DeepAI AI Chat
Log In Sign Up

A Primal Decomposition Algorithm for the Two-dimensional Bin Packing Problem

09/15/2019
by   Jean-François Côté, et al.
Université Laval
Qatar University
University of Modena and Reggio Emilia
0

The Two-dimensional Bin Packing Problem calls for packing a set of rectangular items into a minimal set of larger rectangular bins. Items must be packed with their edges parallel to the borders of the bins, cannot be rotated and cannot overlap among them. The problem is of interest because it models many real-world applications, including production, warehouse management and transportation. It is, unfortunately, very difficult, and instances with just 40 items are unsolved to proven optimality, despite many attempts, since the 1990s. In this paper, we solve the problem with a combinatorial Benders decomposition that is based on a simple model in which the two-dimensional items and bins are just represented by their areas, and infeasible packings are imposed by means of exponentially-many no-good cuts. The basic decomposition scheme is quite naive, but we enrich it with a number of preprocessing techniques, valid inequalities, lower bounding methods, and enhanced algorithms to produce the strongest possible cuts. The resulting algorithm behaved very well on the benchmark sets of instances, improving on average upon previous algorithms from the literature and solving for the first time a number of open instances.

READ FULL TEXT

page 1

page 2

page 3

page 4

10/10/2012

Comparing several heuristics for a packing problem

Packing problems are in general NP-hard, even for simple cases. Since no...
07/30/2020

An Asymptotic Lower Bound for Online Vector Bin Packing

We consider the online vector bin packing problem where n items specifie...
03/01/2023

Hybrid Approach for Solving Real-World Bin Packing Problem Instances Using Quantum Annealers

Efficient packing of items into bins is a common daily task. Known as Bi...
07/16/2020

A Faster Exponential Time Algorithm for Bin Packing With a Constant Number of Bins via Additive Combinatorics

In the Bin Packing problem one is given n items with weights w_1,…,w_n a...
11/22/2020

Harmonic Algorithms for Packing d-dimensional Cuboids Into Bins

We explore approximation algorithms for the d-dimensional geometric bin ...
11/30/2018

Binary Decision Diagrams for Bin Packing with Minimum Color Fragmentation

Bin Packing with Minimum Color Fragmentation (BPMCF) is an extension of ...
06/30/2022

A Constructive Heuristic Algorithm for 3D Bin Packing of Irregular Shaped Items

The three-dimensional bin packing problem (3D-BPP) plays an important ro...