Abstract
Two packing problems are considered in this paper, namely the well-known strip packing problem (SPP) and the variable-sized bin packing problem (VSBPP). A total of 252 strip packing heuristics (and variations thereof) from the literature, as well as novel heuristics proposed by the authors, are compared statistically by means of 1170 SPP benchmark instances in order to identify the best heuristics in various classes. A combination of new heuristics with a new sorting method yields the best results. These heuristics are combined with a previous heuristic for the VSBPP by the authors to find good feasible solutions to 1357 VSBPP benchmark instances. This is the largest statistical comparison of algorithms for the SPP and the VSBPP to the best knowledge of the authors.
Highlights
While cutting and packing (C&P) problems have been studied for many years, e.g. the packing of animals, seafaring vessel, trains and vehicles, these problems have only become an active field of mathematical study since the 1939 landmark paper by Kantorovich [47] and papers by other early researchers in the mid-twentieth century, including those of Eisemann [25] in 1957 and Gilmore and Gomory [32,33,34] in the 1960s
A packing list sorted according to decreasing height may result in a packing that is sparse below a single wide item
The BFDHDW algorithm yields the lowest mean rank, but the results obtained via the B2FA10DHDW algorithm are not significantly different according to the Nemenyi test
Summary
While cutting and packing (C&P) problems have been studied for many years, e.g. the packing of animals, seafaring vessel, trains and vehicles, these problems have only become an active field of mathematical study since the 1939 landmark paper by Kantorovich [47] and papers by other early researchers in the mid-twentieth century, including those of Eisemann [25] in 1957 and Gilmore and Gomory [32,33,34] in the 1960s. The first heuristic for the 2D VSBPP was proposed by Ortmann et al [59], and is a combination of strip packing algorithms, namely the hybrid approach to bin packing by Chung et al [16] and the repacking strategy by Friesen and Langston [30]. While this approach may have been the first heuristic for the problem, Hopper and Turton [40,41] used the bottom-left fill (BLF) algorithm [13] in combination with a number of metaheuristics to find solutions to the 2D RF VSBPP, Pisinger and Sigurd [60] proposed a branch-and-price algorithm to find exact solutions to the 2D VSBPP with variable bin costs, and Yanasse et al [70] used a pattern-generation algorithm to find solutions to the related 2D multiple stock size stock cutting problem.
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