Branch-and-bound placement for building block layout
DAC '91 Proceedings of the 28th ACM/IEEE Design Automation Conference
Exact Solution of the Two-Dimensional Finite Bon Packing Problem
Management Science
Software—Practice & Experience - Special issue on discrete algorithm engineering
Exact Algorithms for Large-Scale Unconstrained Two and Three Staged Cutting Problems
Computational Optimization and Applications
A lower bound for the non-oriented two-dimensional bin packing problem
Discrete Applied Mathematics - Special issue: Third ALIO-EURO meeting on applied combinatorial optimization
A Framework for Constraint Programming Based Column Generation
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
Hybrid Benders Decomposition Algorithms in Constraint Logic Programming
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Branch and Infer: a Unifying Framework for Integer and Finite Domain Constraint Programming
INFORMS Journal on Computing
Heuristic and Metaheuristic Approaches for a Class of Two-Dimensional Bin Packing Problems
INFORMS Journal on Computing
Recent advances on two-dimensional bin packing problems
Discrete Applied Mathematics
Guided Local Search for the Three-Dimensional Bin-Packing Problem
INFORMS Journal on Computing
Algorithm 864: General and robot-packable variants of the three-dimensional bin packing problem
ACM Transactions on Mathematical Software (TOMS)
Principles of Constraint Programming
Principles of Constraint Programming
A Set-Covering-Based Heuristic Approach for Bin-Packing Problems
INFORMS Journal on Computing
An Exact Algorithm for Higher-Dimensional Orthogonal Packing
Operations Research
The two-dimensional bin packing problem with variable bin sizes and costs
Discrete Optimization
On the two-dimensional Knapsack Problem
Operations Research Letters
Heuristic approaches for the two- and three-dimensional knapsack packing problem
Computers and Operations Research
SearchCol: metaheuristic search by column generation
HM'10 Proceedings of the 7th international conference on Hybrid metaheuristics
Local branching-based algorithms for the disjunctively constrained knapsack problem
Computers and Industrial Engineering
Exact algorithms for the two-dimensional guillotine knapsack
Computers and Operations Research
Tree-decomposition based heuristics for the two-dimensional bin packing problem with conflicts
Computers and Operations Research
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
LP bounds in various constraint programming approaches for orthogonal packing
Computers and Operations Research
Bidimensional packing by bilinear programming
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Solving the two-dimensional bin packing problem with a probabilistic multi-start heuristic
LION'05 Proceedings of the 5th international conference on Learning and Intelligent Optimization
Consecutive Ones Matrices for Multi-dimensional Orthogonal Packing Problems
Journal of Mathematical Modelling and Algorithms
A new exact method for the two-dimensional bin-packing problem with fixed orientation
Operations Research Letters
INFORMS Journal on Computing
Learning to place new objects in a scene
International Journal of Robotics Research
Conservative scales in packing problems
OR Spectrum
Models for the two-dimensional two-stage cutting stock problem with multiple stock size
Computers and Operations Research
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The two-dimensional bin-packing problem is the problem of orthogonally packing a given set of rectangles into a minimum number of two-dimensional rectangular bins. The problem is NP-hard and very difficult to solve in practice as no good mixed integer programming (MIP) formulation has been found for the packing problem. We propose an algorithm based on the well-known Dantzig-Wolfe decomposition where the master problem deals with the production constraints on the rectangles while the subproblem deals with the packing of rectangles into a single bin. The latter problem is solved as a constraint-satisfaction problem (CSP), which makes it possible to formulate a number of additional constraints that may be difficult to formulate as MIP models. This includes guillotine-cutting requirements, relative positions, fixed positions and irregular bins. The CSP approach uses forward propagation to prune inferior arrangements of rectangles. Unsuccessful attempts to pack rectangles into a bin are brought back to the master model as valid inequalities. Hence, CSP is used not only to solve the pricing problem but also to generate valid inequalities in a branch-and-cut system. Using delayed column-generation, we obtain lower bounds of very good quality in reasonable time. In all instances considered, we obtain similar or better bounds than previously published. Several instances with up to n = 100 rectangles are solved to optimality through the developed branch-and-price-and-cut algorithm.