Abstract
Two-dimensional rectangular strip packing problems belong to the broader class of Cutting and Packing (C&P) problems, in which small items are required to be cut from or packed on a larger object, so that the waste (unused regions of the large object) is minimized. C&P problems differ from other combinatorial optimization problems by the intrinsic geometric constraints: items may not overlap and have to be fully contained in the large object. This survey approaches the specific C&P problem in which all items are rectangles, therefore fully characterized by a width and a height, and the large object is a strip, i.e. a rectangle with a fixed width but an infinite height, being the problem's goal to place all rectangles on the strip so that the height is minimized. These problems have been intensively and extensively tackled in the literature and this paper will focus on heuristic resolution methods. Both the seminal and the most recent approaches (from the last decade) will be reviewed, in a rather tutorial flavor, and classified according to their type: constructive heuristics, improvement heuristics with search over sequences and improvement heuristics with search over layouts. Building on this review, research gaps are identified and the most interesting research directions pointed out.
Highlights
The Strip Packing Problem (SPP) aims to pack a set of small items inside a larger object, the container, with all dimensions but one fixed, with the objective of minimizing the free dimension of the large object
The small items cannot overlap each other and must be completely inside the large object. This description fits the definition of a Cutting and Packing (C&P) problem and the SPP can be classified as an Open Dimension Problem according to Wascher et al (2007) typology for C&P problems
Heuristics for the SPP that search over sequences resort to modification operators that are common to other problems that rely on sequences to codify their solutions: the insert and the exchange or swap operators
Summary
The Strip Packing Problem (SPP) aims to pack a set of small items inside a larger object, the container, with all dimensions but one fixed, with the objective of minimizing the free dimension of the large object. Conjugating the rectangular shape of the problem with the open dimension characteristic, the large object will be a rectangle with a given width and an infinite height (hereafter called strip), and the objective of the problem is to minimize the actual height used to pack all small items. Riff et al (2009) review both exact and heuristic methods for the two-dimensional SPP and present some benchmark instances commonly used in the literature in the computational validation of algorithms for specific instances This survey will update the previous reviews but will provide a classification of both constructive and improvement heuristics, looking at characteristics they may have in common.
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