Two-dimensional packing problems: A survey

Lodi, Andrea; Martello, Silvano; Monaci, Michele

doi:10.1016/s0377-2217(02)00123-6

Cited by 694 publications

(368 citation statements)

References 32 publications

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“…The first data-set is described in [8] and consists of 5 classes of instances: BENG (10 instances), CGCUT (3 instances), GCUT (4 instances), HT (9 instances) and NGCUT (12 instances). The second data-set is described in [9] and consists of 500 instances, divided into 10 classes of 50 instances, named MV and BW.…”

Section: Computational Resultsmentioning

confidence: 99%

“…This is correct because empty bins do not give any contribution to defining an OOEBPP solution. The effect of this simplification is that y variables disappear (they are all equal to 1) and constraints (8) are now rewritten as inequalities:…”

Section: A Set Covering Formulationmentioning

confidence: 99%

“…The first one is an adaptation of the well-known Best-Fit Decreasing-Height (BFDH) approximation algorithm [8], which we indicate as Best-Fit DecreasingTime (BFDT). The items are iteratively considered from item N down to item 1 and at each iteration the current item is packed into the bin with the minimum residual capacity among those which can accommodate it; if no bin can receive the item, a new bin is initialized.…”

Section: Primal Boundsmentioning

confidence: 99%

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An Optimization Algorithm for the Ordered Open-End Bin-Packing Problem

Ceselli

Righini

2008

Operations Research

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The ordered open-end bin packing problem is a variant of the bin packing problem in which the items to be packed are sorted in a given order and the capacity of each bin can be exceeded by the last item packed into the bin. We present a branch-and-price algorithm for its exact optimization. The pricing subproblem is a special variant of the binary knapsack problem, in which the items are ordered and the last one does not consume capacity. We present a specialized optimization algorithm for this subproblem. The speed of the column generation algorithm is improved by subgradient optimization steps, allowing for multiple pricing and variable fixing. Computational results are presented on instances of different size and items with different correlations between their size and their position in the given order.

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Section: Computational Resultsmentioning

confidence: 99%

Section: A Set Covering Formulationmentioning

confidence: 99%

Section: Primal Boundsmentioning

confidence: 99%

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An Optimization Algorithm for the Ordered Open-End Bin-Packing Problem

Ceselli

Righini

2008

Operations Research

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“…In the two-dimensional strip packing problem (abbreviated 2SP), a set of axis-aligned rectangles of specified dimensions must be packed, without rotation, into a rectangular strip of fixed width, with the goal of minimizing the height of the strip. The 2SP problem is very well-studied [14], and generalizes the bin packing problem, which is equivalent to the case in which all rectangles have unit height. The current best approximation algorithm for 2SP has an approximation factor of 5/3 + ε for any ε > 0 [9], and was achieved after a long sequence of successive improvements [1,16,17,19].…”

Section: Introductionmentioning

confidence: 99%

Smart-Grid Electricity Allocation via Strip Packing with Slicing

Alamdari

Biedl

Chan

et al. 2013

Lecture Notes in Computer Science

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Abstract. One advantage of smart grids is that they can reduce the peak load by distributing electricity-demands over multiple short intervals. Finding a schedule that minimizes the peak load corresponds to a variant of a strip packing problem. Normally, for strip packing problems, a given set of axis-aligned rectangles must be packed into a fixed-width strip, and the goal is to minimize the height of the strip. The electricityallocation application can be modelled as strip packing with slicing: each rectangle may be cut vertically into multiple slices and the slices may be packed into the strip as individual pieces. The stacking constraint forbids solutions in which a vertical line intersects two slices of the same rectangle. We give a fully polynomial time approximation scheme for this problem, as well as a practical polynomial time algorithm that slices each rectangle at most once and yields a solution of height at most 5/3 times the optimal height.

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“…A review of the methods used can be found, for example, in Dyckhoff (1990), Hässler and Sweeney (1991), Sweeney and Paternoster (1992), Dowsland and Dowsland (1992), and Lodi et al (2002).…”

Section: Introductionmentioning

confidence: 99%

A hybrid evolutionary algorithm for the two-dimensional packing problem

Kierkosz

Łuczak

2013

Cent Eur J Oper Res

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This paper presents a hybrid evolutionary algorithm for the two-dimensional non-guillotine packing problem. The problem consists of packing many rectangular pieces into a single rectangular sheet in order to maximize the total area of the pieces packed. Moreover, there is a constraint on the maximum number of times that a piece may be used in a packing pattern. The set of packing patterns is processed by an evolutionary algorithm. Three mutation operators and two types of quality functions are used in the algorithm. The best solution obtained by the evolutionary algorithm is used as the initial solution in a tree search improvement procedure. This approach is tested on a set of benchmark problems taken from the literature and compared with the results published by other authors.

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Two-dimensional packing problems: A survey

Cited by 694 publications

References 32 publications

An Optimization Algorithm for the Ordered Open-End Bin-Packing Problem

An Optimization Algorithm for the Ordered Open-End Bin-Packing Problem

Smart-Grid Electricity Allocation via Strip Packing with Slicing

A hybrid evolutionary algorithm for the two-dimensional packing problem

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