Extreme Point-Based Heuristics for Three-Dimensional Bin Packing

Abstract

One of the main issues in addressing three-dimensional packing problems is finding an efficient and accurate definition of the points where to place the items inside the bins. The performance of exact and heuristic methods is actually strongly influenced by the choice of a placement rule. We introduce the Extreme Point concept and present a new Extreme Point-based rule for packing items inside a three dimensional container. The Extreme Point rule is independent from the particular packing problem addressed and can handle additional constraints, such as fixing the position of the items. The new Extreme Point rule is also used to derive new constructive heuristics for the Three-Dimensional Bin Packing problem. Extensive computational results show the effectiveness of the new heuristics compared to state-of-the-art results. Moreover, the same heuristics, when applied to the Two-Dimensional Bin Packing problem, outperforms those specifically designed for the problem.

Development of Optimization Software to Solve Practical Packing and Cutting Problems

“…Unification of the class library allowing to use it to solve a variety of packing problems, is achieved by using of a common scheme for coding solutions as well as by using of universal packing representation model (the node model) for description of resulting placements [12][13][14]. In this case a position of each placed into a container object is described only with one point that called by node.…”

Una revisión literaria del Problema de Carga del Pallet

“…Thus, the whole quantity of items must be packed in as few bins as possible. This problem can be bidimensional (2D) and three-dimensional (3D) [27].…”

An ACO Algorithm for the 3D Bin Packing Problem in the Steel Industry

“…the bins and boxes are available at a certain date. C&P problems have been addressed by searching heuristics such as tabusearch [1,5], ACO [8] or branch-and-bound techniques [9], by simpler heuristics [4,10] or by mixed integer programming methods using column-approach [11]. However, the last ones are often applied to simpler cases, i.e.…”

“…The extreme points heuristic (EP) is used for boxes positioning inside the bin, once it is used successfully in this type of problems [5]. In an empty bin only one extreme point exists to pack the boxes in (0, 0, 0) position.…”