<s>
Tabu	B-Algorithm
search	I-Algorithm
(	O
TS	O
)	O
is	O
a	O
metaheuristic	B-Algorithm
search	O
method	O
employing	O
local	B-Algorithm
search	I-Algorithm
methods	O
used	O
for	O
mathematical	O
optimization	O
.	O
</s>
<s>
Local	B-Algorithm
search	I-Algorithm
methods	O
have	O
a	O
tendency	O
to	O
become	O
stuck	O
in	O
suboptimal	O
regions	O
or	O
on	O
plateaus	O
where	O
many	O
solutions	O
are	O
equally	O
fit	O
.	O
</s>
<s>
Tabu	B-Algorithm
search	I-Algorithm
enhances	O
the	O
performance	O
of	O
local	B-Algorithm
search	I-Algorithm
by	O
relaxing	O
its	O
basic	O
rule	O
.	O
</s>
<s>
The	O
implementation	O
of	O
tabu	B-Algorithm
search	I-Algorithm
uses	O
memory	O
structures	O
that	O
describe	O
the	O
visited	O
solutions	O
or	O
user-provided	O
sets	O
of	O
rules	O
.	O
</s>
<s>
Tabu	B-Algorithm
search	I-Algorithm
is	O
a	O
metaheuristic	B-Algorithm
algorithm	O
that	O
can	O
be	O
used	O
for	O
solving	O
combinatorial	O
optimization	O
problems	O
(	O
problems	O
where	O
an	O
optimal	O
ordering	O
and	O
selection	O
of	O
options	O
is	O
desired	O
)	O
.	O
</s>
<s>
Current	O
applications	O
of	O
TS	O
span	O
the	O
areas	O
of	O
resource	O
planning	O
,	O
telecommunications	O
,	O
VLSI	O
design	O
,	O
financial	O
analysis	O
,	O
scheduling	O
,	O
space	O
planning	O
,	O
energy	O
distribution	O
,	O
molecular	O
engineering	O
,	O
logistics	O
,	O
pattern	B-General_Concept
classification	I-General_Concept
,	O
flexible	O
manufacturing	O
,	O
waste	O
management	O
,	O
mineral	O
exploration	O
,	O
biomedical	O
analysis	O
,	O
environmental	O
conservation	O
and	O
scores	O
of	O
others	O
.	O
</s>
<s>
In	O
recent	O
years	O
,	O
journals	O
in	O
a	O
wide	O
variety	O
of	O
fields	O
have	O
published	O
tutorial	O
articles	O
and	O
computational	O
studies	O
documenting	O
successes	O
by	O
tabu	B-Algorithm
search	I-Algorithm
in	O
extending	O
the	O
frontier	O
of	O
problems	O
that	O
can	O
be	O
handled	O
effectively	O
—	O
yielding	O
solutions	O
whose	O
quality	O
often	O
significantly	O
surpasses	O
that	O
obtained	O
by	O
methods	O
previously	O
applied	O
.	O
</s>
<s>
Tabu	B-Algorithm
search	I-Algorithm
uses	O
a	O
local	B-Algorithm
or	I-Algorithm
neighborhood	I-Algorithm
search	O
procedure	O
to	O
iteratively	O
move	O
from	O
one	O
potential	O
solution	O
to	O
an	O
improved	O
solution	O
in	O
the	O
neighborhood	O
of	O
,	O
until	O
some	O
stopping	O
criterion	O
has	O
been	O
satisfied	O
(	O
generally	O
,	O
an	O
attempt	O
limit	O
or	O
a	O
score	O
threshold	O
)	O
.	O
</s>
<s>
Local	B-Algorithm
search	I-Algorithm
procedures	O
often	O
become	O
stuck	O
in	O
poor-scoring	O
areas	O
or	O
areas	O
where	O
scores	O
plateau	O
.	O
</s>
<s>
In	O
order	O
to	O
avoid	O
these	O
pitfalls	O
and	O
explore	O
regions	O
of	O
the	O
search	O
space	O
that	O
would	O
be	O
left	O
unexplored	O
by	O
other	O
local	B-Algorithm
search	I-Algorithm
procedures	O
,	O
tabu	B-Algorithm
search	I-Algorithm
carefully	O
explores	O
the	O
neighborhood	O
of	O
each	O
solution	O
as	O
the	O
search	O
progresses	O
.	O
</s>
<s>
Tabu	B-Algorithm
search	I-Algorithm
has	O
several	O
similarities	O
with	O
simulated	B-Algorithm
annealing	I-Algorithm
,	O
as	O
both	O
involve	O
possible	O
downhill	O
moves	O
.	O
</s>
<s>
In	O
fact	O
,	O
simulated	B-Algorithm
annealing	I-Algorithm
could	O
be	O
viewed	O
as	O
a	O
special	O
form	O
of	O
TS	O
,	O
whereby	O
we	O
use	O
"	O
graduated	O
tenure	O
"	O
,	O
that	O
is	O
,	O
a	O
move	O
becomes	O
tabu	O
with	O
a	O
specified	O
probability	O
.	O
</s>
<s>
The	O
memory	O
structures	O
used	O
in	O
tabu	B-Algorithm
search	I-Algorithm
can	O
roughly	O
be	O
divided	O
into	O
three	O
categories	O
:	O
</s>
<s>
Short-term	O
memory	O
alone	O
may	O
be	O
enough	O
to	O
achieve	O
solutions	O
superior	O
to	O
those	O
found	O
by	O
conventional	O
local	B-Algorithm
search	I-Algorithm
methods	O
,	O
but	O
intermediate	O
and	O
long-term	O
structures	O
are	O
often	O
necessary	O
for	O
solving	O
harder	O
problems	O
.	O
</s>
<s>
Tabu	B-Algorithm
search	I-Algorithm
is	O
often	O
benchmarked	O
against	O
other	O
metaheuristic	B-Algorithm
methods	O
—	O
such	O
as	O
simulated	B-Algorithm
annealing	I-Algorithm
,	O
genetic	B-Algorithm
algorithms	I-Algorithm
,	O
ant	B-Algorithm
colony	I-Algorithm
optimization	I-Algorithm
algorithms	I-Algorithm
,	O
reactive	O
search	O
optimization	O
,	O
guided	B-Algorithm
local	I-Algorithm
search	I-Algorithm
,	O
or	O
greedy	B-Algorithm
randomized	I-Algorithm
adaptive	I-Algorithm
search	I-Algorithm
.	O
</s>
<s>
In	O
addition	O
,	O
tabu	B-Algorithm
search	I-Algorithm
is	O
sometimes	O
combined	O
with	O
other	O
metaheuristics	B-Algorithm
to	O
create	O
hybrid	O
methods	O
.	O
</s>
<s>
The	O
most	O
common	O
tabu	B-Algorithm
search	I-Algorithm
hybrid	O
arises	O
by	O
joining	O
TS	O
with	O
scatter	O
search	O
,	O
a	O
class	O
of	O
population-based	O
procedures	O
which	O
has	O
roots	O
in	O
common	O
with	O
tabu	B-Algorithm
search	I-Algorithm
,	O
and	O
is	O
often	O
employed	O
in	O
solving	O
large	O
non-linear	O
optimization	O
problems	O
.	O
</s>
<s>
The	O
following	O
pseudocode	B-Language
presents	O
a	O
simplified	O
version	O
of	O
the	O
tabu	B-Algorithm
search	I-Algorithm
algorithm	O
as	O
described	O
above	O
.	O
</s>
<s>
The	O
traveling	B-Algorithm
salesman	I-Algorithm
problem	I-Algorithm
(	O
TSP	O
)	O
is	O
sometimes	O
used	O
to	O
show	O
the	O
functionality	O
of	O
tabu	B-Algorithm
search	I-Algorithm
.	O
</s>
<s>
Since	O
finding	O
an	O
optimal	O
solution	O
is	O
NP-hard	O
,	O
heuristic-based	O
approximation	O
methods	O
(	O
such	O
as	O
local	B-Algorithm
searches	I-Algorithm
)	O
are	O
useful	O
for	O
devising	O
close-to-optimal	O
solutions	O
.	O
</s>
<s>
The	O
value	O
of	O
exploiting	O
problem	O
structure	O
is	O
a	O
recurring	O
theme	O
in	O
metaheuristic	B-Algorithm
methods	O
,	O
and	O
tabu	B-Algorithm
search	I-Algorithm
is	O
well-suited	O
to	O
this	O
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
a	O
simple	O
tabu	B-Algorithm
search	I-Algorithm
can	O
be	O
used	O
to	O
find	O
a	O
satisficing	O
solution	O
for	O
the	O
traveling	B-Algorithm
salesman	I-Algorithm
problem	I-Algorithm
(	O
that	O
is	O
,	O
a	O
solution	O
that	O
satisfies	O
an	O
adequacy	O
criterion	O
,	O
although	O
not	O
with	O
the	O
high	O
quality	O
obtained	O
by	O
exploiting	O
the	O
graph	O
structure	O
)	O
.	O
</s>
<s>
The	O
search	O
starts	O
with	O
an	O
initial	O
solution	O
,	O
which	O
can	O
be	O
generated	O
randomly	O
or	O
according	O
to	O
some	O
sort	O
of	O
nearest	B-Algorithm
neighbor	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
Once	O
the	O
simple	O
tabu	B-Algorithm
search	I-Algorithm
stops	O
,	O
it	O
returns	O
the	O
best	O
solution	O
found	O
during	O
its	O
execution	O
.	O
</s>
