Best-First Search Methods for Constrained Two-Dimensional Cutting Stock Problems

Best-first search is a widely used problem solving technique in the field of artificial intelligence. The method has useful applications in operations research as well. Here we describe an application to constrained two-dimensional cutting stock problems of the following type: A stock rectangle S of...

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Published inOperations research Vol. 41; no. 4; pp. 768 - 776
Main Authors Viswanathan, K. V, Bagchi, A
Format Journal Article
LanguageEnglish
Published Linthicum, MD INFORMS 01.07.1993
Operations Research Society of America
Institute for Operations Research and the Management Sciences
Subjects
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ISSN0030-364X
1526-5463
DOI10.1287/opre.41.4.768

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Abstract Best-first search is a widely used problem solving technique in the field of artificial intelligence. The method has useful applications in operations research as well. Here we describe an application to constrained two-dimensional cutting stock problems of the following type: A stock rectangle S of dimensions ( L , W ) is supplied. There are n types of demanded rectangles r 1 , r 2 , ..., r n , with the i th type having length l i , width w i , value v i , and demand constraint b i . It is required to produce, from the stock rectangle S , a i copies of r i , 1 i n , to maximize a 1 v 1 + a 2 v 2 + · + a n v n subject to the constraints a i b i . Only orthogonal guillotine cuts are permitted. All parameters are integers. A best-first tree search algorithm based on Wang's bottom-up approach is described that guarantees optimal solutions and is more efficient than existing methods.
AbstractList Best-first search is a widely used problem solving technique in the field of artificial intelligence. The method has useful applications in operations research as well. Here we describe an application to constrained two-dimensional cutting stock problems of the following type: A stock rectangle S of dimensions ( L , W ) is supplied. There are n types of demanded rectangles r 1 , r 2 , …, r n , with the i th type having length l i , width w i , value v i , and demand constraint b i . It is required to produce, from the stock rectangle S , a i copies of r i , 1 ≤ i ≤ n , to maximize a 1 v 1 + a 2 v 2 + · + a n v n subject to the constraints a i ≤ b i . Only orthogonal guillotine cuts are permitted. All parameters are integers. A best-first tree search algorithm based on Wang's bottom-up approach is described that guarantees optimal solutions and is more efficient than existing methods.
Best-first search is a widely used problem-solving technique in the field of artificial intelligence. The method has useful applications in operations research as well. An application of the method to the constrained 2-dimensional cutting stock problem (CTCSP) is described. In the CTCSP a single rectangular stock sheet must be cut in an optimal way into required rectangles of smaller size without violating specified constraints. All cuts must be orthogonal, meaning parallel to one side of the rectangle, and any cut must also be a guillotine cut, meaning it must run from end to end on the rectangle being cut. All parameters are integers. The analysis describes a best-first tree search algorithm based on Wang's (1983) bottom-up approach. The proposed algorithm guarantees optimal solutions and is more effective than existing methods.
Best-first search is a widely used problem solving technique in the field of artificial intelligence. The method has useful applications in operations research as well. Here we describe an application to constrained two-dimensional cutting stock problems of the following type: A stock rectangle S of dimensions ( L , W ) is supplied. There are n types of demanded rectangles r 1 , r 2 , ..., r n , with the i th type having length l i , width w i , value v i , and demand constraint b i . It is required to produce, from the stock rectangle S , a i copies of r i , 1 i n , to maximize a 1 v 1 + a 2 v 2 + · + a n v n subject to the constraints a i b i . Only orthogonal guillotine cuts are permitted. All parameters are integers. A best-first tree search algorithm based on Wang's bottom-up approach is described that guarantees optimal solutions and is more efficient than existing methods.
Best-first search is a widely used problem solving technique in the field of artificial intelligence. The method has useful applications in operations research as well. Here we describe an application to constrained two-dimensional cutting stock problems of the following type. A stock rectangle S of dimensions (L, W) is supplied. There are n types of demanded rectangles r sub(1), r sub(2),...r sub(n) with the ith type having length l sub(1), width w sub(i), value v sub(1), and demand constraint b sub(j). It is required to produce, from the stock rectangle S, a sub(j) copies of r sub(i) 1 < i < n. to maximize a sub(1)v sub(1) + a sub(2)v sub(1) + a sub(2)v sub(2) + ... + a sub(n)v sub(n) subject to the constraints a sub(i) less than or equal to b sub(r). Only orthogonal guillotine cuts are permitted. All parameters are integers. A best-first tree search algorithm based on Wang's bottom-up approach is described that guarantees optimal solutions and is more efficient than existing methods.
Best-first search is a widely used problem solving technique in the field of artificial intelligence. The method has useful applications in operations research as well. Here we describe an application to constrained two-dimensional cutting stock problems of the following type: A stock rectangle S of dimensions (L, W) is supplied. There are n types of demanded rectangles r1,r2,...,rn, with the ith type having length li, width wi, value vi, and demand constraint bi. It is required to produce, from the stock rectangle S, aicopies of ri, 1≤ i≤ n, to maximize a1v1+a2v2+... +anvnsubject to the constraints ai≤ bi. Only orthogonal guillotine cuts are permitted. All parameters are integers. A best-first tree search algorithm based on Wang's bottom-up approach is described that guarantees optimal solutions and is more efficient than existing methods.
Best-first search is a widely used problem solving technique in the field of artificial intelligence. The method has useful applications in operations research as well. Here we describe an application to constrained two-dimensional cutting stock problems of the following type: A stock rectangle S of dimensions (L, W) is supplied. There are n types of demanded rectangles r 1 , r 2 , …, r n , with the ith type having length l i , width w i , value v i , and demand constraint b i . It is required to produce, from the stock rectangle S, a i copies of r i , 1 ≤ i ≤ n, to maximize a 1 v 1 + a 2 v 2 + · + a n v n subject to the constraints a i ≤ b i . Only orthogonal guillotine cuts are permitted. All parameters are integers. A best-first tree search algorithm based on Wang's bottom-up approach is described that guarantees optimal solutions and is more efficient than existing methods.
Author Viswanathan, K. V
Bagchi, A
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Issue 4
Keywords Cutting
Experimental result
Constraint
Combinatorial problem
Trim loss problem
Two dimensional model
Search algorithm
Language English
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Snippet Best-first search is a widely used problem solving technique in the field of artificial intelligence. The method has useful applications in operations research...
Best-first search is a widely used problem-solving technique in the field of artificial intelligence. The method has useful applications in operations research...
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SubjectTerms Algorithms
Applied sciences
Artificial intelligence
artificial intelligence: search methods
computers/computer science
cutting stock/trim: rectangular stock sheets
Dynamic programming
Exact sciences and technology
Experimental results
Flows in networks. Combinatorial problems
Heuristics
Integers
Mathematical models
Maximum value
Operational research and scientific management
Operational research. Management science
Operations research
Optimal solutions
Problem solving
production/scheduling
Rectangles
Recursion
Title Best-First Search Methods for Constrained Two-Dimensional Cutting Stock Problems
URI http://or.journal.informs.org/cgi/content/abstract/41/4/768
https://www.jstor.org/stable/171971
https://www.proquest.com/docview/1303086864
https://www.proquest.com/docview/219170186
https://www.proquest.com/docview/25942677
Volume 41
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