A heuristic approach based on dynamic programming and and/or-graph search for the constrained two-dimensional guillotine cutting problem

In this paper we present a heuristic method to generate constrained two-dimensional guillotine cutting patterns. This problem appears in different industrial processes of cutting rectangular plates to produce ordered items, such as in the glass, furniture and circuit board business. The method uses...

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Published in:	Annals of operations research Vol. 179; no. 1; pp. 297 - 315
Main Authors:	Morabito, Reinaldo, Pureza, Vitória
Format:	Journal Article
Language:	English
Published:	Boston Springer US 01.09.2010 Springer Springer Nature B.V
Subjects:	Algorithms Ascent Business and Management Circuit printing Combinatorics Constraints Cutting Cutting stock problem Dynamic programming Heuristic Heuristic methods Methods Operations research Operations Research/Decision Theory Optimization Packing problem Performance evaluation Printed circuits Searching Studies Theory of Computation Two dimensional Constrained two-dimensional guillotine cutting patterns Heuristics Dynamic programming And/or-graph search Cutting and packing problems
ISSN:	0254-5330, 1572-9338
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Abstract	In this paper we present a heuristic method to generate constrained two-dimensional guillotine cutting patterns. This problem appears in different industrial processes of cutting rectangular plates to produce ordered items, such as in the glass, furniture and circuit board business. The method uses a state space relaxation of a dynamic programming formulation of the problem and a state space ascent procedure of subgradient optimization type. We propose the combination of this existing approach with an and/or-graph search and an inner heuristic that turns infeasible solutions provided in each step of the ascent procedure into feasible solutions. Results for benchmark and randomly generated instances indicate that the method’s performance is competitive compared to other methods proposed in the literature. One of its advantages is that it often produces a relatively tight upper bound to the optimal value. Moreover, in most cases for which an optimal solution is obtained, it also provides a certificate of optimality.
AbstractList	In this paper we present a heuristic method to generate constrained two-dimensional guillotine cutting patterns. This problem appears in different industrial processes of cutting rectangular plates to produce ordered items, such as in the glass, furniture and circuit board business. The method uses a state space relaxation of a dynamic programming formulation of the problem and a state space ascent procedure of subgradient optimization type. We propose the combination of this existing approach with an and/or-graph search and an inner heuristic that turns infeasible solutions provided in each step of the ascent procedure into feasible solutions. Results for benchmark and randomly generated instances indicate that the method's performance is competitive compared to other methods proposed in the literature. One of its advantages is that it often produces a relatively tight upper bound to the optimal value. Moreover, in most cases for which an optimal solution is obtained, it also provides a certificate of optimality. In this paper we present a heuristic method to generate constrained two-dimensional guillotine cutting patterns. This problem appears in different industrial processes of cutting rectangular plates to produce ordered items, such as in the glass, furniture and circuit board business. The method uses a state space relaxation of a dynamic programming formulation of the problem and a state space ascent procedure of subgradient optimization type. We propose the combination of this existing approach with an and/or-graph search and an inner heuristic that turns infeasible solutions provided in each step of the ascent procedure into feasible solutions. Results for benchmark and randomly generated instances indicate that the method's performance is competitive compared to other methods proposed in the literature. One of its advantages is that it often produces a relatively tight upper bound to the optimal value. Moreover, in most cases for which an optimal solution is obtained, it also provides a certificate of optimality. Keywords Cutting and packing problems * Constrained two-dimensional guillotine cutting patterns * Dynamic programming * And/or-graph search * Heuristics In this paper we present a heuristic method to generate constrained twodimensional guillotine cutting patterns. This problem appears in different industrial processes of cutting rectangular plates to produce ordered items, such as in the glass, furniture and circuit board business. The method uses a state space relaxation of a dynamic programming formulation of the problem and a state space ascent procedure of subgradient optimization type. We propose the combination of this existing approach with an and/orgraph search and an inner heuristic that turns infeasible solutions provided in each step of the ascent procedure into feasible solutions. Results for benchmark and randomly generated instances indicate that the method's performance is competitive compared to other methods proposed in the literature. One of its advantages is that it often produces a relatively tight upper bound to the optimal value. Moreover, in most cases for which an optimal solution is obtained, it also provides a certificate of optimality. In this paper we present a heuristic method to generate constrained twodimensional guillotine cutting patterns. This problem appears in different industrial processes of cutting rectangular plates to produce ordered items, such as in the glass, furniture and circuit board business. The method uses a state space relaxation of a dynamic programming formulation of the problem and a state space ascent procedure of subgradient optimization type. We propose the combination of this existing approach with an and/orgraph search and an inner heuristic that turns infeasible solutions provided in each step of the ascent procedure into feasible solutions. Results for benchmark and randomly generated instances indicate that the method's performance is competitive compared to other methods proposed in the literature. One of its advantages is that it often produces a relatively tight upper bound to the optimal value. Moreover, in most cases for which an optimal solution is obtained, it also provides a certificate of optimality. Keywords Cutting and packing problems * Constrained two-dimensional guillotine cutting patterns * Dynamic programming * And/or-graph search * Heuristics In this paper we present a heuristic method to generate constrained two-dimensional guillotine cutting patterns. This problem appears in different industrial processes of cutting rectangular plates to produce ordered items, such as in the glass, furniture and circuit board business. The method uses a state space relaxation of a dynamic programming formulation of the problem and a state space ascent procedure of subgradient optimization type. We propose the combination of this existing approach with an and/or-graph search and an inner heuristic that turns infeasible solutions provided in each step of the ascent procedure into feasible solutions. Results for benchmark and randomly generated instances indicate that the method's performance is competitive compared to other methods proposed in the literature. One of its advantages is that it often produces a relatively tight upper bound to the optimal value. Moreover, in most cases for which an optimal solution is obtained, it also provides a certificate of optimality.[PUBLICATION ABSTRACT]
Audience	Academic
Author	Morabito, Reinaldo Pureza, Vitória
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Keywords	Constrained two-dimensional guillotine cutting patterns Heuristics Dynamic programming And/or-graph search Cutting and packing problems
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Snippet	In this paper we present a heuristic method to generate constrained two-dimensional guillotine cutting patterns. This problem appears in different industrial... In this paper we present a heuristic method to generate constrained twodimensional guillotine cutting patterns. This problem appears in different industrial...
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SubjectTerms	Algorithms Ascent Business and Management Circuit printing Combinatorics Constraints Cutting Cutting stock problem Dynamic programming Heuristic Heuristic methods Methods Operations research Operations Research/Decision Theory Optimization Packing problem Performance evaluation Printed circuits Searching Studies Theory of Computation Two dimensional
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Title	A heuristic approach based on dynamic programming and and/or-graph search for the constrained two-dimensional guillotine cutting problem
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