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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Vydáno v:Annals of operations research Ročník 179; číslo 1; s. 297 - 315
Hlavní autoři: Morabito, Reinaldo, Pureza, Vitória
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 01.09.2010
Springer
Springer Nature B.V
Témata:
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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Shrnutí: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.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-008-0457-4