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

2008 ◽  
Vol 179 (1) ◽  
pp. 297-315 ◽  
Author(s):  
Reinaldo Morabito ◽  
Vitória Pureza
Keyword(s):  
Dynamic Programming ◽  
Heuristic Approach ◽  
Graph Search ◽  
Two Dimensional ◽  
Cutting Problem ◽  
Guillotine Cutting

scholarly journals An improved heuristic-dynamic programming algorithm for rectangular cutting problem

2020 ◽  
Vol 17 (3) ◽  
pp. 717-735
Author(s):  
Aihua Yin ◽  
Chong Chen ◽  
Dongping Hu ◽  
Jianghai Huang ◽  
Fan Yang
Keyword(s):  
Dynamic Programming ◽  
Dynamic Programming Algorithm ◽  
Optimal Solution ◽  
Computation Time ◽  
Programming Algorithm ◽  
Recursive Method ◽  
Two Dimensional ◽  
One Dimensional ◽  
Block Width ◽  
Cutting Problem

In this paper, the two-dimensional cutting problem with defects is discussed. The objective is to cut some rectangles in a given shape and direction without overlapping the defects from the rectangular plate and maximize some profit associated. An Improved Heuristic-Dynamic Program (IHDP) is presented to solve the problem. In this algorithm, the discrete set contains not only the solution of one-dimensional knapsack problem with small rectangular block width and height, but also the cutting positions of one unit outside four boundaries of each defect. In addition, the denormalization recursive method is used to further decompose the sub problem with defects. The algorithm computes thousands of typical instances. The computational experimental results show that IHDP obtains most of the optimal solution of these instances, and its computation time is less than that of the latest literature algorithms.

scholarly journals Novel Methods Generated by Genetic Programming for the Guillotine-Cutting Problem

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Vittorio Bertolini ◽  
Carlos Rey ◽  
Mauricio Sepulveda ◽  
Victor Parada
Keyword(s):  
Genetic Programming ◽  
Evolutionary Computation ◽  
State Of The Art ◽  
Two Dimensional ◽  
Constructive Algorithms ◽  
Constructive Algorithm ◽  
Novel Methods ◽  
Cutting Problem ◽  
New Algorithms ◽  
Guillotine Cutting

New constructive algorithms for the two-dimensional guillotine-cutting problem are presented. The algorithms were produced from elemental algorithmic components using evolutionary computation. A subset of the components was selected from a previously existing constructive algorithm. The algorithms’ evolution and testing process used a set of 46 instances from the literature. The structure of three new algorithms is described, and the results are compared with those of an existing constructive algorithm for the problem. Several of the new algorithms are competitive with respect to a state-of-the-art constructive algorithm. A subset of novel instructions, which are responsible for the majority of the new algorithms’ good performances, has also been found.

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