6,706 research outputs found
Finite Element Simulation of Dense Wire Packings
A finite element program is presented to simulate the process of packing and
coiling elastic wires in two- and three-dimensional confining cavities. The
wire is represented by third order beam elements and embedded into a
corotational formulation to capture the geometric nonlinearity resulting from
large rotations and deformations. The hyperbolic equations of motion are
integrated in time using two different integration methods from the Newmark
family: an implicit iterative Newton-Raphson line search solver, and an
explicit predictor-corrector scheme, both with adaptive time stepping. These
two approaches reveal fundamentally different suitability for the problem of
strongly self-interacting bodies found in densely packed cavities. Generalizing
the spherical confinement symmetry investigated in recent studies, the packing
of a wire in hard ellipsoidal cavities is simulated in the frictionless elastic
limit. Evidence is given that packings in oblate spheroids and scalene
ellipsoids are energetically preferred to spheres.Comment: 17 pages, 7 figures, 1 tabl
Optimal Deployments of UAVs With Directional Antennas for a Power-Efficient Coverage
To provide a reliable wireless uplink for users in a given ground area, one
can deploy Unmanned Aerial Vehicles (UAVs) as base stations (BSs). In another
application, one can use UAVs to collect data from sensors on the ground. For a
power-efficient and scalable deployment of such flying BSs, directional
antennas can be utilized to efficiently cover arbitrary 2-D ground areas. We
consider a large-scale wireless path-loss model with a realistic
angle-dependent radiation pattern for the directional antennas. Based on such a
model, we determine the optimal 3-D deployment of N UAVs to minimize the
average transmit-power consumption of the users in a given target area. The
users are assumed to have identical transmitters with ideal omnidirectional
antennas and the UAVs have identical directional antennas with given half-power
beamwidth (HPBW) and symmetric radiation pattern along the vertical axis. For
uniformly distributed ground users, we show that the UAVs have to share a
common flight height in an optimal power-efficient deployment. We also derive
in closed-form the asymptotic optimal common flight height of UAVs in terms
of the area size, data-rate, bandwidth, HPBW, and path-loss exponent
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
A Vitual-Force Based Swarm Algorithm for Balanced Circular Bin Packing Problems
Balanced circular bin packing problems consist in positioning a given number
of weighted circles in order to minimize the radius of a circular container
while satisfying equilibrium constraints. These problems are NP-hard, highly
constrained and dimensional. This paper describes a swarm algorithm based on a
virtual-force system in order to solve balanced circular bin packing problems.
In the proposed approach, a system of forces is applied to each component
allowing to take into account the constraints and minimizing the objective
function using the fundamental principle of dynamics. The proposed algorithm is
experimented and validated on benchmarks of various balanced circular bin
packing problems with up to 300 circles. The reported results allow to assess
the effectiveness of the proposed approach compared to existing results from
the literature.Comment: 23 pages including reference
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
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Formulation space search for two-dimensional packing problems
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The two-dimension packing problem is concerned with the arrangement of items without overlaps inside a container. In particular we have considered the case when the items are circular objects, some of the general examples that can be found in the industry are related with packing, storing and transportation of circular objects. Although there are several approaches we want to investigate the use of formulation space search. Formulation space search is a fairly recent method that provides an easy way to escape from local optima for non-linear problems allowing to achieve better results. Despite the fact that it has been implemented to solve the packing problem with identical circles, we present an improved implementation of the formulation space search that gives better results for the case of identical and non-identical circles, also considering that they are packed inside different shaped containers, for which we provide the needed modifications for an appropriate implementation. The containers considered are: the unit circle, the unit square, two rectangles with different dimension (length 5, width 1 and length 10 width 1), a right-isosceles triangle, a semicircle and a right-circular quadrant. Results from the tests conducted shown several improvements over the best previously known for the case of identical circles inside three different containers: a right-isosceles triangle, a semicircle and a circular quadrant. In order to extend the scope of the formulation space search approach we used it to solve mixed-integer non-linear problems, in particular those with zero-one variables. Our findings suggest that our implementation provides a competitive way to solve these kind of problems.This study was funded by the Mexican National Council for Science and Technology
(CONACyT)
改进区域划分的圆Packing变分算法
通过改进基于Power图的区域划分,提出一种收敛速度更快的圆packing算法.首先固定容器面积,将输入圆缩小一定的倍数,随机撒在容器中;之后对圆心点进行三角化,并根据相邻圆的半径比值对容器进行区域划分;再让所有圆在不超出自己区域边界的条件下尽量等比例增长至最大;最后将划分区域-长大的过程迭代下去,得到最大增长倍数.实验结果表明,该算法能够使得圆packing的过程更快地达到收敛.国家自然科学基金(61472332);;福建省自然科学基金(2018J01104
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