A matheuristic framework for the Three-dimensional Single Large Object Placement Problem with practical constraints

Abstract

The Three-dimensional Single Large Object Placement Problem consists of a set of weakly heterogeneous items that must be placed inside a single larger object without overlapping each other. Many constraints can be considered depending on the practical specifications of the problem being solved, such as orientation, stability, weight limit and positioning. Although this is a well-known problem which has received considerable academic attention, most of the research limits itself to considering only three basic constraints: non-overlap, orientation and stability of the placed items. Recent literature concerning the problem has indicated that there is a pressing need for solution methods which consider a more realistic number of sets of practical constraints given that it is very uncommon to find real-world situations where only a few of these constraints are considered together. Therefore, this paper introduced a well-performing matheuristic framework which considers multiple practical constraints: orientation, load balance, loading priorities, positioning, stability, stacking and weight limit. An extension of the developed method considering multiple containers is also discussed. Results are compared against the state of the art from the literature and demonstrate the robustness of the proposed matheuristic with respect to different combinations of constraints.

A Multi-Heuristic Algorithm for Multi-Container 3-D Bin Packing Problem Optimization Using Real World Constraints

“…In order to generate loading patterns for the items a placement strategy needs to be developed. In the literature, placement strategies are classified into the following major types: horizontal layer building [11]- [13], [22], [27], [30]- [32], [36], [37], [40], [52]- [54], block building [7], [19], [21], [24], [33], [35], [54], [55], stack building [23], guillotine cutting [8], wall building [34], [56], [57] and cuboid building [15]. Different loading patterns will manage the usable packing volume in slightly different ways (prioritizing a certain packing orientation and direction over others, restricting the placement to specific areas, enforcing certain contact points between the packed items, etc.).…”

“…A hybrid strategy is reported in [24] where blocks are first created using the work described in [35] and then loaded into the container using an exact method. A similar approach is described in [19], however, instead of using an exact method for the placement of the blocks, a meta-heuristic framework using simulated annealing is considered. An approach with close affinity to block building consists of a three-step process whereby similar items are optimally packed into cartons, and cartons are then packed into crates, which are subsequently loaded into a container using a multi-search heuristic algorithm [7].…”

“…• HBMLS → Heuristic block-loading algorithm based on multi-layer search [54] • WGMA → Wall generation meta-heuristic algorithm [19] • CLTRS → Container loading by tree search algorithm [55] • VNS → Variable neighborhood search [68] • BSG-VCS → Beam search algorithm [69] • GRASP → Greedy random adaptive search [37] • HGA → Hybrid genetic algorithm [70] Their performance, in respect to average volume utilization, on the BR datasets is detailed in Table 7. Virtually all these algorithms are capable of using at least 90% of the available packing volume.…”

A Genetic Algorithm with Lower Neighborhood Search for the Three-Dimensional Multiorder Open-Size Rectangular Packing Problem

“…Researchers have explored integrating metaheuristics with exact solvers, giving rise to metaheuristics [18,19]. Metaheuristics combines the global exploration capabilities of metaheuristics with the local optimization power of exact solvers, demonstrating superior performance in routing [20,21], scheduling [22], and packing problems [23,24].…”

Last Mile Delivery Box Packing

“…learning articles are related to the bin packing problem[Hu et al (2017), Jiang, Cao and Zhang (2021)], and the single math-heuristic was applied to the container loading problem [daSilva et al (2020)]. …”