2024/10/02 by Heßler, Katrin, Hintsch, Timo, Wienkamp, Lukas
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2410.01445
We investigate a real-life air cargo loading problem which is a variant of the three-dimensional Variable Size Bin Packing Problem with special bin forms of cuboid and non-cuboid unit load devices (ULDs). Packing is constrained by additional practical restrictions, such as load stability, (non-)stackable items, and weight distribution constraints. To solve the problem, we present an insertion heuristic embedded into a Randomized Greedy Search. The solution space is limited by only considering certain candidate points (so-called extreme points), which are promising positions to load an item. We extend the concept of extreme points proposed in the literature and allow moving extreme points for non-cuboid ULDs. A special sorting of the items is suggested, which combines a layered structure and free packing. Moreover, we propose dividing the space of each ULD into smaller cells to accelerate the collision, non-floating, and stackability check while loading items. In a computational study, we analyze individual algorithm components and show the effectiveness of our method on adapted real-life instances from the literature.