Cutting path optimization for an automatic cutter in polynomial time using a 3/2 approximation algorithm

The optimal path to be followed by an automatic cutter to cut a set of shapes arranged on a material is termed as the cutting path determination problem. The shapes are often considered as polygons. Each polygon can be either cut entirely (complete cutting approach) or partially (partial cutting app...

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Vydáno v:International journal of advanced manufacturing technology Ročník 113; číslo 11-12; s. 3667 - 3679
Hlavní autoři: Eapen, Neeta A., Heckendorn, Robert B.
Médium: Journal Article
Jazyk:angličtina
Vydáno: London Springer London 01.04.2021
Springer Nature B.V
Témata:
Algorithms
Apexes
Approximation
CAE) and Design
Computer-Aided Engineering (CAD
Engineering
Industrial and Production Engineering
Mathematical analysis
Mechanical Engineering
Media Management
Metal cutting
Metal sheets
Optimization
Original Article
Polygons
Polynomials
Delaunay triangulation
Cutting path optimization
Approximation algorithm
Endpoint cutting problem
Perfect matching
Minimum spanning tree
ISSN:0268-3768, 1433-3015
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Shrnutí:The optimal path to be followed by an automatic cutter to cut a set of shapes arranged on a material is termed as the cutting path determination problem. The shapes are often considered as polygons. Each polygon can be either cut entirely (complete cutting approach) or partially (partial cutting approach) before cutting the next polygon. This work solves the cutting path determination problem using the partial cutting approach. The proposed approximation algorithm uses the concepts of ma tching, s panning tree, and tri angulation, and is hence termed as MASTRI. The MASTRI algorithm has a time complexity of O ( n log n ) where n is the total number of vertices of all the polygons. The cutting path computed by the MASTRI algorithm is guaranteed to be within a factor of 3/2 of optimum travel distance of the cutter. No other algorithm has been developed for the partial cutting approach which runs in polynomial time. The MASTRI algorithm is evaluated on 285 input problems, of which 192 problems are randomly generated, and 93 problems are taken from literature. The experimental analysis shows that the MASTRI algorithm computes the cutting path in a very short amount of time. The comparison of MASTRI algorithm with existing works in the literature shows that the MASTRI algorithm gives a shorter cutting path in less time. The MASTRI algorithm can be used for computing cutting path in industries like sheet metal cutting.
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ISSN:0268-3768
1433-3015
DOI:10.1007/s00170-021-06842-9