692 research outputs found
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
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
Augmented neural networks and problem-structure based heuristics for the bin-packing problem
In this paper, we apply the Augmented-neural-networks (AugNN) approach for solving the classical bin-packing problem (BPP). AugNN is a metaheuristic that combines a priority- rule heuristic with the iterative search approach of neural networks to generate good solutions fast. This is the first time this approach has been applied to the BPP. We also propose a decomposition approach for solving harder BPP, in which sub problems are solved using a combination of AugNN approach and heuristics that exploit the problem structure. We discuss the characteristics of problems on which such problem-structure based heuristics could be applied. We empirically show the effectiveness of the AugNN and the decomposition approach on many benchmark problems in the literature. For the 1210 benchmark problems tested, 917 problems were solved to optimality and the average gap between the obtained solution and the upper bound for all the problems was reduced to under 0.66% and computation time averaged below 33 seconds per problem. We also discuss the computational complexity of our approach
A tabu search heuristic for the vehicle routing problem with two-dimensional loading constraints
This article addresses the well-known Capacitated Vehicle Routing Problem (CVRP), in the special case where the demand of a customer consists of a certain number of two-dimensional weighted items. The problem calls for the minimization of the cost of transportation needed for the delivery of the goods demanded by the customers, and carried out by a fleet of vehicles based at a central depot. In order to accommodate all items on the vehicles, a feasibility check of the two-dimensional packing (2L) must be executed on each vehicle. The overall problem, denoted as 2L-CVRP, is NP-hard and particularly difficult to solve in practice. We propose a Tabu Search algorithm, in which the loading component of the problem is solved through heuristics, lower bounds, and a truncated branch-and-bound procedure. The effectiveness of the algorithm is demonstrated through extensivecomputational experiments
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
Automating the packing heuristic design process with genetic programming
The literature shows that one-, two-, and three-dimensional bin packing and knapsack packing are difficult problems in operational research. Many techniques, including exact, heuristic, and metaheuristic approaches, have been investigated to solve these problems and it is often not clear which method to use when presented with a new instance. This paper presents an approach which is motivated by the goal of building computer systems which can design heuristic methods. The overall aim is to explore the possibilities for automating the heuristic design process. We present a genetic programming system to automatically generate a good quality heuristic for each instance. It is not necessary to change the methodology depending on the problem type (one-, two-, or three-dimensional knapsack and bin packing problems), and it therefore has a level of generality unmatched by other systems in the literature. We carry out an extensive suite of experiments and compare with the best human designed heuristics in the literature. Note that our heuristic design methodology uses the same parameters for all the experiments. The contribution of this paper is to present a more general packing methodology than those currently available, and to show that, by using this methodology, it is possible for a computer system to design heuristics which are competitive with the human designed heuristics from the literature. This represents the first packing algorithm in the literature able to claim human competitive results in such a wide variety of packing domains
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