<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
local	B-Algorithm
search	I-Algorithm
is	O
a	O
heuristic	B-Algorithm
method	O
for	O
solving	O
computationally	O
hard	O
optimization	O
problems	O
.	O
</s>
<s>
Local	B-Algorithm
search	I-Algorithm
can	O
be	O
used	O
on	O
problems	O
that	O
can	O
be	O
formulated	O
as	O
finding	O
a	O
solution	O
maximizing	O
a	O
criterion	O
among	O
a	O
number	O
of	O
candidate	O
solutions	O
.	O
</s>
<s>
Local	B-Algorithm
search	I-Algorithm
algorithms	I-Algorithm
move	O
from	O
solution	O
to	O
solution	O
in	O
the	O
space	O
of	O
candidate	O
solutions	O
(	O
the	O
search	O
space	O
)	O
by	O
applying	O
local	O
changes	O
,	O
until	O
a	O
solution	O
deemed	O
optimal	O
is	O
found	O
or	O
a	O
time	O
bound	O
is	O
elapsed	O
.	O
</s>
<s>
Local	B-Algorithm
search	I-Algorithm
algorithms	I-Algorithm
are	O
widely	O
applied	O
to	O
numerous	O
hard	O
computational	O
problems	O
,	O
including	O
problems	O
from	O
computer	B-General_Concept
science	I-General_Concept
(	O
particularly	O
artificial	B-Application
intelligence	I-Application
)	O
,	O
mathematics	O
,	O
operations	O
research	O
,	O
engineering	O
,	O
and	O
bioinformatics	O
.	O
</s>
<s>
Examples	O
of	O
local	B-Algorithm
search	I-Algorithm
algorithms	I-Algorithm
are	O
WalkSAT	B-Application
,	O
the	O
2-opt	B-Algorithm
algorithm	I-Algorithm
for	I-Algorithm
the	I-Algorithm
Traveling	I-Algorithm
Salesman	I-Algorithm
Problem	I-Algorithm
and	O
the	O
Metropolis	B-Algorithm
–	I-Algorithm
Hastings	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
Some	O
problems	O
where	O
local	B-Algorithm
search	I-Algorithm
has	O
been	O
applied	O
are	O
:	O
</s>
<s>
The	O
Hopfield	B-Algorithm
Neural	I-Algorithm
Networks	I-Algorithm
problem	O
for	O
which	O
finding	O
stable	O
configurations	O
in	O
Hopfield	B-Algorithm
network	I-Algorithm
.	O
</s>
<s>
For	O
example	O
,	O
for	O
the	O
traveling	B-Algorithm
salesman	I-Algorithm
problem	I-Algorithm
a	O
solution	O
can	O
be	O
a	O
route	O
visiting	O
all	O
cities	O
and	O
the	O
goal	O
is	O
to	O
find	O
the	O
shortest	O
route	O
.	O
</s>
<s>
A	O
local	B-Algorithm
search	I-Algorithm
algorithm	I-Algorithm
starts	O
from	O
a	O
candidate	O
solution	O
and	O
then	O
iteratively	B-Algorithm
moves	O
to	O
a	O
neighbor	O
solution	O
;	O
a	O
neighborhood	O
being	O
the	O
set	O
of	O
all	O
potential	O
solutions	O
that	O
differ	O
from	O
the	O
current	O
solution	O
by	O
the	O
minimal	O
possible	O
extent	O
.	O
</s>
<s>
For	O
boolean	B-Algorithm
satisfiability	I-Algorithm
,	O
the	O
neighbors	O
of	O
a	O
boolean	O
assignment	O
are	O
those	O
that	O
have	O
a	O
single	O
variable	O
in	O
an	O
opposite	O
state	O
.	O
</s>
<s>
The	O
same	O
problem	O
may	O
have	O
multiple	O
distinct	O
neighborhoods	O
defined	O
on	O
it	O
;	O
local	O
optimization	O
with	O
neighborhoods	O
that	O
involve	O
changing	O
up	O
to	O
k	O
components	O
of	O
the	O
solution	O
is	O
often	O
referred	O
to	O
as	O
k-opt	B-Algorithm
.	O
</s>
<s>
Typically	O
,	O
every	O
candidate	O
solution	O
has	O
more	O
than	O
one	O
neighbor	O
solution	O
;	O
the	O
choice	O
of	O
which	O
one	O
to	O
select	O
is	O
taken	O
using	O
only	O
information	O
about	O
the	O
solutions	O
in	O
the	O
neighborhood	O
of	O
the	O
current	O
assignment	O
,	O
hence	O
the	O
name	O
local	B-Algorithm
search	I-Algorithm
.	O
</s>
<s>
:	O
a	O
greedy	O
search	O
,	O
the	O
metaheuristic	B-Algorithm
takes	O
the	O
name	O
hill	B-Algorithm
climbing	I-Algorithm
.	O
</s>
<s>
When	O
no	O
improving	O
neighbors	O
are	O
present	O
,	O
local	B-Algorithm
search	I-Algorithm
is	O
stuck	O
at	O
a	O
locally	O
optimal	O
point	O
.	O
</s>
<s>
This	O
local-optima	O
problem	O
can	O
be	O
cured	O
by	O
using	O
restarts	O
(	O
repeated	O
local	B-Algorithm
search	I-Algorithm
with	O
different	O
initial	O
conditions	O
)	O
,	O
randomization	O
,	O
or	O
more	O
complex	O
schemes	O
based	O
on	O
iterations	O
,	O
like	O
iterated	B-Algorithm
local	I-Algorithm
search	I-Algorithm
,	O
on	O
memory	O
,	O
like	O
reactive	O
search	O
optimization	O
,	O
on	O
memory-less	O
stochastic	O
modifications	O
,	O
like	O
simulated	B-Algorithm
annealing	I-Algorithm
.	O
</s>
<s>
Local	B-Algorithm
search	I-Algorithm
does	O
not	O
provide	O
a	O
guarantee	O
that	O
any	O
given	O
solution	O
is	O
optimal	O
.	O
</s>
<s>
Local	B-Algorithm
search	I-Algorithm
is	O
an	O
anytime	B-Algorithm
algorithm	I-Algorithm
:	O
</s>
<s>
Local	B-Algorithm
search	I-Algorithm
is	O
typically	O
an	O
approximation	B-Algorithm
or	O
incomplete	O
algorithm	O
,	O
because	O
the	O
search	O
may	O
stop	O
even	O
if	O
the	O
current	O
best	O
solution	O
found	O
is	O
not	O
optimal	O
.	O
</s>
<s>
Schuurman	O
&	O
Southey	O
propose	O
three	O
measures	O
of	O
effectiveness	O
for	O
local	B-Algorithm
search	I-Algorithm
(	O
depth	O
,	O
mobility	O
,	O
and	O
coverage	O
)	O
:	O
</s>
<s>
They	O
hypothesize	O
that	O
local	B-Algorithm
search	I-Algorithm
algorithms	I-Algorithm
work	O
well	O
,	O
not	O
because	O
they	O
have	O
some	O
understanding	O
of	O
the	O
search	O
space	O
,	O
but	O
because	O
they	O
quickly	O
move	O
to	O
promising	O
regions	O
,	O
and	O
explore	O
the	O
search	O
space	O
at	O
low	O
depths	O
as	O
quickly	O
,	O
broadly	O
,	O
and	O
systematically	O
as	O
possible	O
.	O
</s>
