7,682 research outputs found
Comparing several heuristics for a packing problem
Packing problems are in general NP-hard, even for simple cases. Since now
there are no highly efficient algorithms available for solving packing
problems. The two-dimensional bin packing problem is about packing all given
rectangular items, into a minimum size rectangular bin, without overlapping.
The restriction is that the items cannot be rotated. The current paper is
comparing a greedy algorithm with a hybrid genetic algorithm in order to see
which technique is better for the given problem. The algorithms are tested on
different sizes data.Comment: 5 figures, 2 tables; accepted: International Journal of Advanced
Intelligence Paradigm
TS2PACK: A Two-Level Tabu Search for the Three-dimensional Bin Packing Problem
Three-dimensional orthogonal bin packing is a problem NP-hard in the strong sense where a set of boxes must be orthogonally packed into the minimum number of three-dimensional bins. We present a two-level tabu search for this problem. The first-level aims to reduce the number of bins. The second optimizes the packing of the bins. This latter procedure is based on the Interval Graph representation of the packing, proposed by Fekete and Schepers, which reduces the size of the search space. We also introduce a general method to increase the size of the associated neighborhoods, and thus the quality of the search, without increasing the overall complexity of the algorithm. Extensive computational results on benchmark problem instances show the effectiveness of the proposed approach, obtaining better results compared to the existing one
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
Comparative study of different approaches to solve batch process scheduling and optimisation problems
Effective approaches are important to batch process scheduling problems, especially those with complex constraints. However, most research focus on improving optimisation techniques, and those concentrate on comparing their difference are inadequate. This study develops an optimisation model of batch process scheduling problems with complex constraints and investigates the performance of different optimisation techniques, such as Genetic Algorithm (GA) and Constraint Programming (CP). It finds that CP has a better capacity to handle batch process problems with complex constraints but it costs longer time
Solving Irregular Strip Packing Problems With Free Rotations Using Separation Lines
Solving nesting problems or irregular strip packing problems is to position
polygons in a fixed width and unlimited length strip, obeying polygon integrity
containment constraints and non-overlapping constraints, in order to minimize
the used length of the strip. To ensure non-overlapping, we used separation
lines. A straight line is a separation line if given two polygons, all vertices
of one of the polygons are on one side of the line or on the line, and all
vertices of the other polygon are on the other side of the line or on the line.
Since we are considering free rotations of the polygons and separation lines,
the mathematical model of the studied problem is nonlinear. Therefore, we use
the nonlinear programming solver IPOPT (an algorithm of interior points type),
which is part of COIN-OR. Computational tests were run using established
benchmark instances and the results were compared with the ones obtained with
other methodologies in the literature that use free rotation
Ant colony optimisation and local search for bin-packing and cutting stock problems
The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimization problems. Exact solution methods can only be used for very small instances, so for real-world problems, we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary Programming. In the work presented here, we used an ant colony optimization (ACO) approach to solve both Bin Packing and Cutting Stock Problems. We present a pure ACO approach, as well as an ACO approach augmented with a simple but very effective local search algorithm. It is shown that the pure ACO approach can compete with existing evolutionary methods, whereas the hybrid approach can outperform the best-known hybrid evolutionary solution methods for certain problem classes. The hybrid ACO approach is also shown to require different parameter values from the pure ACO approach and to give a more robust performance across different problems with a single set of parameter values. The local search algorithm is also run with random restarts and shown to perform significantly worse than when combined with ACO
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
A study on exponential-size neighborhoods for the bin packing problem with conflicts
We propose an iterated local search based on several classes of local and
large neighborhoods for the bin packing problem with conflicts. This problem,
which combines the characteristics of both bin packing and vertex coloring,
arises in various application contexts such as logistics and transportation,
timetabling, and resource allocation for cloud computing. We introduce
evaluation procedures for classical local-search moves, polynomial variants of
ejection chains and assignment neighborhoods, an adaptive set covering-based
neighborhood, and finally a controlled use of 0-cost moves to further diversify
the search. The overall method produces solutions of good quality on the
classical benchmark instances and scales very well with an increase of problem
size. Extensive computational experiments are conducted to measure the
respective contribution of each proposed neighborhood. In particular, the
0-cost moves and the large neighborhood based on set covering contribute very
significantly to the search. Several research perspectives are open in relation
to possible hybridizations with other state-of-the-art mathematical programming
heuristics for this problem.Comment: 26 pages, 8 figure
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