4,974 research outputs found
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
Constraint programming methods in three-dimensional container packing
Cutting and packing problems are present in many, at first glance
unconnected, areas, therefore it's beneficial to have a good understanding of
their underlying structure, to select proper techniques for finding solutions.
Cutting and packing problems are a class of combinatorial problems in which
there are specified two classes of objects: big and small items and the task is
to place the small items within big items. Even in the 1-dimensional case,
bin-packing is strongly NP-hard (Garey 1978), which suggests, that exact
solutions may not be found in a reasonable time for bigger instances. In the
literature, there are presented many various approaches to packing problems,
e.g. mixed-integer programming, approximation algorithms, heuristic solutions,
and local search algorithms, including metaheuristic approaches like Tabu
Search or Simulated Annealing.
The main goal of this work is to review existing solutions, survey the
variants arising from the industry applications, present a solution based on
constraint programming and compare its performance with the results in the
literature. Optimization with constraint programming is a method searching for
the global optima, hence it may require a higher workload compared to the
heuristic and local search approaches, which may finish in a local optimum. The
performance of the presented model will be measured on test data used in the
literature, which were used in many articles presenting a variety of approaches
to three-dimensional container packing, which will allow us to compare the
efficiency of the constraint programming model with other methods used in the
operational research
Overcommitment in Cloud Services -- Bin packing with Chance Constraints
This paper considers a traditional problem of resource allocation, scheduling
jobs on machines. One such recent application is cloud computing, where jobs
arrive in an online fashion with capacity requirements and need to be
immediately scheduled on physical machines in data centers. It is often
observed that the requested capacities are not fully utilized, hence offering
an opportunity to employ an overcommitment policy, i.e., selling resources
beyond capacity. Setting the right overcommitment level can induce a
significant cost reduction for the cloud provider, while only inducing a very
low risk of violating capacity constraints. We introduce and study a model that
quantifies the value of overcommitment by modeling the problem as a bin packing
with chance constraints. We then propose an alternative formulation that
transforms each chance constraint into a submodular function. We show that our
model captures the risk pooling effect and can guide scheduling and
overcommitment decisions. We also develop a family of online algorithms that
are intuitive, easy to implement and provide a constant factor guarantee from
optimal. Finally, we calibrate our model using realistic workload data, and
test our approach in a practical setting. Our analysis and experiments
illustrate the benefit of overcommitment in cloud services, and suggest a cost
reduction of 1.5% to 17% depending on the provider's risk tolerance
Dagstuhl Reports : Volume 1, Issue 2, February 2011
Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn
Structural characterization and statistical-mechanical model of epidermal patterns
In proliferating epithelia of mammalian skin, cells of irregular
polygonal-like shapes pack into complex nearly flat two-dimensional structures
that are pliable to deformations. In this work, we employ various sensitive
correlation functions to quantitatively characterize structural features of
evolving packings of epithelial cells across length scales in mouse skin. We
find that the pair statistics in direct and Fourier spaces of the cell
centroids in the early stages of embryonic development show structural
directional dependence, while in the late stages the patterns tend towards
statistically isotropic states. We construct a minimalist four-component
statistical-mechanical model involving effective isotropic pair interactions
consisting of hard-core repulsion and extra short-ranged soft-core repulsion
beyond the hard core, whose length scale is roughly the same as the hard core.
The model parameters are optimized to match the sample pair statistics in both
direct and Fourier spaces. By doing this, the parameters are biologically
constrained. Our model predicts essentially the same polygonal shape
distribution and size disparity of cells found in experiments as measured by
Voronoi statistics. Moreover, our simulated equilibrium liquid-like
configurations are able to match other nontrivial unconstrained statistics,
which is a testament to the power and novelty of the model. We discuss ways in
which our model might be extended so as to better understand morphogenesis (in
particular the emergence of planar cell polarity), wound-healing, and disease
progression processes in skin, and how it could be applied to the design of
synthetic tissues
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
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