irregular stock cutting with guillotine cuts han wei, julia bennell nanjing,china
Post on 06Jan2018
215 views
Embed Size (px)
DESCRIPTION
Problem description Problem arises in the glass cutting industry, in this instance, specifically for conservatories (glass houses)TRANSCRIPT
Irregular stock cutting with guillotine cutsHan Wei, Julia BennellNanJing ,China
SummaryProblem definitionCurrent practiceDirect packing approachGenerate candidate combinationsEvaluate candidate combinationsEvolve layouts in a self adaptive forestExample solutions/demoFuture work
Problem descriptionProblem arises in the glass cutting industry, in this instance, specifically for conservatories (glass houses)
Problem descriptionAll pieces are convexSingle size stock sheet (multiple sizes and offcuts will be considered in the future)Pieces are broken out using guillotine cuts (orthogonal and nonorthogonal)No limit to the number of stages/cutsPieces can be continuously rotatedDemand met exactly
Current practiceNest pairs of all nonrectangular pieces into a rectangleSelect best pairs according to following ratio
Use standard rectangle bin packing with guillotine constraints
Research aimCurrent software encloses two pieces into rectangles then packs the rectangles to be guillotine cutable.Our aimInvestigate nesting more than two pieces into rectanglesRemoving the requirement to nest into rectangles while meeting guillotine constraint.
Direct packing approach overviewIn words ..Evolve many layouts by recursively combining pieces, or configurations of subsets of pieces, together. Layouts evolve via a forest structure, where the size is controlled by an acceptance thresholdAn accepted combination of pieces becomes a single piece defined by the convex hull of the combinationPieces must be combined in such a way to result in a feasible layout
Direct packing approach overviewGenerate candidate combinations of two (sets of) piecesNon overlappingGuillotine cutableEvaluate candidate configurations Evolve solutions in self adaptive forest search
Generating candidate combinationsFor each i in P1, and j in P2, and sliding distance d,Attach
Slide
Evaluating candidate configurations
Match algorithmInitialise best_i, best_j, best_d, max_UFor each i in P1, and j in P2, Attach(P1,P2,i,j)
If
do d = 0, max{0,length(ei)length(ej)} Slide(d)If Uwf(P1,P2)> max_Uset best_i, best_j, best_d, max_U
Attach(P1,P2,best_i,best_j) , Slide(best_d)
FeasibilityGiven all pieces are convex and the described attach procedure, the nooverlap and guillotine constraints are clearly met for two original pieces.Once the best match is found the combination is defined by its convex hull, hence combining sets of pieces, defined by their convex hull is the same as 1.
Guillotine cut
More assumptions and definitions
Evolve layout in self adaptive forestm = 1m = 2m = 3m = 4m = 5
The maximum population of D given and maxg:At level m, the candidate set of configurations are:The mth generation of the population is described by:
Example results
Example results
Software demo
Future workExplore the followingHow scalable is the approachSensitivity to parameters; w, d and Incorporate full constraints
Additional constraintsMinimum angle of 30for cuts intersecting an edge
No more than two cuts can intersect
Both are permitted if a 20mil gap is added
Thank youQuestions
2
,
1
of
rectangle
enclosing
of
Area
rectangle
nest
of
Area
=
i
P
i
i
j
)}
(
length
)
(
length
,
0
max{
,
0
of
increments
in
distance
Slide
j
i
e
e
d
d

=
))
,
(
(
)
(
)
(
2
1
2
1
)
,
(
2
1
P
P
f
O
P
Area
P
Area
U
P
P
f
O
+
=
))
,
(
(
2
1
P
P
f
O
))
,
(
(
)
(
)
(
2
1
2
1
)
,
(
2
1
P
P
f
R
P
Area
P
Area
U
P
P
f
R
+
=
))
,
(
(
2
1
P
P
f
R
]
1
,
0
[
where
,
)
1
(
)
,
(
)
,
(
)
,
(
2
1
2
1
2
1

+
=
w
U
w
wU
U
P
P
f
O
P
P
f
R
P
P
f
w
d
j
i
j
i
e
e
e
e
j
i
md
q
>


=
)}
(
length
),
(
length
max{
)
(
length
)
(
length
1
)
,
(
q
q

+
=
=
=
=
=
)
(
2
1
)
(
)
(
)
(
)
(
)
(
2
2
2
1
1
2
1
2
1
if
match
accepted
an
is
)
(
*
match
weighted
optimal
the
,
value
critical
a
Given
)
1
(
)))
(
(
(
)
(
and
)))
(
(
(
)
(
)
(
)...
(
)
(
)
(
,
of
ation
transform
the
is
}
,..
,
{
,
of
subset
a
is
T
T
f
w
T
f
O
T
f
R
t
f
w
T
P
j
T
f
R
T
P
j
T
f
O
t
t
U
T
T
f
U
w
wU
U
T
f
R
Area
P
Area
U
T
f
O
Area
P
Area
U
P
f
P
f
P
f
T
f
T
f
P
P
P
T
D
T
j
j
U
U
U
g
m
m
m
j
i
j
i
T
f
w
j
j
i
i
j
i
w
m
T
f
w
m
w
g
D
Forrest
m
m
m
T
T
U
g
T
g
T
T
T
f
G
g
m
T
U
T
f
G
max
,..
1
)
*(
0
)
(
,
)
(
2
1
0
}
,
,
,
)
,
(
*
{
}
and
)
(
{
=
=
+
=
=
=
=
=
=
=
q
q
q
q
q
q
f
q
Recommended