PARALLEL ALGORITHMS for 2 D cutting stock problems

PARALLEL ALGORITHMS for 2 D cutting stock problems -Derya AKBULUT- CENG 505 – Parallel Computing I Instructor: Cem ÖZDOĞAN 1

OUTLINE • 2 D Cutting Stock Problems • Parallel algorithms for 2 D cutting stock Problems – Example from literature – Some computational results • Parallel computing for my M. S. thesis 2

2 D Cutting Stock Problem In general: A rectangular stock material in two dimension Examples: glass, paper, sheet metal, fabric and etc. Parts to be produced by cutting the stock material in pieces 3

2 D Cutting Stock Problem The problem is generating a cutting pattern for the pieces 4

2 D Cutting Stock Problem scrap such that the scrap of the stock material is minimized (utilization of stock is maximized) 5

2 D Cutting Stock Problem • Discrete • Combinatorial Problems • High computational effort as number of pieces increases • So parallelisation may be advantageous 6

Parallel Algorithms on 2 DCSP “Fine and coarse grained parallel algorithms for the 2 D cutting stock problem” Jesica de Armas – Coromoto Leon – Gara Miranda • About the problem: two-staged guillotine: – 2 D – rectangular shapes – with guillotine constraint non-guillotine: 7

Parallel Algorithms on 2 DCSP “Fine and coarse grained parallel algorithms for the 2 D cutting stock problem” Jesica de Armas – Coromoto Leon – Gara Miranda • About the problem: – 2 D – rectangular shapes – with guillotine constraint • Solution method: – Viswanathan and Bagchi (VB) Algorithm. – Parallel Algorithms: • Fine Grained Parallel Scheme (shared-memory scheme – Open. MP) • Coarse Grained Algorithm (distributed scheme - MPI) 8

Parallel Algorithms on 2 DCSP “Fine and coarse grained parallel algorithms for the 2 D cutting stock problem” Jesica de Armas – Coromoto Leon – Gara Miranda • Solution method: Viswanathan and Bagchi (VB) Algorithm. (sequential) – Two lists: OPEN and CLIST – Best build of piece is combined with the already found best meta-rectangle • To produce horizontal and vertical builds – F`(α) = g(α) + h`(α) • g(α): profit obtained from piece • h`(α): Profit can be obtained from remainin area 9

Parallel Algorithms on 2 DCSP “Fine and coarse grained parallel algorithms for the 2 D cutting stock problem” Jesica de Armas – Coromoto Leon – Gara Miranda • Solution method: Viswanathan and Bagchi (VB) Algorithm. (sequential) – Two lists: OPEN and CLIST – Best build of piece is combined with the already found best meta-rectangle • To produce horizontal and vertical builds – F`(α) = g(α) + h`(α) • g(α): profit obtained from piece • h`(α): Profit can be obtained from remainin area 10

Parallel Algorithms on 2 DCSP “Fine and coarse grained parallel algorithms for the 2 D cutting stock problem” Jesica de Armas – Coromoto Leon – Gara Miranda • Solution method: Fine Grained Parallel Scheme (shared-memory scheme – Open. MP) – Implementation uses Open. MP for the parallel execution of the horizontal and vertical combination loops. – Each processor works on a section of CLIST structure – Each processor keeps a replicated copy of CLIST – OPEN is distributed 11

Parallel Algorithms on 2 DCSP “Fine and coarse grained parallel algorithms for the 2 D cutting stock problem” Jesica de Armas – Coromoto Leon – Gara Miranda • Solution method: Fine Grained Parallel Scheme – Implementation uses Open. MP for the parallel execution of the horizontal and vertical combination loops. – Each processor works on a section of CLIST structure – Each processor keeps a replicated copy of CLIST – OPEN is distributed 12

Parallel Algorithms on 2 DCSP “Fine and coarse grained parallel algorithms for the 2 D cutting stock problem” Jesica de Armas – Coromoto Leon – Gara Miranda • Solution method: Coarse Grained Parallel Scheme (distributed memory – MPI) – Implementation uses MPI for the parallel execution of the main search loop together with a flexible synchronization scheme and load balancing – Each processor works on a section of CLIST structure – Each processor keeps a replicated copy of CLIST – OPEN is distributed 13

Parallel Algorithms on 2 DCSP “Fine and coarse grained parallel algorithms for the 2 D cutting stock problem” Jesica de Armas – Coromoto Leon – Gara Miranda • Solution method: Coarse Grained Parallel Scheme – Implementation uses MPI for the parallel execution of the main search loop together with a flexible synchronization scheme and load balancing – Each processor works on a section of CLIST structure – Each processor keeps a replicated copy of CLIST – OPEN is distributed 14

Parallel Algorithms on 2 DCSP “Fine and coarse grained parallel algorithms for the 2 D cutting stock problem” Jesica de Armas – Coromoto Leon – Gara Miranda • Execution times: 15

In my thesis A rectangular stock material in two dimension Examples: glass, paper, sheet metal, fabric and etc. 16

In my thesis 17

In my thesis An Edge Matching Approach for two dimensional irregular shaped cutting stock problems. 18

In my thesis An Edge Matching Approach for two dimensional irregular shaped cutting stock problems. Inputs: • x and y coordinates for the vertices of each shape • x and y coordinates for the vertices of stock material 19

In my thesis Initialize: boundary, shapes smoothshapes(shapes) list = sortshapes (shapes) shape. L = getlargestshape(list) list = updatelist(list) defineincrement() shape. L=alignshape(shape. L, boundary) boundary = getboundary(boundary, shape. L) barea = bound. Area(boundary) List =Null STOP shape. L = getlargestshape(list) Barea < shape. L list = updatelist(list) X 20

In my thesis Possible tasks to be parallelized: • Smooth • Sort and find largest: • Find areas for all shapes Initialize: boundary, shapes smoothshapes(shapes) list = sortshapes (shapes) shape. L = getlargestshape(list) • Align function • Interior angles for all shapes • Rotation angles • Coordinates after rotation list = updatelist(list) defineincrement() shape. L=alignshape(shape. L, boundary) • Best fit to current boundary = getboundary(boundary, shape. L) barea = bound. Area(boundary) List =Null STOP shape. L = getlargestshape(list) Barea < shape. L list = updatelist(list) X Ta 21

QUESTIONS? 22