<s>
In	O
computer	B-General_Concept
science	I-General_Concept
and	O
mathematical	O
optimization	O
,	O
a	O
metaheuristic	B-Algorithm
is	O
a	O
higher-level	O
procedure	O
or	O
heuristic	B-Algorithm
designed	O
to	O
find	O
,	O
generate	O
,	O
tune	O
,	O
or	O
select	O
a	O
heuristic	B-Algorithm
(	O
partial	O
search	B-Application
algorithm	I-Application
)	O
that	O
may	O
provide	O
a	O
sufficiently	O
good	O
solution	O
to	O
an	O
optimization	O
problem	O
or	O
a	O
machine	O
learning	O
problem	O
,	O
especially	O
with	O
incomplete	O
or	O
imperfect	O
information	O
or	O
limited	O
computation	O
capacity	O
.	O
</s>
<s>
Metaheuristics	B-Algorithm
sample	O
a	O
subset	O
of	O
solutions	O
which	O
is	O
otherwise	O
too	O
large	O
to	O
be	O
completely	O
enumerated	O
or	O
otherwise	O
explored	O
.	O
</s>
<s>
Metaheuristics	B-Algorithm
may	O
make	O
relatively	O
few	O
assumptions	O
about	O
the	O
optimization	O
problem	O
being	O
solved	O
and	O
so	O
may	O
be	O
usable	O
for	O
a	O
variety	O
of	O
problems	O
.	O
</s>
<s>
Compared	O
to	O
optimization	O
algorithms	O
and	O
iterative	B-Algorithm
methods	I-Algorithm
,	O
metaheuristics	B-Algorithm
do	O
not	O
guarantee	O
that	O
a	O
globally	O
optimal	O
solution	O
can	O
be	O
found	O
on	O
some	O
class	O
of	O
problems	O
.	O
</s>
<s>
Many	O
metaheuristics	B-Algorithm
implement	O
some	O
form	O
of	O
stochastic	B-Algorithm
optimization	I-Algorithm
,	O
so	O
that	O
the	O
solution	O
found	O
is	O
dependent	O
on	O
the	O
set	O
of	O
random	O
variables	O
generated	O
.	O
</s>
<s>
In	O
combinatorial	O
optimization	O
,	O
by	O
searching	O
over	O
a	O
large	O
set	O
of	O
feasible	O
solutions	O
,	O
metaheuristics	B-Algorithm
can	O
often	O
find	O
good	O
solutions	O
with	O
less	O
computational	O
effort	O
than	O
optimization	O
algorithms	O
,	O
iterative	B-Algorithm
methods	I-Algorithm
,	O
or	O
simple	O
heuristics	B-Algorithm
.	O
</s>
<s>
Most	O
literature	O
on	O
metaheuristics	B-Algorithm
is	O
experimental	O
in	O
nature	O
,	O
describing	O
empirical	O
results	O
based	O
on	O
computer	O
experiments	O
with	O
the	O
algorithms	O
.	O
</s>
<s>
But	O
some	O
formal	O
theoretical	O
results	O
are	O
also	O
available	O
,	O
often	O
on	O
convergence	B-Algorithm
and	O
the	O
possibility	O
of	O
finding	O
the	O
global	O
optimum	O
.	O
</s>
<s>
Many	O
metaheuristic	B-Algorithm
methods	O
have	O
been	O
published	O
with	O
claims	O
of	O
novelty	O
and	O
practical	O
efficacy	O
.	O
</s>
<s>
These	O
are	O
properties	O
that	O
characterize	O
most	O
metaheuristics	B-Algorithm
:	O
</s>
<s>
Metaheuristics	B-Algorithm
are	O
strategies	O
that	O
guide	O
the	O
search	O
process	O
.	O
</s>
<s>
Techniques	O
which	O
constitute	O
metaheuristic	B-Algorithm
algorithms	O
range	O
from	O
simple	B-Algorithm
local	I-Algorithm
search	I-Algorithm
procedures	O
to	O
complex	O
learning	O
processes	O
.	O
</s>
<s>
Metaheuristic	B-Algorithm
algorithms	O
are	O
approximate	O
and	O
usually	O
non-deterministic	O
.	O
</s>
<s>
Metaheuristics	B-Algorithm
are	O
not	O
problem-specific	O
.	O
</s>
<s>
There	O
are	O
a	O
wide	O
variety	O
of	O
metaheuristics	B-Algorithm
and	O
a	O
number	O
of	O
properties	O
with	O
respect	O
to	O
which	O
to	O
classify	O
them	O
.	O
</s>
<s>
One	O
type	O
of	O
search	O
strategy	O
is	O
an	O
improvement	O
on	O
simple	B-Algorithm
local	I-Algorithm
search	I-Algorithm
algorithms	O
.	O
</s>
<s>
A	O
well	O
known	O
local	B-Algorithm
search	I-Algorithm
algorithm	I-Algorithm
is	O
the	O
hill	B-Algorithm
climbing	I-Algorithm
method	I-Algorithm
which	O
is	O
used	O
to	O
find	O
local	O
optimums	O
.	O
</s>
<s>
However	O
,	O
hill	B-Algorithm
climbing	I-Algorithm
does	O
not	O
guarantee	O
finding	O
global	O
optimum	O
solutions	O
.	O
</s>
<s>
Many	O
metaheuristic	B-Algorithm
ideas	O
were	O
proposed	O
to	O
improve	O
local	B-Algorithm
search	I-Algorithm
heuristic	B-Algorithm
in	O
order	O
to	O
find	O
better	O
solutions	O
.	O
</s>
<s>
Such	O
metaheuristics	B-Algorithm
include	O
simulated	B-Algorithm
annealing	I-Algorithm
,	O
tabu	B-Algorithm
search	I-Algorithm
,	O
iterated	B-Algorithm
local	I-Algorithm
search	I-Algorithm
,	O
variable	B-Algorithm
neighborhood	I-Algorithm
search	I-Algorithm
,	O
and	O
GRASP	B-Algorithm
.	O
</s>
<s>
These	O
metaheuristics	B-Algorithm
can	O
both	O
be	O
classified	O
as	O
local	O
search-based	O
or	O
global	O
search	O
metaheuristics	B-Algorithm
.	O
</s>
<s>
Other	O
global	O
search	O
metaheuristic	B-Algorithm
that	O
are	O
not	O
local	O
search-based	O
are	O
usually	O
population-based	O
metaheuristics	B-Algorithm
.	O
</s>
<s>
Single	O
solution	O
approaches	O
focus	O
on	O
modifying	O
and	O
improving	O
a	O
single	O
candidate	O
solution	O
;	O
single	O
solution	O
metaheuristics	B-Algorithm
include	O
simulated	B-Algorithm
annealing	I-Algorithm
,	O
iterated	B-Algorithm
local	I-Algorithm
search	I-Algorithm
,	O
variable	B-Algorithm
neighborhood	I-Algorithm
search	I-Algorithm
,	O
and	O
guided	B-Algorithm
local	I-Algorithm
search	I-Algorithm
.	O
</s>
<s>
Population-based	O
approaches	O
maintain	O
and	O
improve	O
multiple	O
candidate	O
solutions	O
,	O
often	O
using	O
population	O
characteristics	O
to	O
guide	O
the	O
search	O
;	O
population	O
based	O
metaheuristics	B-Algorithm
include	O
evolutionary	O
computation	O
,	O
genetic	B-Algorithm
algorithms	I-Algorithm
,	O
and	O
particle	B-Algorithm
swarm	I-Algorithm
optimization	I-Algorithm
.	O
</s>
<s>
Another	O
category	O
of	O
metaheuristics	B-Algorithm
is	O
Swarm	B-Architecture
intelligence	I-Architecture
which	O
is	O
a	O
collective	O
behavior	O
of	O
decentralized	O
,	O
self-organized	O
agents	O
in	O
a	O
population	O
or	O
swarm	O
.	O
</s>
<s>
Ant	B-Algorithm
colony	I-Algorithm
optimization	I-Algorithm
,	O
particle	B-Algorithm
swarm	I-Algorithm
optimization	I-Algorithm
,	O
social	B-Algorithm
cognitive	I-Algorithm
optimization	I-Algorithm
are	O
examples	O
of	O
this	O
category	O
.	O
</s>
<s>
A	O
hybrid	O
metaheuristic	B-Algorithm
is	O
one	O
that	O
combines	O
a	O
metaheuristic	B-Algorithm
with	O
other	O
optimization	O
approaches	O
,	O
such	O
as	O
algorithms	O
from	O
mathematical	O
programming	O
,	O
constraint	B-Application
programming	I-Application
,	O
and	O
machine	O
learning	O
.	O
</s>
<s>
Both	O
components	O
of	O
a	O
hybrid	O
metaheuristic	B-Algorithm
may	O
run	O
concurrently	O
and	O
exchange	O
information	O
to	O
guide	O
the	O
search	O
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
Memetic	B-Algorithm
algorithms	I-Algorithm
represent	O
the	O
synergy	O
of	O
evolutionary	O
or	O
any	O
population-based	O
approach	O
with	O
separate	O
individual	O
learning	O
or	O
local	O
improvement	O
procedures	O
for	O
problem	O
search	O
.	O
</s>
<s>
An	O
example	O
of	O
memetic	B-Algorithm
algorithm	I-Algorithm
is	O
the	O
use	O
of	O
a	O
local	B-Algorithm
search	I-Algorithm
algorithm	I-Algorithm
instead	O
of	O
a	O
basic	O
mutation	O
operator	O
in	O
evolutionary	B-Algorithm
algorithms	I-Algorithm
.	O
</s>
<s>
A	O
parallel	B-Algorithm
metaheuristic	I-Algorithm
is	O
one	O
that	O
uses	O
the	O
techniques	O
of	O
parallel	B-Operating_System
programming	I-Operating_System
to	O
run	O
multiple	O
metaheuristic	B-Algorithm
searches	O
in	O
parallel	O
;	O
these	O
may	O
range	O
from	O
simple	O
distributed	B-Architecture
schemes	O
to	O
concurrent	B-Operating_System
search	O
runs	O
that	O
interact	O
to	O
improve	O
the	O
overall	O
solution	O
.	O
</s>
<s>
A	O
very	O
active	O
area	O
of	O
research	O
is	O
the	O
design	O
of	O
nature-inspired	O
metaheuristics	B-Algorithm
.	O
</s>
<s>
Many	O
recent	O
metaheuristics	B-Algorithm
,	O
especially	O
evolutionary	O
computation-based	O
algorithms	O
,	O
are	O
inspired	O
by	O
natural	O
systems	O
.	O
</s>
<s>
Such	O
metaheuristics	B-Algorithm
include	O
simulated	B-Algorithm
annealing	I-Algorithm
,	O
evolutionary	B-Algorithm
algorithms	I-Algorithm
,	O
ant	B-Algorithm
colony	I-Algorithm
optimization	I-Algorithm
and	O
particle	B-Algorithm
swarm	I-Algorithm
optimization	I-Algorithm
.	O
</s>
<s>
A	O
large	O
number	O
of	O
more	O
recent	O
metaphor-inspired	O
metaheuristics	B-Algorithm
have	O
started	O
to	O
attract	O
criticism	O
in	O
the	O
research	O
community	O
for	O
hiding	O
their	O
lack	O
of	O
novelty	O
behind	O
an	O
elaborate	O
metaphor	O
.	O
</s>
<s>
Metaheuristics	B-Algorithm
are	O
used	O
for	O
combinatorial	O
optimization	O
in	O
which	O
an	O
optimal	O
solution	O
is	O
sought	O
over	O
a	O
discrete	O
search-space	O
.	O
</s>
<s>
An	O
example	O
problem	O
is	O
the	O
travelling	B-Algorithm
salesman	I-Algorithm
problem	I-Algorithm
where	O
the	O
search-space	O
of	O
candidate	O
solutions	O
grows	O
faster	O
than	O
exponentially	O
as	O
the	O
size	O
of	O
the	O
problem	O
increases	O
,	O
which	O
makes	O
an	O
exhaustive	B-Algorithm
search	I-Algorithm
for	O
the	O
optimal	O
solution	O
infeasible	O
.	O
</s>
<s>
Additionally	O
,	O
multidimensional	O
combinatorial	O
problems	O
,	O
including	O
most	O
design	O
problems	O
in	O
engineering	O
such	O
as	O
form-finding	O
and	O
behavior-finding	O
,	O
suffer	O
from	O
the	O
curse	B-Algorithm
of	I-Algorithm
dimensionality	I-Algorithm
,	O
which	O
also	O
makes	O
them	O
infeasible	O
for	O
exhaustive	B-Algorithm
search	I-Algorithm
or	O
analytical	O
methods	O
.	O
</s>
<s>
Metaheuristics	B-Algorithm
are	O
also	O
widely	O
used	O
for	O
jobshop	O
scheduling	O
and	O
job	O
selection	O
problems	O
.	O
</s>
<s>
Popular	O
metaheuristics	B-Algorithm
for	O
combinatorial	O
problems	O
include	O
simulated	B-Algorithm
annealing	I-Algorithm
by	O
Kirkpatrick	O
et	O
al.	O
,	O
genetic	B-Algorithm
algorithms	I-Algorithm
by	O
Holland	O
et	O
al.	O
,	O
scatter	O
search	O
and	O
tabu	B-Algorithm
search	I-Algorithm
by	O
Glover	O
.	O
</s>
<s>
Literature	O
review	O
on	O
metaheuristic	B-Algorithm
optimization	O
,	O
</s>
<s>
suggested	O
that	O
it	O
was	O
Fred	O
Glover	O
who	O
coined	O
the	O
word	O
metaheuristics	B-Algorithm
.	O
</s>
<s>
A	O
MOF	O
can	O
be	O
defined	O
as	O
‘‘	O
a	O
set	O
of	O
software	O
tools	O
that	O
provide	O
a	O
correct	O
and	O
reusable	O
implementation	O
of	O
a	O
set	O
of	O
metaheuristics	B-Algorithm
,	O
and	O
the	O
basic	O
mechanisms	O
to	O
accelerate	O
the	O
implementation	O
of	O
its	O
partner	O
subordinate	O
heuristics	B-Algorithm
(	O
possibly	O
including	O
solution	O
encodings	O
and	O
technique-specific	O
operators	O
)	O
,	O
which	O
are	O
necessary	O
to	O
solve	O
a	O
particular	O
problem	O
instance	O
using	O
techniques	O
provided’’	O
.	O
</s>
<s>
There	O
are	O
many	O
candidate	O
optimization	O
tools	O
which	O
can	O
be	O
considered	O
as	O
a	O
MOF	O
of	O
varying	O
feature	O
:	O
Comet	O
,	O
EvA2	O
,	O
evolvica	O
,	O
Evolutionary::Algorithm	O
,	O
GAPlayground	O
,	O
jaga	O
,	O
JCLEC	O
,	O
JGAP	O
,	O
jMetal	O
,	O
n-genes	O
,	O
Open	O
Beagle	O
,	O
Opt4j	O
,	O
ParadisEO/EO	O
,	O
Pisa	O
,	O
Watchmaker	O
,	O
FOM	O
,	O
Hypercube	O
,	O
HotFrame	O
,	O
Templar	O
,	O
EasyLocal	O
,	O
iOpt	O
,	O
OptQuest	O
,	O
JDEAL	O
,	O
Optimization	O
Algorithm	O
Toolkit	O
,	O
HeuristicLab	O
,	O
MAFRA	O
,	O
Localizer	O
,	O
GALIB	O
,	O
DREAM	O
,	O
Discropt	O
,	O
MALLBA	O
,	O
MAGMA	O
,	O
Metaheuristics.jl	O
,	O
UOF	O
and	O
OptaPlanner	O
.	O
</s>
<s>
Many	O
different	O
metaheuristics	B-Algorithm
are	O
in	O
existence	O
and	O
new	O
variants	O
are	O
continually	O
being	O
proposed	O
.	O
</s>
<s>
1952	O
:	O
Robbins	O
and	O
Monro	O
work	O
on	O
stochastic	B-Algorithm
optimization	I-Algorithm
methods	O
.	O
</s>
<s>
1963	O
:	O
Rastrigin	O
proposes	O
random	B-Algorithm
search	I-Algorithm
.	O
</s>
<s>
1965	O
:	O
Matyas	O
proposes	O
random	B-Algorithm
optimization	I-Algorithm
.	O
</s>
<s>
1965	O
:	O
Nelder	O
and	O
Mead	O
propose	O
a	O
simplex	B-Algorithm
heuristic	I-Algorithm
,	O
which	O
was	O
shown	O
by	O
Powell	O
to	O
converge	O
to	O
non-stationary	O
points	O
on	O
some	O
problems	O
.	O
</s>
<s>
1965	O
:	O
Ingo	O
Rechenberg	O
discovers	O
the	O
first	O
Evolution	B-Algorithm
Strategies	I-Algorithm
algorithm	O
.	O
</s>
<s>
propose	O
evolutionary	B-Algorithm
programming	I-Algorithm
.	O
</s>
<s>
1970	O
:	O
Hastings	O
proposes	O
the	O
Metropolis	B-Algorithm
–	I-Algorithm
Hastings	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
1975	O
:	O
Holland	O
proposes	O
the	O
genetic	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
1978	O
:	O
Mercer	O
and	O
Sampson	O
propose	O
a	O
metaplan	B-Algorithm
for	O
tuning	O
an	O
optimizer	O
's	O
parameters	O
by	O
using	O
another	O
optimizer	O
.	O
</s>
<s>
1980	O
:	O
Smith	O
describes	O
genetic	B-Algorithm
programming	I-Algorithm
.	O
</s>
<s>
propose	O
simulated	B-Algorithm
annealing	I-Algorithm
.	O
</s>
<s>
1986	O
:	O
Glover	O
proposes	O
tabu	B-Algorithm
search	I-Algorithm
,	O
first	O
mention	O
of	O
the	O
term	O
metaheuristic	B-Algorithm
.	O
</s>
<s>
1989	O
:	O
Moscato	O
proposes	O
memetic	B-Algorithm
algorithms	I-Algorithm
.	O
</s>
<s>
1990	O
:	O
Moscato	O
and	O
Fontanari	O
,	O
and	O
Dueck	O
and	O
Scheuer	O
,	O
independently	O
proposed	O
a	O
deterministic	O
update	O
rule	O
for	O
simulated	B-Algorithm
annealing	I-Algorithm
which	O
accelerated	O
the	O
search	O
.	O
</s>
<s>
This	O
led	O
to	O
the	O
threshold	O
accepting	O
metaheuristic	B-Algorithm
.	O
</s>
<s>
1992	O
:	O
Dorigo	O
introduces	O
ant	B-Algorithm
colony	I-Algorithm
optimization	I-Algorithm
in	O
his	O
PhD	O
thesis	O
.	O
</s>
