<s>
Variable	B-Algorithm
neighborhood	I-Algorithm
search	I-Algorithm
(	O
VNS	O
)	O
,	O
proposed	O
by	O
Mladenović	O
&	O
Hansen	O
in	O
1997	O
,	O
is	O
a	O
metaheuristic	B-Algorithm
method	O
for	O
solving	O
a	O
set	O
of	O
combinatorial	O
optimization	O
and	O
global	O
optimization	O
problems	O
.	O
</s>
<s>
VNS	O
was	O
designed	O
for	O
approximating	O
solutions	O
of	O
discrete	O
and	O
continuous	O
optimization	O
problems	O
and	O
according	O
to	O
these	O
,	O
it	O
is	O
aimed	O
for	O
solving	O
linear	B-Algorithm
program	I-Algorithm
problems	O
,	O
integer	B-Algorithm
program	I-Algorithm
problems	O
,	O
mixed	O
integer	B-Algorithm
program	I-Algorithm
problems	O
,	O
nonlinear	B-Algorithm
program	I-Algorithm
problems	O
,	O
etc	O
.	O
</s>
<s>
Applications	O
are	O
rapidly	O
increasing	O
in	O
number	O
and	O
pertain	O
to	O
many	O
fields	O
:	O
location	O
theory	O
,	O
cluster	B-Algorithm
analysis	I-Algorithm
,	O
scheduling	B-Application
,	O
vehicle	B-Algorithm
routing	I-Algorithm
,	O
network	B-Architecture
design	I-Architecture
,	O
lot-sizing	O
,	O
artificial	B-Application
intelligence	I-Application
,	O
engineering	O
,	O
pooling	O
problems	O
,	O
biology	O
,	O
phylogeny	O
,	O
reliability	O
,	O
geometry	O
,	O
telecommunication	O
design	O
,	O
etc	O
.	O
</s>
<s>
There	O
are	O
several	O
books	O
important	O
for	O
understanding	O
VNS	O
,	O
such	O
as	O
:	O
Handbook	O
of	O
Metaheuristics	B-Algorithm
,	O
2010	O
,	O
Handbook	O
of	O
Metaheuristics	B-Algorithm
,	O
2003	O
and	O
Search	O
methodologies	O
,	O
2005	O
.	O
</s>
<s>
According	O
to	O
(	O
Mladenović	O
,	O
1995	O
)	O
,	O
VNS	O
is	O
a	O
metaheuristic	B-Algorithm
which	O
systematically	O
performs	O
the	O
procedure	O
of	O
neighborhood	O
change	O
,	O
both	O
in	O
descent	O
to	O
local	O
minima	O
and	O
in	O
escape	O
from	O
the	O
valleys	O
which	O
contain	O
them	O
.	O
</s>
<s>
Unlike	O
many	O
other	O
metaheuristics	B-Algorithm
,	O
the	O
basic	O
schemes	O
of	O
VNS	O
and	O
its	O
extensions	O
are	O
simple	O
and	O
require	O
few	O
,	O
and	O
sometimes	O
no	O
parameters	O
.	O
</s>
<s>
The	O
Basic	O
VNS	O
(	O
BVNS	O
)	O
method	O
(	O
Handbook	O
of	O
Metaheuristics	B-Algorithm
,	O
2010	O
)	O
combines	O
deterministic	O
and	O
stochastic	O
changes	O
of	O
neighborhood	O
.	O
</s>
<s>
RVNS	O
is	O
akin	O
to	O
a	O
Monte-Carlo	B-Algorithm
method	I-Algorithm
,	O
but	O
is	O
more	O
systematic	O
.	O
</s>
<s>
Three	O
Parallel	O
VNS	O
strategies	O
are	O
also	O
suggested	O
for	O
solving	O
the	O
Travelling	B-Algorithm
purchaser	I-Algorithm
problem	I-Algorithm
in	O
Ochi	O
et	O
al	O
.	O
</s>
<s>
The	O
mixed	O
integer	O
linear	B-Algorithm
programming	I-Algorithm
(	O
MILP	O
)	O
problem	O
consists	O
of	O
maximizing	O
or	O
minimizing	O
a	O
linear	O
function	O
,	O
subject	O
to	O
equality	O
or	O
inequality	O
constraints	O
,	O
and	O
integrality	O
restrictions	O
on	O
some	O
of	O
the	O
variables	O
.	O
</s>
<s>
Local	O
search	O
systematically	O
alternates	O
between	O
different	O
formulations	O
which	O
was	O
investigated	O
for	O
circle	O
packing	O
problem	O
(	O
CPP	O
)	O
where	O
stationary	O
point	O
for	O
a	O
nonlinear	B-Algorithm
programming	I-Algorithm
formulation	O
of	O
CPP	O
in	O
Cartesian	O
coordinates	O
is	O
not	O
strictly	O
a	O
stationary	O
point	O
in	O
polar	O
coordinates	O
.	O
</s>
