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 in | Operations research Vol. 41; no. 4; pp. 768 - 776 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Linthicum, MD
INFORMS
01.07.1993
Operations Research Society of America Institute for Operations Research and the Management Sciences |
Subjects | |
Online Access | Get full text |
ISSN | 0030-364X 1526-5463 |
DOI | 10.1287/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. |
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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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Copyright | Copyright 1993 The Operations Research Society of America 1994 INIST-CNRS Copyright Institute for Operations Research and the Management Sciences Jul/Aug 1993 |
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Keywords | Cutting Experimental result Constraint Combinatorial problem Trim loss problem Two dimensional model Search algorithm |
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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 |
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