Lower bounds and reduction procedures for the bin packing problem
Discrete Applied Mathematics - Combinatorial Optimization
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
BISON: a fast hybrid procedure for exactly solving the one-dimensional bin packing problem
Computers and Operations Research
Heuristic Solution of Open Bin Packing Problems
Journal of Heuristics
A Hybrid Improvement Heuristic for the One-Dimensional Bin Packing Problem
Journal of Heuristics
Search Strategies for Rectangle Packing
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
A Geometric Constraint over k-Dimensional Objects and Shapes Subject to Business Rules
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
From approximate to optimal solutions: constructing pruning and propagation rules
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
An improved algorithm for optimal bin packing
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Propagating the bin packing constraint using linear programming
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
CPAIOR'11 Proceedings of the 8th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Bin repacking scheduling in virtualized datacenters
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Consistency check for the bin packing constraint revisited
CPAIOR'10 Proceedings of the 7th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
A SAT encoding for multi-dimensional packing problems
CPAIOR'10 Proceedings of the 7th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
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Bin packing is a ubiquitous problem that arises in many practical applications. The motivation for the work presented here comes from the domain of data centre optimisation. In this paper we present a parameterisable benchmark generator for bin packing instances based on the well-known Weibull distribution. Using the shape and scale parameters of this distribution we can generate benchmarks that contain a variety of item size distributions. We show that real-world bin packing benchmarks can be modelled extremely well using our approach. We also study both systematic and heuristic bin packing methods under a variety of Weibull settings. We observe that for all bin capacities, the number of bins required in an optimal solution increases as the Weibull shape parameter increases. However, for each bin capacity, there is a range of Weibull shape settings, corresponding to different item size distributions, for which bin packing is hard for a CP-based method.