Bin Packing

Extending Two-Dimensional Bin Packing Problem: Consideration of Priority for Items

In this paper a two-dimensional non-oriented guillotine bin packing problem is studied when items have different priorities. Our objective is to maximize the total profit which is total revenues minus costs of used bins and wasted area. A genetic algorithm is developed to solve this problem where a new coding scheme is introduced. To evaluate the performance of the proposed GA, first an upper b...

A Parallel Genetic Algorithm for Three Dimensional Bin Packing with Heterogeneous Bins

This paper presents a parallel genetic algorithm for three dimensional bin packing with heterogeneous bins using Hadoop Map-Reduce framework. The most common three dimensional bin packing problem which packs given set of boxes into minimum number of equal sized bins is proven to be NP Hard. The variation of three dimensional bin packing problem that allows heterogeneous bin sizes and rotation o...

Colorful Bin Packing

We study a variant of online bin packing, called colorful bin packing. In this problem, items that are presented one by one are to be packed into bins of size 1. Each item i has a size si ∈ [0, 1] and a color ci ∈ C, where C is a set of colors (that is not necessarily known in advance). The total size of items packed into a bin cannot exceed its size, thus an item i can always be packed into a ...

A Constraint for Bin Packing

We introduce a constraint for one-dimensional bin packing. This constraint uses propagation rules incorporating knapsack-based reasoning, as well as a lower bound on the number of bins needed. We show that this constraint can significantly reduce search on bin packing problems. We also demonstrate that when coupled with a standard bin packing search strategy, our constraint can be a competitive...

Bin-Completion Algorithms for Multicontainer Packing and Covering Problems

Bin-completion, a bin-oriented branch-and-bound approach, was recently shown to be promising for the bin packing problem. We propose several improvements to bin-completion that significantly improves search efficiency. We also show the generality of bin-completion for packing and covering problems involving multiple containers, and present bin-completion algorithms for the multiple knapsack, bi...

 Abstract: Packing rectangular shapes into a rectangular space is one of the most important discussions on Cutting & Packing problems (C;P) such as: cutting problem, bin-packing problem and distributor's pallet loading problem, etc. Assume a set of rectangular pieces with specific lengths, widths and utility values. Also assume a rectangular packing space with specific width and length. The obj...