irregular stock cutting with guillotine cuts han wei, julia bennell nanjing,china

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Problem description Problem arises in the glass cutting industry, in this instance, specifically for conservatories (glass houses)

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  • 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 off-cuts will be considered in the future)Pieces are broken out using guillotine cuts (orthogonal and non-orthogonal)No limit to the number of stages/cutsPieces can be continuously rotatedDemand met exactly

  • Current practiceNest pairs of all non-rectangular 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 cut-able.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 cut-ableEvaluate 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 no-overlap 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

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