Matheuristics for the irregular bin packing problem with free rotations

Abstract

We present a number of variants of a constructive algorithm able to solve a wide variety of variants of the Two-Dimensional Irregular Bin Packing Problem (2DIBPP). The aim of the 2DIBPP is to pack a set of irregular pieces, which may have concavities, into stock sheets (bins) with fixed dimensions in such a way that the utilization is maximized. This problem is inspired by a real application from a ceramic company in Spain. In addition, this problem arises in other industries such as the garment industry or ship building. The constructive procedure presented in this paper allows both free orientation for the pieces, as in the case of the ceramic industry, or a finite set of orientations as in the case of the garment industry. We explicitly model the assignment of pieces to bins and compare with the more common strategy of packing bins sequentially. There are very few papers in the literature that address the bin packing problem with irregular pieces and to our knowledge this is the first to additionally consider free rotation of pieces with bin packing. We propose several Integer Programming models to determine the association between pieces and bins and then we use a Mixed Integer Programming model for placing the pieces into the bins. The computational results show that the algorithm obtains high quality results in sets of instances with different properties. We have used both industry data and the available data in the literature of 2D irregular strip packing and bin packing problems.

Jostle heuristics for the 2D-irregular shapes bin packing problems with free rotation

“…In this case we compare our results with the work of Lopez-Camacho et al (2013a) and Martinez-Sykora et al (2017). Since these algorithms are run on different computing platforms, it is not possible to run for the same amount of time.…”

Efficient Local Search Heuristics for Packing Irregular Shapes in Two-Dimensional Heterogeneous Bins

“…Instead of placing pieces into bins the aim is to place all the pieces into a strip with fixed width and infinite length in such a way the total required length is minimized. However, recent publications of packing algorithms for irregular pieces consider the bin packing problem with homogeneous bins, see [14], [20], [16] and [1]. However, in many situations bins are readily available to purchase as rectangular sheets in different standard sizes.…”

“…Han et al [13] and Martinez-Sykora et al [15] considered free rotation for the 2D irregular bin packing problem with guillotine cuts, solving an application derived from the glass industry. More recently, Martinez-Sykora et al [16] and Abeysooriya et al [1] considered free rotation for the problem with homogeneous bins and also report results with restricted and fixed rotations. For comparison purposes, we also address the problem where a finite set of rotations are allowed.…”

Resolução de problemas de empacotamento de itens irregulares usando técnicas de programação não-linear

“…Adicionalmente, encontramos na recente literatura dois trabalhos em que são apresentadas math-heurísticas. (CHERRI; CARRAVILLA; TOLEDO, 2016; MARTINEZ-SYKORA et al, 2017). Também, diferentes modelos de programação não-linear (CHERNOV; STOYAN; ROMANOVA, 2010; JONES, 2013; ROCHA et al, 2015; STOYAN; PANKRATOV; ROMANOVA, 2016) têm sido propostos.…”

“…Porém, encontramos uma math-heurística (MARTINEZ-SYKORA et al, 2017) e uma heurística (ABEYSOORIYA; BENNELL; MARTINEZ-SYKORA, 2018) que podem considerar qualquer ângulo de rotação. Em (MARTINEZ-SYKORA et al, 2017), um modelo de Programação Linear Inteira Mista (PLIM) é executado várias vezes, uma para cada orientação que se queira considerar. Em (ABEYSOORIYA; BENNELL; MARTINEZ-SYKORA, 2018), um subconjunto de possíveis rotações é avaliado; para a escolha deste subconjunto é elaborado um mecanismo que identifica ângulos promissores de acordo com o arranjo dos itens em cada solução parcial.…”