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a hybrid approach for saint-gobain cutting glass problem Mirsad - - PowerPoint PPT Presentation

May 22, 2023 23 likes •1.03k views

a hybrid approach for saint-gobain cutting glass problem Mirsad Buljuba si c, Michel Vasquez LGI2P Introduction Saint Gobain Manufacture and sale of flat glass #1 in Europe #2 worldwide 2 Saint Gobain Manufacture and

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a hybrid approach for saint-gobain cutting glass problem

Mirsad Buljubaˇ si´ c, Michel Vasquez

LGI2P

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Introduction

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Saint Gobain

Manufacture and sale of flat glass

  • #1 in Europe
  • #2 worldwide

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Saint Gobain

Manufacture and sale of flat glass

  • #1 in Europe
  • #2 worldwide

ROADEF/EURO Challenge 2018

  • Feb 2017 - Jan 2018
  • 64 registered teams
  • combinatorial optimization problem
  • http://www.roadef.org/challenge/2018/en/

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Saint Gobain

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Saint Gobain

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Saint Gobain

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Saint Gobain

The glass float is cut in jumbo’s of standard size (3m x 6m) Jumbo’s are then stacked and sent to transformers Transformers cut jumbo’s in smaller glass pieces Glass pieces are then sold to customers to match their needs

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Specific constraints

Defects

Defects arise on jumbo’s due to the complicated glass melting process, due to the moving of jumbo’s,... (air bubbles trapped in the glass, cracks or impacts from moving, stone - not melted material) Do not produce a glass piece having defects!

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Problem Definition

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Problem

Input: a set of jumbo’s with their defects and a set of glass pieces to cut

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Problem

Input: a set of jumbo’s with their defects and a set of glass pieces to cut Objective: design a set of cutting patterns for the jumbo’s of minimal glass loss

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Problem

Input: a set of jumbo’s with their defects and a set of glass pieces to cut Objective: design a set of cutting patterns for the jumbo’s of minimal glass loss Constraints: Cut all pieces ordered by a customer Each piece has to be defect free Respect cutting (from technical limitation and glass property) and organisationnal (from organisation in production units) constraints

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Problem

Input: a set of jumbo’s with their defects and a set of glass pieces to cut Objective: design a set of cutting patterns for the jumbo’s of minimal glass loss Constraints: Cut all pieces ordered by a customer Each piece has to be defect free Respect cutting (from technical limitation and glass property) and organisationnal (from organisation in production units) constraints This problem is a two-dimensional bin-packing problem (a jumbo = a bin, a glass piece = an item)

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Cutting constraints

Only guillotine cuts are allowed

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Cutting constraints

Only guillotine cuts are allowed 1 2 3 4 5 1 2 3 5 4

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Cutting constraints

The number of cuts to obtain an item is at most 3

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Cutting constraints

Only one extra cut is allowed after a 3-cut to remove waste

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Cutting constraints

Only one extra cut is allowed after a 3-cut to remove waste

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Cutting constraints

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Valid cutting example

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Organisationnal constraints

Bins have the same size and may contain rectangular defects Bins are stacked and have to be considered as ordered when designing cutting patterns

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Organisationnal constraints

Bins have the same size and may contain rectangular defects Bins are stacked and have to be considered as ordered when designing cutting patterns

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Organisationnal constraints

Items have to be cut in a given order (a stack) to respect production planning

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Problem

The problem to deal with is a two-dimensional bin-packing problem with: Defects on bins Order on bins Order on items Considering unrestricted 3-stage guillotine cutting patterns with trimming

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Problem

Find a set of cutting patterns ensuring all constraints and of minimal loss (dashed lines) A typical problem size: 300 items (< 700), 3 defects per bin, 20 item stacks

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Proposed solution

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Task

distribution of items to bins

  • rder of items inside each bin

cutting the the items inside the bin

items 1 2 3 4 5 6 7 8 9 ... 98 99 100 sol 1 100 75 20 3 19 12 5 6 ... 42 35 72 17

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Task

distribution of items to bins

  • rder of items inside each bin

cutting the the items inside the bin

items 1 2 3 4 5 6 7 8 9 ... 98 99 100 sol 1 100 75 20 3 19 12 5 6 ... 42 35 72

Greedy Heuristic Local Search Enumeration

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Greedy global: Bin by bin

Build solution by filling the bins one by one, put as much as possible in each bin

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Greedy global: Bin by bin

Build solution by filling the bins one by one, put as much as possible in each bin

Greedy + Enumeration + LS to fill the bin 1 as much as possible Greedy + Enumeration + LS to fill the bin 2 as much as possible . Greedy + Enumeration + LS to fill the last bin

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Greedy global: Bin by bin

Build solution by filling the bins one by one, put as much as possible in each bin

Greedy + Enumeration + LS to fill the bin 1 as much as possible Greedy + Enumeration + LS to fill the bin 2 as much as possible . Greedy + Enumeration + LS to fill the last bin

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Greedy global: Bin by bin

Build solution by filling the bins one by one, put as much as possible in each bin

Greedy + Enumeration + LS to fill the bin 1 as much as possible Greedy + Enumeration + LS to fill the bin 2 as much as possible . Greedy + Enumeration + LS to fill the last bin

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Greedy global: Bin by bin

Build solution by filling the bins one by one, put as much as possible in each bin

Greedy + Enumeration + LS to fill the bin 1 as much as possible Greedy + Enumeration + LS to fill the bin 2 as much as possible . Greedy + Enumeration + LS to fill the last bin

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Filling the bin

Task

Find the subset of non-assigned items that maximizes the usage

  • f bin i.e. minimizes the waste.

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Filling the bin

Task

Find the subset of non-assigned items that maximizes the usage

  • f bin i.e. minimizes the waste.

How? Local Search: add new item, swap two items,...

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Filling the bin

Task

Find the subset of non-assigned items that maximizes the usage

  • f bin i.e. minimizes the waste.

How? Local Search: add new item, swap two items,... Can we pack a given set of items in the bin? Greedy + Enumeration (backtracking)

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Packing: greedy + enumeration

Fill the bin by making 1-cuts one by one in a greedy way: always choose the 1-cut with minimum local waste Minimum waste 1-cut is found by enumerating all possible cuts

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sequence: 0 1 2 19 3 4 5 20 6 7 8 9 10 11 12 13 14 15 16 17 18

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sequence: 0 1 2 19 3 4 5 20 6 7 8 9 10 11 12 13 14 15 16 17 18

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sequence: 0 1 2 19 3 4 5 20 6 7 8 9 10 11 12 13 14 15 16 17 18 1

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sequence: 0 1 2 19 3 4 5 20 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2

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sequence: 0 1 2 19 3 4 5 20 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 19

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sequence: 0 1 2 19 3 4 5 20 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 19

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sequence: 0 1 2 19 3 4 5 20 6 7 8 9 10 11 12 13 14 15 16 17 18

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sequence: 0 1 2 19 3 4 5 20 6 7 8 9 10 11 12 13 14 15 16 17 18 1

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sequence: 0 1 2 19 3 4 5 20 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2

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sequence: 0 1 2 19 3 4 5 20 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 19

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sequence: 0 1 2 19 3 4 5 20 6 7 8 9 10 11 12 13 14 15 16 17 18 1

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sequence: 0 1 2 19 3 4 5 20 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 19

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sequence: 0 1 2 19 3 4 5 20 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 19

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sequence: 0 1 2 19 3 4 5 20 6 7 8 9 10 11 12 13 14 15 16 17 18 3 1 2 19

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sequence: 0 1 2 19 3 4 5 20 6 7 8 9 10 11 12 13 14 15 16 17 18 3 4 5 1 2 19

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Consistent Neighborhood Tabu search

explores partial and ”consistent” solutions, rearranging the items assigned to a single bin and non-assigned items Consistent Neighborhood Search for One-Dimensional Bin Packing and Two-Dimensional Vector Packing Computers & Operations Research, 2016

BIN NON-ASSIGNED ITEMS Local Search Moves

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Consistent Neighborhood Tabu search

explores partial and ”consistent” solutions, rearranging the items assigned to a single bin and non-assigned items Consistent Neighborhood Search for One-Dimensional Bin Packing and Two-Dimensional Vector Packing Computers & Operations Research, 2016

BIN NON-ASSIGNED ITEMS Local Search Moves

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B6 Solution

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B6 Solution

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B6 Solution

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B6 Solution

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B6 Solution

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B6 Solution

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B6 Solution

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B6 Solution

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B6 Solution

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B6 Solution

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Computational results

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Results

Dataset B Inst loss BKS loss(%) B1 2722308 2661318 3.48 B2 15137885 13674125 4.38 B3 18191093 18191093 4.64 B4 9857995 8269045 5.64 B5 72155615 72155615 18.41 B6 11407117 11195257 5.40 B7 8891889 8355819 4.36 B8 16067959 16067959 4.05 B9 17484577 17484577 5.38 B10 24095813 21951533 6.25 B11 22584380 22584380 5.73 B12 15903967 13958707 5.60 B13 26634915 24471375 5.26 B14 9449200 8656330 4.93 B15 26616371 24517031 5.11 avg 5.91 26

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Results

Dataset B Inst loss BKS loss(%) B1 2722308 2661318 3.48 B2 15137885 13674125 4.38 B3 18191093 18191093 4.64 B4 9857995 8269045 5.64 B5 72155615 72155615 18.41 B6 11407117 11195257 5.40 B7 8891889 8355819 4.36 B8 16067959 16067959 4.05 B9 17484577 17484577 5.38 B10 24095813 21951533 6.25 B11 22584380 22584380 5.73 B12 15903967 13958707 5.60 B13 26634915 24471375 5.26 B14 9449200 8656330 4.93 B15 26616371 24517031 5.11 avg 5.91 B + X: 8/30 best solutions 26

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thanks