
)	O
path	O
from	O
the	O
colony	O
to	O
a	O
food	O
source	O
,	O
other	O
ants	B-Application
are	O
more	O
likely	O
to	O
follow	O
that	O
path	O
,	O
and	O
positive	O
feedback	O
eventually	O
leads	O
to	O
many	O
ants	B-Application
following	O
a	O
single	O
path	O
.	O
</s>
<s>
The	O
idea	O
of	O
the	O
ant	B-Algorithm
colony	I-Algorithm
algorithm	I-Algorithm
is	O
to	O
mimic	O
this	O
behavior	O
with	O
"	O
simulated	O
ants	B-Application
"	O
walking	O
around	O
the	O
graph	O
representing	O
the	O
problem	O
to	O
solve	O
.	O
</s>
<s>
Ambient	B-Architecture
networks	I-Architecture
of	O
intelligent	O
objects	O
and	O
,	O
sooner	O
or	O
later	O
,	O
a	O
new	O
generation	O
of	O
information	O
systems	O
that	O
are	O
even	O
more	O
diffused	O
and	O
based	O
on	O
nanotechnology	O
,	O
will	O
profoundly	O
change	O
this	O
concept	O
.	O
</s>
<s>
However	O
,	O
once	O
those	O
objects	O
are	O
interconnected	O
they	O
dispose	O
of	O
a	O
form	O
of	O
intelligence	O
that	O
can	O
be	O
compared	O
to	O
a	O
colony	O
of	O
ants	B-Application
or	O
bees	O
.	O
</s>
<s>
A	O
colony	O
of	O
ants	B-Application
,	O
for	O
example	O
,	O
represents	O
numerous	O
qualities	O
that	O
can	O
also	O
be	O
applied	O
to	O
a	O
network	O
of	O
ambient	O
objects	O
.	O
</s>
<s>
Colonies	O
of	O
ants	B-Application
have	O
a	O
very	O
high	O
capacity	O
to	O
adapt	O
themselves	O
to	O
changes	O
in	O
the	O
environment	O
as	O
well	O
as	O
an	O
enormous	O
strength	O
in	O
dealing	O
with	O
situations	O
where	O
one	O
individual	O
fails	O
to	O
carry	O
out	O
a	O
given	O
task	O
.	O
</s>
<s>
Parcels	O
of	O
information	O
that	O
move	O
from	O
a	O
computer	O
to	O
a	O
digital	O
object	O
behave	O
in	O
the	O
same	O
way	O
as	O
ants	B-Application
would	O
do	O
.	O
</s>
<s>
bees	O
,	O
ants	B-Application
and	O
termites	O
;	O
both	O
for	O
inter-agent	O
and	O
agent-swarm	O
communications	O
.	O
</s>
<s>
In	O
the	O
ant	B-Algorithm
colony	I-Algorithm
optimization	I-Algorithm
algorithms	I-Algorithm
,	O
an	O
artificial	O
ant	B-Application
is	O
a	O
simple	O
computational	O
agent	O
that	O
searches	O
for	O
good	O
solutions	O
to	O
a	O
given	O
optimization	O
problem	O
.	O
</s>
<s>
To	O
apply	O
an	O
ant	B-Algorithm
colony	I-Algorithm
algorithm	I-Algorithm
,	O
the	O
optimization	O
problem	O
needs	O
to	O
be	O
converted	O
into	O
the	O
problem	O
of	O
finding	O
the	O
shortest	O
path	O
on	O
a	O
weighted	O
graph	O
.	O
</s>
<s>
In	O
the	O
first	O
step	O
of	O
each	O
iteration	B-Algorithm
,	O
each	O
ant	B-Application
stochastically	O
constructs	O
a	O
solution	O
,	O
i.e.	O
</s>
<s>
In	O
the	O
second	O
step	O
,	O
the	O
paths	O
found	O
by	O
the	O
different	O
ants	B-Application
are	O
compared	O
.	O
</s>
<s>
Each	O
ant	B-Application
needs	O
to	O
construct	O
a	O
solution	O
to	O
move	O
through	O
the	O
graph	O
.	O
</s>
<s>
To	O
select	O
the	O
next	O
edge	O
in	O
its	O
tour	O
,	O
an	O
ant	B-Application
will	O
consider	O
the	O
length	O
of	O
each	O
edge	O
available	O
from	O
its	O
current	O
position	O
,	O
as	O
well	O
as	O
the	O
corresponding	O
pheromone	O
level	O
.	O
</s>
<s>
At	O
each	O
step	O
of	O
the	O
algorithm	O
,	O
each	O
ant	B-Application
moves	O
from	O
a	O
state	O
to	O
state	O
,	O
corresponding	O
to	O
a	O
more	O
complete	O
intermediate	O
solution	O
.	O
</s>
<s>
Thus	O
,	O
each	O
ant	B-Application
computes	O
a	O
set	O
of	O
feasible	O
expansions	O
to	O
its	O
current	O
state	O
in	O
each	O
iteration	B-Algorithm
,	O
and	O
moves	O
to	O
one	O
of	O
these	O
in	O
probability	O
.	O
</s>
<s>
For	O
ant	B-Application
,	O
the	O
probability	O
of	O
moving	O
from	O
state	O
to	O
state	O
depends	O
on	O
the	O
combination	O
of	O
two	O
values	O
,	O
the	O
attractiveness	O
of	O
the	O
move	O
,	O
as	O
computed	O
by	O
some	O
heuristic	O
indicating	O
the	O
a	O
priori	O
desirability	O
of	O
that	O
move	O
and	O
the	O
trail	O
level	O
of	O
the	O
move	O
,	O
indicating	O
how	O
proficient	O
it	O
has	O
been	O
in	O
the	O
past	O
to	O
make	O
that	O
particular	O
move	O
.	O
</s>
<s>
Trails	O
are	O
usually	O
updated	O
when	O
all	O
ants	B-Application
have	O
completed	O
their	O
solution	O
,	O
increasing	O
or	O
decreasing	O
the	O
level	O
of	O
trails	O
corresponding	O
to	O
moves	O
that	O
were	O
part	O
of	O
"	O
good	O
"	O
or	O
"	O
bad	O
"	O
solutions	O
,	O
respectively	O
.	O
</s>
<s>
where	O
is	O
the	O
cost	O
of	O
the	O
th	O
ant	B-Application
's	O
tour	O
(	O
typically	O
length	O
)	O
and	O
is	O
a	O
constant	O
.	O
</s>
<s>
The	O
ant	B-Algorithm
system	I-Algorithm
is	O
the	O
first	O
ACO	O
algorithm	O
.	O
</s>
<s>
In	O
the	O
ant	B-Application
colony	O
system	O
algorithm	O
,	O
the	O
original	O
ant	B-Algorithm
system	I-Algorithm
was	O
modified	O
in	O
three	O
aspects	O
:	O
</s>
<s>
While	O
building	O
a	O
solution	O
,	O
ants	B-Application
change	O
the	O
pheromone	O
level	O
of	O
the	O
edges	O
they	O
are	O
selecting	O
by	O
applying	O
a	O
local	O
pheromone	O
updating	O
rule	O
;	O
</s>
<s>
At	O
the	O
end	O
of	O
each	O
iteration	B-Algorithm
,	O
only	O
the	O
best	O
ant	B-Application
is	O
allowed	O
to	O
update	O
the	O
trails	O
by	O
applying	O
a	O
modified	O
global	O
pheromone	O
updating	O
rule	O
.	O
</s>
<s>
In	O
this	O
algorithm	O
,	O
the	O
global	O
best	O
solution	O
deposits	O
pheromone	O
on	O
its	O
trail	O
after	O
every	O
iteration	B-Algorithm
(	O
even	O
if	O
this	O
trail	O
has	O
not	O
been	O
revisited	O
)	O
,	O
along	O
with	O
all	O
the	O
other	O
ants	B-Application
.	O
</s>
<s>
The	O
elitist	O
strategy	O
has	O
as	O
its	O
objective	O
directing	O
the	O
search	O
of	O
all	O
ants	B-Application
to	O
construct	O
a	O
solution	O
to	O
contain	O
links	O
of	O
the	O
current	O
best	O
route	O
.	O
</s>
<s>
Only	O
the	O
global	O
best	O
tour	O
or	O
the	O
iteration	B-Algorithm
best	O
tour	O
are	O
allowed	O
to	O
add	O
pheromone	O
to	O
its	O
trail	O
.	O
</s>
<s>
Only	O
a	O
fixed	O
number	O
of	O
the	O
best	O
ants	B-Application
in	O
this	O
iteration	B-Algorithm
are	O
allowed	O
to	O
update	O
their	O
trials	O
.	O
</s>
<s>
An	O
ant	B-Application
colony	O
system	O
(	O
ACS	O
)	O
with	O
communication	O
strategies	O
is	O
developed	O
.	O
</s>
<s>
The	O
artificial	B-Algorithm
ants	I-Algorithm
are	O
partitioned	O
into	O
several	O
groups	O
.	O
</s>
<s>
methods	O
for	O
updating	O
the	O
pheromone	O
level	O
between	O
groups	O
in	O
ACS	O
are	O
proposed	O
and	O
work	O
on	O
the	O
traveling	B-Algorithm
salesman	I-Algorithm
problem	I-Algorithm
.	O
</s>
<s>
The	O
pheromone	O
deposit	O
mechanism	O
of	O
COAC	O
is	O
to	O
enable	O
ants	B-Application
to	O
search	O
for	O
solutions	O
collaboratively	O
and	O
effectively	O
.	O
</s>
<s>
By	O
using	O
an	O
orthogonal	O
design	O
method	O
,	O
ants	B-Application
in	O
the	O
feasible	O
domain	O
can	O
explore	O
their	O
chosen	O
regions	O
rapidly	O
and	O
efficiently	O
,	O
with	O
enhanced	O
global	O
search	O
capability	O
and	O
accuracy	O
.	O
</s>
<s>
It	O
is	O
a	O
recursive	O
form	O
of	O
ant	B-Algorithm
system	I-Algorithm
which	O
divides	O
the	O
whole	O
search	O
domain	O
into	O
several	O
sub-domains	O
and	O
solves	O
the	O
objective	O
on	O
these	O
subdomains	O
.	O
</s>
<s>
The	O
first	O
evidence	O
of	O
convergence	B-Algorithm
for	O
an	O
ant	B-Algorithm
colony	I-Algorithm
algorithm	I-Algorithm
was	O
made	O
in	O
2000	O
,	O
the	O
graph-based	O
ant	B-Algorithm
system	I-Algorithm
algorithm	O
,	O
and	O
later	O
on	O
for	O
the	O
ACS	O
and	O
MMAS	O
algorithms	O
.	O
</s>
<s>
Like	O
most	O
metaheuristics	B-Algorithm
,	O
it	O
is	O
very	O
difficult	O
to	O
estimate	O
the	O
theoretical	O
speed	O
of	O
convergence	B-Algorithm
.	O
</s>
<s>
A	O
performance	O
analysis	O
of	O
a	O
continuous	O
ant	B-Algorithm
colony	I-Algorithm
algorithm	I-Algorithm
with	O
respect	O
to	O
its	O
various	O
parameters	O
(	O
edge	O
selection	O
strategy	O
,	O
distance	O
measure	O
metric	O
,	O
and	O
pheromone	O
evaporation	O
rate	O
)	O
showed	O
that	O
its	O
performance	O
and	O
rate	O
of	O
convergence	B-Algorithm
are	O
sensitive	O
to	O
the	O
chosen	O
parameter	O
values	O
,	O
and	O
especially	O
to	O
the	O
value	O
of	O
the	O
pheromone	O
evaporation	O
rate	O
.	O
</s>
<s>
In	O
2004	O
,	O
Zlochin	O
and	O
his	O
colleagues	O
showed	O
that	O
COAC-type	O
algorithms	O
could	O
be	O
assimilated	O
methods	O
of	O
stochastic	B-Algorithm
gradient	I-Algorithm
descent	I-Algorithm
,	O
on	O
the	O
cross-entropy	O
and	O
estimation	O
of	O
distribution	O
algorithm	O
.	O
</s>
<s>
They	O
proposed	O
these	O
metaheuristics	B-Algorithm
as	O
a	O
"	O
research-based	O
model	O
"	O
.	O
</s>
<s>
Ant	B-Algorithm
colony	I-Algorithm
optimization	I-Algorithm
algorithms	I-Algorithm
have	O
been	O
applied	O
to	O
many	O
combinatorial	O
optimization	O
problems	O
,	O
ranging	O
from	O
quadratic	O
assignment	O
to	O
protein	O
folding	O
or	O
routing	B-Algorithm
vehicles	I-Algorithm
and	O
a	O
lot	O
of	O
derived	O
methods	O
have	O
been	O
adapted	O
to	O
dynamic	O
problems	O
in	O
real	O
variables	O
,	O
stochastic	O
problems	O
,	O
multi-targets	O
and	O
parallel	B-Operating_System
implementations	O
.	O
</s>
<s>
It	O
has	O
also	O
been	O
used	O
to	O
produce	O
near-optimal	O
solutions	O
to	O
the	O
travelling	B-Algorithm
salesman	I-Algorithm
problem	I-Algorithm
.	O
</s>
<s>
They	O
have	O
an	O
advantage	O
over	O
simulated	B-Algorithm
annealing	I-Algorithm
and	O
genetic	B-Algorithm
algorithm	I-Algorithm
approaches	O
of	O
similar	O
problems	O
when	O
the	O
graph	O
may	O
change	O
dynamically	O
;	O
the	O
ant	B-Algorithm
colony	I-Algorithm
algorithm	I-Algorithm
can	O
be	O
run	O
continuously	O
and	O
adapt	O
to	O
changes	O
in	O
real	O
time	O
.	O
</s>
<s>
This	O
is	O
of	O
interest	O
in	O
network	B-Protocol
routing	I-Protocol
and	O
urban	O
transportation	O
systems	O
.	O
</s>
<s>
The	O
first	O
ACO	O
algorithm	O
was	O
called	O
the	O
ant	B-Algorithm
system	I-Algorithm
and	O
it	O
was	O
aimed	O
to	O
solve	O
the	O
travelling	B-Algorithm
salesman	I-Algorithm
problem	I-Algorithm
,	O
in	O
which	O
the	O
goal	O
is	O
to	O
find	O
the	O
shortest	O
round-trip	O
to	O
link	O
a	O
series	O
of	O
cities	O
.	O
</s>
<s>
The	O
general	O
algorithm	O
is	O
relatively	O
simple	O
and	O
based	O
on	O
a	O
set	O
of	O
ants	B-Application
,	O
each	O
making	O
one	O
of	O
the	O
possible	O
round-trips	O
along	O
the	O
cities	O
.	O
</s>
<s>
At	O
each	O
stage	O
,	O
the	O
ant	B-Application
chooses	O
to	O
move	O
from	O
one	O
city	O
to	O
another	O
according	O
to	O
some	O
rules	O
:	O
</s>
<s>
Having	O
completed	O
its	O
journey	O
,	O
the	O
ant	B-Application
deposits	O
more	O
pheromones	O
on	O
all	O
edges	O
it	O
traversed	O
,	O
if	O
the	O
journey	O
is	O
short	O
;	O
</s>
<s>
After	O
each	O
iteration	B-Algorithm
,	O
trails	O
of	O
pheromones	O
evaporate	O
.	O
</s>
<s>
Ant	B-Algorithm
colony	I-Algorithm
optimization	I-Algorithm
(	O
ACO	O
)	O
based	O
optimization	O
of	O
45nm	O
CMOS-based	O
sense	O
amplifier	O
circuit	O
could	O
converge	O
to	O
optimal	O
solutions	O
in	O
very	O
minimal	O
time	O
.	O
</s>
<s>
Ant	B-Algorithm
colony	I-Algorithm
optimization	I-Algorithm
(	O
ACO	O
)	O
based	O
reversible	O
circuit	O
synthesis	O
could	O
improve	O
efficiency	O
significantly	O
.	O
</s>
<s>
To	O
optimize	O
the	O
form	O
of	O
antennas	O
,	O
ant	B-Algorithm
colony	I-Algorithm
algorithms	I-Algorithm
can	O
be	O
used	O
.	O
</s>
<s>
The	O
ACO	O
algorithm	O
is	O
used	O
in	O
image	O
processing	O
for	O
image	B-Algorithm
edge	I-Algorithm
detection	O
and	O
edge	O
linking	O
.	O
</s>
<s>
Edge	B-Algorithm
detection	I-Algorithm
:	O
</s>
<s>
The	O
graph	O
here	O
is	O
the	O
2-D	O
image	O
and	O
the	O
ants	B-Application
traverse	O
from	O
one	O
pixel	B-Algorithm
depositing	O
pheromone	O
.	O
</s>
<s>
The	O
movement	O
of	O
ants	B-Application
from	O
one	O
pixel	B-Algorithm
to	O
another	O
is	O
directed	O
by	O
the	O
local	O
variation	O
of	O
the	O
image	O
's	O
intensity	O
values	O
.	O
</s>
<s>
The	O
following	O
are	O
the	O
steps	O
involved	O
in	O
edge	B-Algorithm
detection	I-Algorithm
using	O
ACO	O
:	O
</s>
<s>
Randomly	O
place	O
ants	B-Application
on	O
the	O
image	O
where	O
.	O
</s>
<s>
the	O
local	O
statistics	O
at	O
the	O
pixel	B-Algorithm
position	O
.	O
</s>
<s>
The	O
ant	B-Application
's	O
movement	O
is	O
based	O
on	O
4-connected	B-Algorithm
pixels	B-Algorithm
or	O
8-connected	B-Algorithm
pixels	B-Algorithm
.	O
</s>
<s>
in	O
step	O
3	O
the	O
trail	O
of	O
the	O
ant	B-Application
(	O
given	O
by	O
)	O
is	O
updated	O
where	O
as	O
in	O
step	O
5	O
the	O
evaporation	O
rate	O
of	O
the	O
trail	O
is	O
updated	O
which	O
is	O
given	O
by	O
:	O
</s>
<s>
Once	O
the	O
K	O
ants	B-Application
have	O
moved	O
a	O
fixed	O
distance	O
L	O
for	O
N	O
iteration	B-Algorithm
,	O
the	O
decision	O
whether	O
it	O
is	O
an	O
edge	O
or	O
not	O
is	O
based	O
on	O
the	O
threshold	O
T	O
on	O
the	O
pheromone	O
matrixτ	O
.	O
</s>
<s>
Threshold	O
for	O
the	O
below	O
example	O
is	O
calculated	O
based	O
on	O
Otsu	B-Algorithm
's	I-Algorithm
method	I-Algorithm
.	O
</s>
<s>
Image	B-Algorithm
edge	I-Algorithm
detected	O
using	O
ACO	O
:	O
The	O
images	O
below	O
are	O
generated	O
using	O
different	O
functions	O
given	O
by	O
the	O
equation	O
(	O
1	O
)	O
to	O
(	O
4	O
)	O
.	O
</s>
<s>
It	O
is	O
not	O
easy	O
to	O
give	O
a	O
precise	O
definition	O
of	O
what	O
algorithm	O
is	O
or	O
is	O
not	O
an	O
ant	B-Application
colony	O
,	O
because	O
the	O
definition	O
may	O
vary	O
according	O
to	O
the	O
authors	O
and	O
uses	O
.	O
</s>
<s>
Broadly	O
speaking	O
,	O
ant	B-Algorithm
colony	I-Algorithm
algorithms	I-Algorithm
are	O
regarded	O
as	O
populated	O
metaheuristics	B-Algorithm
with	O
each	O
solution	O
represented	O
by	O
an	O
ant	B-Application
moving	O
in	O
the	O
search	O
space	O
.	O
</s>
<s>
Ants	B-Application
mark	O
the	O
best	O
solutions	O
and	O
take	O
account	O
of	O
previous	O
markings	O
to	O
optimize	O
their	O
search	O
.	O
</s>
<s>
They	O
can	O
be	O
seen	O
as	O
probabilistic	O
multi-agent	O
algorithms	O
using	O
a	O
probability	O
distribution	O
to	O
make	O
the	O
transition	O
between	O
each	O
iteration	B-Algorithm
.	O
</s>
<s>
In	O
their	O
versions	O
for	O
combinatorial	O
problems	O
,	O
they	O
use	O
an	O
iterative	B-Algorithm
construction	O
of	O
solutions	O
.	O
</s>
<s>
According	O
to	O
some	O
authors	O
,	O
the	O
thing	O
which	O
distinguishes	O
ACO	O
algorithms	O
from	O
other	O
relatives	O
(	O
such	O
as	O
algorithms	O
to	O
estimate	O
the	O
distribution	O
or	O
particle	B-Algorithm
swarm	I-Algorithm
optimization	I-Algorithm
)	O
is	O
precisely	O
their	O
constructive	O
aspect	O
.	O
</s>
<s>
In	O
combinatorial	O
problems	O
,	O
it	O
is	O
possible	O
that	O
the	O
best	O
solution	O
eventually	O
be	O
found	O
,	O
even	O
though	O
no	O
ant	B-Application
would	O
prove	O
effective	O
.	O
</s>
<s>
Thus	O
,	O
in	O
the	O
example	O
of	O
the	O
Travelling	B-Algorithm
salesman	I-Algorithm
problem	I-Algorithm
,	O
it	O
is	O
not	O
necessary	O
that	O
an	O
ant	B-Application
actually	O
travels	O
the	O
shortest	O
route	O
:	O
the	O
shortest	O
route	O
can	O
be	O
built	O
from	O
the	O
strongest	O
segments	O
of	O
the	O
best	O
solutions	O
.	O
</s>
<s>
The	O
wide	O
variety	O
of	O
algorithms	O
(	O
for	O
optimization	O
or	O
not	O
)	O
seeking	O
self-organization	O
in	O
biological	O
systems	O
has	O
led	O
to	O
the	O
concept	O
of	O
"	O
swarm	B-Architecture
intelligence	I-Architecture
"	O
,	O
which	O
is	O
a	O
very	O
general	O
framework	O
in	O
which	O
ant	B-Algorithm
colony	I-Algorithm
algorithms	I-Algorithm
fit	O
.	O
</s>
<s>
There	O
is	O
in	O
practice	O
a	O
large	O
number	O
of	O
algorithms	O
claiming	O
to	O
be	O
"	O
ant	B-Application
colonies	O
"	O
,	O
without	O
always	O
sharing	O
the	O
general	O
framework	O
of	O
optimization	O
by	O
canonical	O
ant	B-Application
colonies	O
.	O
</s>
<s>
In	O
practice	O
,	O
the	O
use	O
of	O
an	O
exchange	O
of	O
information	O
between	O
ants	B-Application
via	O
the	O
environment	O
(	O
a	O
principle	O
called	O
"	O
stigmergy	O
"	O
)	O
is	O
deemed	O
enough	O
for	O
an	O
algorithm	O
to	O
belong	O
to	O
the	O
class	O
of	O
ant	B-Algorithm
colony	I-Algorithm
algorithms	I-Algorithm
.	O
</s>
<s>
An	O
evolutionary	B-Algorithm
algorithm	I-Algorithm
that	O
substitutes	O
traditional	O
reproduction	O
operators	O
by	O
model-guided	O
operators	O
.	O
</s>
<s>
Similar	O
to	O
simulated	B-Algorithm
annealing	I-Algorithm
in	O
that	O
both	O
traverse	O
the	O
solution	O
space	O
by	O
testing	O
mutations	O
of	O
an	O
individual	O
solution	O
.	O
</s>
<s>
While	O
simulated	B-Algorithm
annealing	I-Algorithm
generates	O
only	O
one	O
mutated	O
solution	O
,	O
tabu	B-Algorithm
search	I-Algorithm
generates	O
many	O
mutated	O
solutions	O
and	O
moves	O
to	O
the	O
solution	O
with	O
the	O
lowest	O
fitness	O
of	O
those	O
generated	O
.	O
</s>
<s>
A	O
swarm	B-Architecture
intelligence	I-Architecture
method	O
.	O
</s>
<s>
A	O
swarm	B-Architecture
intelligence	I-Architecture
method	O
.	O
</s>
<s>
Chronology	O
of	O
ant	B-Algorithm
colony	I-Algorithm
optimization	I-Algorithm
algorithms	I-Algorithm
.	O
</s>
<s>
1983	O
,	O
Deneubourg	O
and	O
his	O
colleagues	O
studied	O
the	O
collective	O
behavior	O
of	O
ants	B-Application
;	O
</s>
<s>
1988	O
,	O
and	O
Moyson	O
Manderick	O
have	O
an	O
article	O
on	O
self-organization	O
among	O
ants	B-Application
;	O
</s>
<s>
1989	O
,	O
the	O
work	O
of	O
Goss	O
,	O
Aron	O
,	O
Deneubourg	O
and	O
Pasteels	O
on	O
the	O
collective	O
behavior	O
of	O
Argentine	O
ants	B-Application
,	O
which	O
will	O
give	O
the	O
idea	O
of	O
ant	B-Algorithm
colony	I-Algorithm
optimization	I-Algorithm
algorithms	I-Algorithm
;	O
</s>
<s>
1991	O
,	O
M	O
.	O
Dorigo	O
proposed	O
the	O
ant	B-Algorithm
system	I-Algorithm
in	O
his	O
doctoral	O
thesis	O
(	O
which	O
was	O
published	O
in	O
1992	O
)	O
.	O
</s>
<s>
1995	O
,	O
Gambardella	O
and	O
Dorigo	O
proposed	O
ant-q	O
,	O
the	O
preliminary	O
version	O
of	O
ant	B-Application
colony	O
system	O
as	O
first	O
extension	O
of	O
ant	B-Algorithm
system	I-Algorithm
;	O
.	O
</s>
<s>
1996	O
,	O
publication	O
of	O
the	O
article	O
on	O
ant	B-Algorithm
system	I-Algorithm
;	O
</s>
<s>
1997	O
,	O
Dorigo	O
and	O
Gambardella	O
proposed	O
ant	B-Application
colony	O
system	O
hybridized	O
with	O
local	B-Algorithm
search	I-Algorithm
;	O
</s>
<s>
1998	O
,	O
Stützle	O
proposes	O
initial	O
parallel	B-Operating_System
implementations	O
;	O
</s>
<s>
1999	O
,	O
Gambardella	O
,	O
Taillard	O
and	O
Agazzi	O
proposed	O
macs-vrptw	O
,	O
first	O
multi	O
ant	B-Application
colony	O
system	O
applied	O
to	O
vehicle	B-Algorithm
routing	I-Algorithm
problems	I-Algorithm
with	O
time	O
windows	O
,	O
</s>
<s>
2000	O
,	O
Hoos	O
and	O
Stützle	O
invent	O
the	O
max-min	O
ant	B-Algorithm
system	I-Algorithm
;	O
</s>
<s>
2000	O
,	O
first	O
applications	O
to	O
the	O
scheduling	O
,	O
scheduling	O
sequence	O
and	O
the	O
satisfaction	B-Application
of	I-Application
constraints	I-Application
;	O
</s>
<s>
2012	O
,	O
Prabhakar	O
and	O
colleagues	O
publish	O
research	O
relating	O
to	O
the	O
operation	O
of	O
individual	O
ants	B-Application
communicating	O
in	O
tandem	O
without	O
pheromones	O
,	O
mirroring	O
the	O
principles	O
of	O
computer	O
network	O
organization	O
.	O
</s>
<s>
The	O
communication	O
model	O
has	O
been	O
compared	O
to	O
the	O
Transmission	B-Protocol
Control	I-Protocol
Protocol	I-Protocol
.	O
</s>
<s>
2017	O
,	O
successful	O
integration	O
of	O
the	O
multi-criteria	O
decision-making	O
method	O
PROMETHEE	O
into	O
the	O
ACO	O
algorithm	O
(	O
HUMANT	B-Algorithm
algorithm	I-Algorithm
)	O
.	O
</s>
