LP bounds in various constraint programming approaches for orthogonal packing

Authors:
M. Mesyagutov;G. Scheithauer;G. Belov
Affiliations:
Technische Universität Dresden, Institute of Numerical Mathematics, Germany;Technische Universität Dresden, Institute of Numerical Mathematics, Germany;Technische Universität Dresden, Institute of Numerical Mathematics, Germany
Venue:
Computers and Operations Research
Year:
2012

Citing 15
Cited 0

Exact algorithms for the guillotine strip cutting/packing problem

Computers and Operations Research
Dynamic Programming and Strong Bounds for the 0-1 Knapsack Problem

Management Science
An Exact Approach to the Strip-Packing Problem

INFORMS Journal on Computing
A Combinatorial Characterization of Higher-Dimensional Orthogonal Packing

Mathematics of Operations Research
New reduction procedures and lower bounds for the two-dimensional bin packing problem with fixed orientation

Computers and Operations Research
Using Decomposition Techniques and Constraint Programming for Solving the Two-Dimensional Bin-Packing Problem

INFORMS Journal on Computing
Principles of Constraint Programming

Principles of Constraint Programming
A new constraint programming approach for the orthogonal packing problem

Computers and Operations Research
A stabilized branch-and-price-and-cut algorithm for the multiple length cutting stock problem

Computers and Operations Research
Bin packing with items uniformly distributed over intervals [a,b]

SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Search Strategies for Rectangle Packing

CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Arc-flow model for the two-dimensional guillotine cutting stock problem

Computers and Operations Research
New filtering for the cumulative constraint in the context of non-overlapping rectangles

CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
A new graph-theoretical model for k-dimensional guillotine-cutting problems

WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Packing of one-dimensional bins with contiguous selection of identical items: An exact method of optimal solution

Automation and Remote Control

Quantified Score

Hi-index	0.01

Visualization

Abstract

We consider the 2D orthogonal feasibility problem (OPP-2) and the 2D strip packing problem (SPP-2). Given a set of rectangular items, the OPP-2 is to decide whether all items can be orthogonally packed into the given rectangular container; the SPP-2 is to find a packing of all items occupying the minimal height of the given semi-infinite strip. Both OPP-2 and SPP-2 are considered without items rotation. We investigate the known Constraint Programming (CP) approaches for OPP-2, in particular the dichotomy and disjunctive branching strategies and adapt 1D relaxation bounds based on linear programming (LP) into the constraint propagation process of the CP. Using the dichotomic search procedure the developed methods for OPP-2 are transformed for the case of SPP-2. Numerical results demonstrate the efficiency of the proposed strategies and of the combination of CP and LP-based pruning rules.