<s>
In	O
mathematical	O
optimization	O
and	O
computer	B-General_Concept
science	I-General_Concept
,	O
heuristic	B-Algorithm
(	O
from	O
Greek	O
εὑρίσκω	O
"	O
I	O
find	O
,	O
discover	O
"	O
)	O
is	O
a	O
technique	O
designed	O
for	O
solving	O
a	O
problem	O
more	O
quickly	O
when	O
classic	O
methods	O
are	O
too	O
slow	O
for	O
finding	O
an	O
approximate	O
solution	O
,	O
or	O
when	O
classic	O
methods	O
fail	O
to	O
find	O
any	O
exact	O
solution	O
.	O
</s>
<s>
A	O
heuristic	B-Algorithm
function	I-Algorithm
,	O
also	O
simply	O
called	O
a	O
heuristic	B-Algorithm
,	O
is	O
a	O
function	O
that	O
ranks	O
alternatives	O
in	O
search	B-Application
algorithms	I-Application
at	O
each	O
branching	O
step	O
based	O
on	O
available	O
information	O
to	O
decide	O
which	O
branch	O
to	O
follow	O
.	O
</s>
<s>
The	O
objective	O
of	O
a	O
heuristic	B-Algorithm
is	O
to	O
produce	O
a	O
solution	O
in	O
a	O
reasonable	O
time	O
frame	O
that	O
is	O
good	O
enough	O
for	O
solving	O
the	O
problem	O
at	O
hand	O
.	O
</s>
<s>
Heuristics	B-Algorithm
may	O
produce	O
results	O
by	O
themselves	O
,	O
or	O
they	O
may	O
be	O
used	O
in	O
conjunction	O
with	O
optimization	O
algorithms	O
to	O
improve	O
their	O
efficiency	O
(	O
e.g.	O
,	O
they	O
may	O
be	O
used	O
to	O
generate	O
good	O
seed	O
values	O
)	O
.	O
</s>
<s>
Results	O
about	O
NP-hardness	O
in	O
theoretical	O
computer	B-General_Concept
science	I-General_Concept
make	O
heuristics	B-Algorithm
the	O
only	O
viable	O
option	O
for	O
a	O
variety	O
of	O
complex	O
optimization	O
problems	O
that	O
need	O
to	O
be	O
routinely	O
solved	O
in	O
real-world	O
applications	O
.	O
</s>
<s>
Heuristics	B-Algorithm
underlie	O
the	O
whole	O
field	O
of	O
Artificial	O
Intelligence	O
and	O
the	O
computer	O
simulation	O
of	O
thinking	O
,	O
as	O
they	O
may	O
be	O
used	O
in	O
situations	O
where	O
there	O
are	O
no	O
known	O
algorithms	O
.	O
</s>
<s>
The	O
trade-off	O
criteria	O
for	O
deciding	O
whether	O
to	O
use	O
a	O
heuristic	B-Algorithm
for	O
solving	O
a	O
given	O
problem	O
include	O
the	O
following	O
:	O
</s>
<s>
Optimality	O
:	O
When	O
several	O
solutions	O
exist	O
for	O
a	O
given	O
problem	O
,	O
does	O
the	O
heuristic	B-Algorithm
guarantee	O
that	O
the	O
best	O
solution	O
will	O
be	O
found	O
?	O
</s>
<s>
Completeness	O
:	O
When	O
several	O
solutions	O
exist	O
for	O
a	O
given	O
problem	O
,	O
can	O
the	O
heuristic	B-Algorithm
find	O
them	O
all	O
?	O
</s>
<s>
Many	O
heuristics	B-Algorithm
are	O
only	O
meant	O
to	O
find	O
one	O
solution	O
.	O
</s>
<s>
Accuracy	O
and	O
precision	O
:	O
Can	O
the	O
heuristic	B-Algorithm
provide	O
a	O
confidence	O
interval	O
for	O
the	O
purported	O
solution	O
?	O
</s>
<s>
Execution	O
time	O
:	O
Is	O
this	O
the	O
best	O
known	O
heuristic	B-Algorithm
for	O
solving	O
this	O
type	O
of	O
problem	O
?	O
</s>
<s>
Some	O
heuristics	B-Algorithm
converge	O
faster	O
than	O
others	O
.	O
</s>
<s>
Some	O
heuristics	B-Algorithm
are	O
only	O
marginally	O
quicker	O
than	O
classic	O
methods	O
,	O
in	O
which	O
case	O
the	O
'	O
overhead	O
 '	O
on	O
calculating	O
the	O
heuristic	B-Algorithm
might	O
have	O
negative	O
impact	O
.	O
</s>
<s>
In	O
some	O
cases	O
,	O
it	O
may	O
be	O
difficult	O
to	O
decide	O
whether	O
the	O
solution	O
found	O
by	O
the	O
heuristic	B-Algorithm
is	O
good	O
enough	O
,	O
because	O
the	O
theory	O
underlying	O
heuristics	B-Algorithm
is	O
not	O
very	O
elaborate	O
.	O
</s>
<s>
One	O
way	O
of	O
achieving	O
the	O
computational	O
performance	O
gain	O
expected	O
of	O
a	O
heuristic	B-Algorithm
consists	O
of	O
solving	O
a	O
simpler	O
problem	O
whose	O
solution	O
is	O
also	O
a	O
solution	O
to	O
the	O
initial	O
problem	O
.	O
</s>
<s>
An	O
example	O
of	O
approximation	O
is	O
described	O
by	O
Jon	O
Bentley	O
for	O
solving	O
the	O
travelling	B-Algorithm
salesman	I-Algorithm
problem	I-Algorithm
(	O
TSP	O
)	O
:	O
</s>
<s>
Instead	O
,	O
the	O
greedy	B-Algorithm
algorithm	I-Algorithm
can	O
be	O
used	O
to	O
give	O
a	O
good	O
but	O
not	O
optimal	O
solution	O
(	O
it	O
is	O
an	O
approximation	O
to	O
the	O
optimal	O
answer	O
)	O
in	O
a	O
reasonably	O
short	O
amount	O
of	O
time	O
.	O
</s>
<s>
The	O
greedy	B-Algorithm
algorithm	I-Algorithm
heuristic	B-Algorithm
says	O
to	O
pick	O
whatever	O
is	O
currently	O
the	O
best	O
next	O
step	O
regardless	O
of	O
whether	O
that	O
prevents	O
(	O
or	O
even	O
makes	O
impossible	O
)	O
good	O
steps	O
later	O
.	O
</s>
<s>
It	O
is	O
a	O
heuristic	B-Algorithm
in	O
the	O
sense	O
that	O
practice	O
indicates	O
it	O
is	O
a	O
good	O
enough	O
solution	O
,	O
while	O
theory	O
indicates	O
that	O
there	O
are	O
better	O
solutions	O
(	O
and	O
even	O
indicates	O
how	O
much	O
better	O
,	O
in	O
some	O
cases	O
)	O
.	O
</s>
<s>
Another	O
example	O
of	O
heuristic	B-Algorithm
making	O
an	O
algorithm	O
faster	O
occurs	O
in	O
certain	O
search	O
problems	O
.	O
</s>
<s>
Initially	O
,	O
the	O
heuristic	B-Algorithm
tries	O
every	O
possibility	O
at	O
each	O
step	O
,	O
like	O
the	O
full-space	O
search	B-Application
algorithm	I-Application
.	O
</s>
<s>
In	O
such	O
search	O
problems	O
,	O
a	O
heuristic	B-Algorithm
can	O
be	O
used	O
to	O
try	O
good	O
choices	O
first	O
so	O
that	O
bad	O
paths	O
can	O
be	O
eliminated	O
early	O
(	O
see	O
alpha-beta	B-Algorithm
pruning	I-Algorithm
)	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
best-first	B-Algorithm
search	I-Algorithm
algorithms	O
,	O
such	O
as	O
A*	B-Protocol
search	I-Protocol
,	O
the	O
heuristic	B-Algorithm
improves	O
the	O
algorithm	O
's	O
convergence	O
while	O
maintaining	O
its	O
correctness	O
as	O
long	O
as	O
the	O
heuristic	B-Algorithm
is	O
admissible	B-General_Concept
.	O
</s>
<s>
In	O
their	O
Turing	O
Award	O
acceptance	O
speech	O
,	O
Allen	O
Newell	O
and	O
Herbert	O
A	O
.	O
Simon	O
discuss	O
the	O
heuristic	B-Algorithm
search	O
hypothesis	O
:	O
a	O
physical	O
symbol	O
system	O
will	O
repeatedly	O
generate	O
and	O
modify	O
known	O
symbol	O
structures	O
until	O
the	O
created	O
structure	O
matches	O
the	O
solution	O
structure	O
.	O
</s>
<s>
Each	O
following	O
step	O
depends	O
upon	O
the	O
step	O
before	O
it	O
,	O
thus	O
the	O
heuristic	B-Algorithm
search	O
learns	O
what	O
avenues	O
to	O
pursue	O
and	O
which	O
ones	O
to	O
disregard	O
by	O
measuring	O
how	O
close	O
the	O
current	O
step	O
is	O
to	O
the	O
solution	O
.	O
</s>
<s>
A	O
heuristic	B-Algorithm
method	O
can	O
accomplish	O
its	O
task	O
by	O
using	O
search	O
trees	O
.	O
</s>
<s>
However	O
,	O
instead	O
of	O
generating	O
all	O
possible	O
solution	O
branches	O
,	O
a	O
heuristic	B-Algorithm
selects	O
branches	O
more	O
likely	O
to	O
produce	O
outcomes	O
than	O
other	O
branches	O
.	O
</s>
<s>
Antivirus	B-Application
software	I-Application
often	O
uses	O
heuristic	B-Algorithm
rules	O
for	O
detecting	O
viruses	O
and	O
other	O
forms	O
of	O
malware	O
.	O
</s>
<s>
Heuristic	B-Algorithm
scanning	O
looks	O
for	O
code	O
and/or	O
behavioral	O
patterns	O
common	O
to	O
a	O
class	O
or	O
family	O
of	O
viruses	O
,	O
with	O
different	O
sets	O
of	O
rules	O
for	O
different	O
viruses	O
.	O
</s>
<s>
The	O
most	O
advanced	O
part	O
of	O
behavior-based	O
heuristic	B-Algorithm
scanning	O
is	O
that	O
it	O
can	O
work	O
against	O
highly	O
randomized	O
self-modifying/mutating	O
(	O
polymorphic	O
)	O
viruses	O
that	O
cannot	O
be	O
easily	O
detected	O
by	O
simpler	O
string	O
scanning	O
methods	O
.	O
</s>
<s>
Heuristic	B-Algorithm
scanning	O
has	O
the	O
potential	O
to	O
detect	O
future	O
viruses	O
without	O
requiring	O
the	O
virus	O
to	O
be	O
first	O
detected	O
somewhere	O
else	O
,	O
submitted	O
to	O
the	O
virus	B-Application
scanner	I-Application
developer	O
,	O
analyzed	O
,	O
and	O
a	O
detection	O
update	O
for	O
the	O
scanner	O
provided	O
to	O
the	O
scanner	O
's	O
users	O
.	O
</s>
<s>
Some	O
heuristics	B-Algorithm
have	O
a	O
strong	O
underlying	O
theory	O
;	O
they	O
are	O
either	O
derived	O
in	O
a	O
top-down	O
manner	O
from	O
the	O
theory	O
or	O
are	O
arrived	O
at	O
based	O
on	O
either	O
experimental	O
or	O
real	O
world	O
data	O
.	O
</s>
<s>
When	O
a	O
heuristic	B-Algorithm
is	O
reused	O
in	O
various	O
contexts	O
because	O
it	O
has	O
been	O
seen	O
to	O
"	O
work	O
"	O
in	O
one	O
context	O
,	O
without	O
having	O
been	O
mathematically	O
proven	O
to	O
meet	O
a	O
given	O
set	O
of	O
requirements	O
,	O
it	O
is	O
possible	O
that	O
the	O
current	O
data	O
set	O
does	O
not	O
necessarily	O
represent	O
future	O
data	O
sets	O
(	O
see	O
:	O
overfitting	B-Error_Name
)	O
and	O
that	O
purported	O
"	O
solutions	O
"	O
turn	O
out	O
to	O
be	O
akin	O
to	O
noise	O
.	O
</s>
<s>
Statistical	O
analysis	O
can	O
be	O
conducted	O
when	O
employing	O
heuristics	B-Algorithm
to	O
estimate	O
the	O
probability	O
of	O
incorrect	O
outcomes	O
.	O
</s>
<s>
To	O
use	O
a	O
heuristic	B-Algorithm
for	O
solving	O
a	O
search	O
problem	O
or	O
a	O
knapsack	B-Algorithm
problem	I-Algorithm
,	O
it	O
is	O
necessary	O
to	O
check	O
that	O
the	O
heuristic	B-Algorithm
is	O
admissible	B-General_Concept
.	O
</s>
<s>
Given	O
a	O
heuristic	B-Algorithm
function	I-Algorithm
meant	O
to	O
approximate	O
the	O
true	O
optimal	O
distance	O
to	O
the	O
goal	O
node	O
in	O
a	O
directed	O
graph	O
containing	O
total	O
nodes	O
or	O
vertices	O
labeled	O
,	O
"	O
admissible	B-General_Concept
"	O
means	O
roughly	O
that	O
the	O
heuristic	B-Algorithm
underestimates	O
the	O
cost	O
to	O
the	O
goal	O
or	O
formally	O
that	O
for	O
all	O
where	O
.	O
</s>
<s>
If	O
a	O
heuristic	B-Algorithm
is	O
not	O
admissible	B-General_Concept
,	O
it	O
may	O
never	O
find	O
the	O
goal	O
,	O
either	O
by	O
ending	O
up	O
in	O
a	O
dead	O
end	O
of	O
graph	O
or	O
by	O
skipping	O
back	O
and	O
forth	O
between	O
two	O
nodes	O
and	O
where	O
.	O
</s>
<s>
The	O
word	O
"	O
heuristic	B-Algorithm
"	O
came	O
into	O
usage	O
in	O
the	O
early	O
19th	O
century	O
.	O
</s>
