About Casting 2D-Bin Packing into Network Flow Theory
نویسندگان
چکیده
In this paper, we aim at making appear the way Flow and Multicommodity Flow Theory may be used in order to deal with combinatorial geometry problems like the 2D-Bin Packing problem. In order to do it, we introduce a notion of no circuit double flow, we state a Reformulation Theorem which ties some multicommodity flow model with a given bin-packing problem, and we provide an algorithm whose purpose is to study the way one may deal with the no circuit constraint which is at the core of our multicommodity flow.
منابع مشابه
A Scanline-based Algorithm for the 2d Free-form Bin Packing Problem
This paper describes a heuristic algorithm for the two-dimensional free-form bin packing (2DFBP) problem, which is also called the irregular cutting and packing, or nesting problem. Given a set of 2D free-form bins, which in practice may be plate materials, and a set of 2D free-form items, which in practice may be plate parts to be cut out of the materials, the 2D-FBP problem is to lay out item...
متن کاملProblem Generators for Rectangular packing problems
In order to verify and test the performance of new packing algorithms relative to existing algorithms, test problems are needed. The scope of published test instances for 2D rectangular and irregular packing has been fairly limited in terms of object size, number and dimension of items. A systematic investigation into the performance of new algorithms requires the use of a range of test problem...
متن کاملOn solving multiobjective bin packing problems using evolutionary particle swarm optimization
The bin packing problem is widely found in applications such as loading of tractor trailer trucks, cargo airplanes and ships, where a balanced load provides better fuel efficiency and safer ride. In these applications, there are often conflicting criteria to be satisfied, i.e., to minimize the bins used and to balance the load of each bin, subject to a number of practical constraints. Unlike ex...
متن کاملExtending 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...
متن کاملMultiple-choice Vector Bin Packing: Arc-flow Formulation with Graph Compression
The vector bin packing problem (VBP) is a generalization of bin packing with multiple constraints. In this problem we are required to pack items, represented by p-dimensional vectors, into as few bins as possible. The multiple-choice vector bin packing (MVBP) is a variant of the VBP in which bins have several types and items have several incarnations. We present an exact method, based on an arc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010