1,350 research outputs found
Extreme-Point-based Heuristics for the Three-Dimensional Bin Packing problem
One of the main issues in addressing three-dimensional packing problems is finding an efficient and accurate definition of the points at which to place the items inside the bins, because the performance of exact and heuristic solution methods is actually strongly influenced by the choice of a placement rule. We introduce the extreme point concept and present a new extreme point-based rule for packing items inside a three-dimensional container. The extreme point rule is independent from the particular packing problem addressed and can handle additional constraints, such as fixing the position of the items. The new extreme point rule is also used to derive new constructive heuristics for the three-dimensional bin-packing problem. Extensive computational results show the effectiveness of the new heuristics compared to state-of-the-art results. Moreover, the same heuristics, when applied to the two-dimensional bin-packing problem, outperform those specifically designed for the proble
Logic based Benders' decomposition for orthogonal stock cutting problems
We consider the problem of packing a set of rectangular items into a strip of fixed width, without overlapping, using minimum height. Items must be packed with their edges parallel to those of the strip, but rotation by 90\ub0 is allowed. The problem is usually solved through branch-and-bound algorithms. We propose an alternative method, based on Benders' decomposition. The master problem is solved through a new ILP model based on the arc flow formulation, while constraint programming is used to solve the slave problem. The resulting method is hybridized with a state-of-the-art branch-and-bound algorithm. Computational experiments on classical benchmarks from the literature show the effectiveness of the proposed approach. We additionally show that the algorithm can be successfully used to solve relevant related problems, like rectangle packing and pallet loading
Three-Dimensional Container Loading: A Simulated Annealing Approach
High utilization of cargo volume is an essential factor in the success of modern enterprises in the market. Although mathematical models have been presented for container loading problems in the literature, there is still a lack of studies that consider practical constraints. In this paper, a Mixed Integer Linear Programming is developed for the problem of packing a subset of rectangular boxes inside a container such that the total value of the packed boxes is maximized while some realistic constraints, such as vertical stability, are considered. The packing is orthogonal, and the boxes can be freely rotated into any of the six orientations. Moreover, a sequence triple-based solution methodology is proposed, simulated annealing is used as modeling technique, and the situation where some boxes are preplaced in the container is investigated. These preplaced boxes represent potential obstacles. Numerical experiments are conducted for containers with and without obstacles. The results show that the simulated annealing approach is successful and can handle large number of packing instances
A beam search approach to solve the convex irregular bin packing problem with guillotine cuts
This paper presents a two dimensional convex irregular bin packing problem with guillotine cuts. The problem combines the challenges of tackling the complexity of packing irregular pieces, guaranteeing guillotine cuts that are not always orthogonal to the edges of the bin, and allocating pieces to bins that are not necessarily of the same size. This problem is known as a two-dimensional multi bin size bin packing problem with convex irregular pieces and guillotine cuts. Since pieces are separated by means of guillotine cuts, our study is restricted to convex pieces.A beam search algorithm is described, which is successfully applied to both the multi and single bin size instances. The algorithm is competitive with the results reported in the literature for the single bin size problem and provides the first results for the multi bin size problem
An anytime tree search algorithm for two-dimensional two- and three-staged guillotine packing problems
[libralesso_anytime_2020] proposed an anytime tree search algorithm for the
2018 ROADEF/EURO challenge glass cutting problem
(https://www.roadef.org/challenge/2018/en/index.php). The resulting program was
ranked first among 64 participants. In this article, we generalize it and show
that it is not only effective for the specific problem it was originally
designed for, but is also very competitive and even returns state-of-the-art
solutions on a large variety of Cutting and Packing problems from the
literature. We adapted the algorithm for two-dimensional Bin Packing, Multiple
Knapsack, and Strip Packing Problems, with two- or three-staged exact or
non-exact guillotine cuts, the orientation of the first cut being imposed or
not, and with or without item rotation. The combination of efficiency, ability
to provide good solutions fast, simplicity and versatility makes it
particularly suited for industrial applications, which require quickly
developing algorithms implementing several business-specific constraints. The
algorithm is implemented in a new software package called PackingSolver
Two-dimensional placement compaction using an evolutionary approach: a study
The placement problem of two-dimensional objects over planar surfaces optimizing
given utility functions is a combinatorial optimization problem. Our main drive is that of
surveying genetic algorithms and hybrid metaheuristics in terms of final positioning area
compaction of the solution. Furthermore, a new hybrid evolutionary approach, combining
a genetic algorithm merged with a non-linear compaction method is introduced and
compared with referenced literature heuristics using both randomly generated instances
and benchmark problems. A wide variety of experiments is made, and the respective
results and discussions are presented. Finally, conclusions are drawn, and future research
is defined
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