Cutting Stock with Rotation: Packing Square Items into Square Bins

2020 ◽  
pp. 530-544
Author(s):  
Shahin Kamali ◽  
Pooya Nikbakht
Keyword(s):  
Cutting Stock

An algorithm for the 2D guillotine cutting stock problem

1993 ◽  
Vol 68 (3) ◽  
pp. 400-412 ◽  
Author(s):  
Bruce MacLeod ◽  
Robert Moll ◽  
Mahesh Girkar ◽  
Nassim Hanifi
Keyword(s):  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Guillotine Cutting

scholarly journals An analytics-based heuristic decomposition of a bilevel multiple-follower cutting stock problem

OR Spectrum ◽  
2021 ◽  
Author(s):  
Adejuyigbe O. Fajemisin ◽  
Laura Climent ◽  
Steven D. Prestwich
Keyword(s):  
Real Life ◽  
Forest Harvesting ◽  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Decomposition Approach ◽  
New Class ◽  
Bilevel Problem ◽  
Programming Techniques ◽  
Bilevel Problems ◽  
Better Than

AbstractThis paper presents a new class of multiple-follower bilevel problems and a heuristic approach to solving them. In this new class of problems, the followers may be nonlinear, do not share constraints or variables, and are at most weakly constrained. This allows the leader variables to be partitioned among the followers. We show that current approaches for solving multiple-follower problems are unsuitable for our new class of problems and instead we propose a novel analytics-based heuristic decomposition approach. This approach uses Monte Carlo simulation and k-medoids clustering to reduce the bilevel problem to a single level, which can then be solved using integer programming techniques. The examples presented show that our approach produces better solutions and scales up better than the other approaches in the literature. Furthermore, for large problems, we combine our approach with the use of self-organising maps in place of k-medoids clustering, which significantly reduces the clustering times. Finally, we apply our approach to a real-life cutting stock problem. Here a forest harvesting problem is reformulated as a multiple-follower bilevel problem and solved using our approach.

Combined cutting stock and scheduling: a matheuristic approach

2016 ◽  
Vol 7 (3) ◽  
pp. 135 ◽  
Author(s):  
Nuno Braga ◽  
Cláudio Alves ◽  
Rita Macedo ◽  
José Valério De Carvalho
Keyword(s):  
Cutting Stock

The Nesting of Two-Dimensional Shapes Using Genetic Algorithms

1995 ◽  
Vol 209 (2) ◽  
pp. 115-124 ◽  
Author(s):  
H S Ismail ◽  
K K B Hon
Keyword(s):  
Genetic Algorithms ◽  
Evolutionary Process ◽  
Search Space ◽  
Cutting Stock ◽  
Two Dimensional ◽  
Optimal Solutions ◽  
Spatial Constraints ◽  
Global Optimal ◽  
Optimum Solution ◽  
Rapid Conversion

The general two-dimensional cutting stock problem is concerned with the optimum layout and arrangement of two-dimensional shapes within the spatial constraints imposed by the cutting stock. The main objective is to maximize the utilization of the cutting stock material. This paper presents some of the results obtained from applying a combination of genetic algorithms and heuristic approaches to the nesting of dissimilar shapes. Genetic algorithms are stochastically based optimization approaches which mimic nature's evolutionary process in finding global optimal solutions in a large search space. The paper discusses the method by which the problem is defined and represented for analysis and introduces a number of new problem-specific genetic algorithm operators that aid in the rapid conversion to an optimum solution.

An approach to two-dimensional cutting stock problems

1987 ◽  
Vol 25 (2) ◽  
pp. 175-190 ◽  
Author(s):  
CİHAN H. DAGLI ◽  
M. YALÇIN TATOGLU
Keyword(s):  
Cutting Stock ◽  
Two Dimensional
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