A Survey on Heuristics for the Two-Dimensional Rectangular Strip Packing Problem

Abstract

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.

Exact solutions for the 2d-strip packing problem using the positions-and-covering methodology

“…Other approaches that consider hierarchical or multi-stage methodologies can be found in the works of [ 48 – 50 ]. A survey of heuristics for the two-dimensional rectangular strip packing problem is presented in [ 51 ], and upper bounds for heuristic approaches in [ 52 ].…”

Solving the Problem of Packing Objects of Complex Geometric Shape into a Container of Arbitrary Dimension

“…), covering problems, modeling the microstructure of materials, active electronically scanned arrays generation and other relevant problems [1][2][3][4][5]. All the packing problems including the classic orthogonal packing problem are NP-hard [6,7] and require the use of heuristic [8,9] or metaheuristic optimization algorithms [10][11][12][13][14]. Therefore, it is important to develop effective algorithms that provide good layout of objects at an acceptable time.…”

Hierarchical Search-Embedded Hybrid Heuristic Algorithm for Two-Dimensional Strip Packing Problem

“…The two-dimensional strip packing problem (2DSPP), similar to the bin packing problem, is a classical combinatorial optimization problem, which attempts to arrange a given set of rectangles on a strip of finite width and infinite height without overlapping while minimizing the region waste of the strip. It has many real-world applications, such as cutting teel plates or paper rolls and cutting large boards of wood into smaller rectangular panels in the furniture industry [1], [2]. These practical problems are defined in order to minimize the material waste or maximize the use of material.…”

“…Oliveira et al [1] investigated the application of heuristic algorithm in 2DSPP. The results show that 40% of heuristic algorithms are fitness-based heuristics, which has become a research trend in this field, especially heuristic algorithms based on scoring rules.…”