<s>
Algorithm	B-Application
selection	I-Application
(	O
sometimes	O
also	O
called	O
per-instance	O
algorithm	B-Application
selection	I-Application
or	O
offline	O
algorithm	B-Application
selection	I-Application
)	O
is	O
a	O
meta-algorithmic	O
technique	O
to	O
choose	O
an	O
algorithm	O
from	O
a	O
portfolio	O
on	O
an	O
instance-by-instance	O
basis	O
.	O
</s>
<s>
This	O
is	O
what	O
algorithm	B-Application
selection	I-Application
aims	O
to	O
do	O
.	O
</s>
<s>
The	O
only	O
prerequisite	O
for	O
applying	O
algorithm	B-Application
selection	I-Application
techniques	O
is	O
that	O
there	O
exists	O
(	O
or	O
that	O
there	O
can	O
be	O
constructed	O
)	O
a	O
set	O
of	O
complementary	O
algorithms	O
.	O
</s>
<s>
Given	O
a	O
portfolio	O
of	O
algorithms	O
,	O
a	O
set	O
of	O
instances	O
and	O
a	O
cost	O
metric	O
,	O
the	O
algorithm	B-Application
selection	I-Application
problem	O
consists	O
of	O
finding	O
a	O
mapping	O
from	O
instances	O
to	O
algorithms	O
such	O
that	O
the	O
cost	O
across	O
all	O
instances	O
is	O
optimized	O
.	O
</s>
<s>
A	O
well-known	O
application	O
of	O
algorithm	B-Application
selection	I-Application
is	O
the	O
Boolean	B-Algorithm
satisfiability	I-Algorithm
problem	I-Algorithm
.	O
</s>
<s>
Here	O
,	O
the	O
portfolio	O
of	O
algorithms	O
is	O
a	O
set	O
of	O
(	O
complementary	O
)	O
SAT	B-Application
solvers	I-Application
,	O
the	O
instances	O
are	O
Boolean	O
formulas	O
,	O
the	O
cost	O
metric	O
is	O
for	O
example	O
average	O
runtime	O
or	O
number	O
of	O
unsolved	O
instances	O
.	O
</s>
<s>
So	O
,	O
the	O
goal	O
is	O
to	O
select	O
a	O
well-performing	O
SAT	B-Application
solver	I-Application
for	O
each	O
individual	O
instance	O
.	O
</s>
<s>
In	O
the	O
same	O
way	O
,	O
algorithm	B-Application
selection	I-Application
can	O
be	O
applied	O
to	O
many	O
other	O
-hard	O
problems	O
(	O
such	O
as	O
mixed	B-Algorithm
integer	I-Algorithm
programming	I-Algorithm
,	O
CSP	B-Application
,	O
AI	B-Application
planning	I-Application
,	O
TSP	B-Algorithm
,	O
MAXSAT	B-Application
,	O
QBF	O
and	O
answer	B-Application
set	I-Application
programming	I-Application
)	O
.	O
</s>
<s>
In	O
machine	O
learning	O
,	O
algorithm	B-Application
selection	I-Application
is	O
better	O
known	O
as	O
meta-learning	B-General_Concept
.	O
</s>
<s>
The	O
algorithm	B-Application
selection	I-Application
problem	O
is	O
mainly	O
solved	O
with	O
machine	O
learning	O
techniques	O
.	O
</s>
<s>
By	O
representing	O
the	O
problem	O
instances	O
by	O
numerical	O
features	O
,	O
algorithm	B-Application
selection	I-Application
can	O
be	O
seen	O
as	O
a	O
multi-class	B-General_Concept
classification	I-General_Concept
problem	O
by	O
learning	O
a	O
mapping	O
for	O
a	O
given	O
instance	O
.	O
</s>
<s>
Static	O
features	O
are	O
in	O
most	O
cases	O
some	O
counts	O
and	O
statistics	O
(	O
e.g.	O
,	O
clauses-to-variables	O
ratio	O
in	O
SAT	B-Algorithm
)	O
.	O
</s>
<s>
For	O
example	O
,	O
if	O
we	O
use	O
running	O
time	O
as	O
performance	O
metric	O
,	O
we	O
include	O
the	O
time	O
to	O
compute	O
our	O
instance	O
features	O
into	O
the	O
performance	O
of	O
an	O
algorithm	B-Application
selection	I-Application
system	O
.	O
</s>
<s>
SAT	B-Algorithm
solving	O
is	O
a	O
concrete	O
example	O
,	O
where	O
such	O
feature	O
costs	O
cannot	O
be	O
neglected	O
,	O
since	O
instance	O
features	O
for	O
CNF	B-Application
formulas	O
can	O
be	O
either	O
very	O
cheap	O
(	O
e.g.	O
,	O
to	O
get	O
the	O
number	O
of	O
variables	O
can	O
be	O
done	O
in	O
constant	O
time	O
for	O
CNFs	O
in	O
the	O
DIMACs	O
format	O
)	O
or	O
very	O
expensive	O
(	O
e.g.	O
,	O
graph	O
features	O
which	O
can	O
cost	O
tens	O
or	O
hundreds	O
of	O
seconds	O
)	O
.	O
</s>
<s>
It	O
is	O
important	O
to	O
take	O
the	O
overhead	O
of	O
feature	O
computation	O
into	O
account	O
in	O
practice	O
in	O
such	O
scenarios	O
;	O
otherwise	O
a	O
misleading	O
impression	O
of	O
the	O
performance	O
of	O
the	O
algorithm	B-Application
selection	I-Application
approach	O
is	O
created	O
.	O
</s>
<s>
One	O
of	O
the	O
first	O
successful	O
algorithm	B-Application
selection	I-Application
approaches	O
predicted	O
the	O
performance	O
of	O
each	O
algorithm	O
and	O
selected	O
the	O
algorithm	O
with	O
the	O
best	O
predicted	O
performance	O
for	O
an	O
instance	O
.	O
</s>
<s>
A	O
more	O
modern	O
approach	O
is	O
cost-sensitive	O
hierarchical	B-Algorithm
clustering	I-Algorithm
using	O
supervised	O
learning	O
to	O
identify	O
the	O
homogeneous	O
instance	O
subsets	O
.	O
</s>
<s>
The	O
algorithm	B-Application
selection	I-Application
problem	O
can	O
be	O
effectively	O
applied	O
under	O
the	O
following	O
assumptions	O
:	O
</s>
<s>
In	O
such	O
cases	O
,	O
the	O
cost	O
to	O
compute	O
features	O
should	O
not	O
be	O
larger	O
than	O
the	O
performance	O
gain	O
through	O
algorithm	B-Application
selection	I-Application
.	O
</s>
<s>
Algorithm	B-Application
selection	I-Application
is	O
not	O
limited	O
to	O
single	O
domains	O
but	O
can	O
be	O
applied	O
to	O
any	O
kind	O
of	O
algorithm	O
if	O
the	O
above	O
requirements	O
are	O
satisfied	O
.	O
</s>
<s>
For	O
an	O
extensive	O
list	O
of	O
literature	O
about	O
algorithm	B-Application
selection	I-Application
,	O
we	O
refer	O
to	O
a	O
literature	O
overview	O
.	O
</s>
<s>
Online	O
algorithm	B-Application
selection	I-Application
refers	O
to	O
switching	O
between	O
different	O
algorithms	O
during	O
the	O
solving	O
process	O
.	O
</s>
<s>
This	O
is	O
useful	O
as	O
a	O
hyper-heuristic	B-Algorithm
.	O
</s>
<s>
In	O
contrast	O
,	O
offline	O
algorithm	B-Application
selection	I-Application
selects	O
an	O
algorithm	O
for	O
a	O
given	O
instance	O
only	O
once	O
and	O
before	O
the	O
solving	O
process	O
.	O
</s>
<s>
An	O
extension	O
of	O
algorithm	B-Application
selection	I-Application
is	O
the	O
per-instance	O
algorithm	O
scheduling	O
problem	O
,	O
in	O
which	O
we	O
do	O
not	O
select	O
only	O
one	O
solver	O
,	O
but	O
we	O
select	O
a	O
time	O
budget	O
for	O
each	O
algorithm	O
on	O
a	O
per-instance	O
base	O
.	O
</s>
<s>
an	O
extension	O
of	O
algorithm	B-Application
selection	I-Application
for	O
parallel	O
computation	O
is	O
parallel	O
portfolio	O
selection	O
,	O
</s>
