Optimal bin covering with items of random size
SIAM Journal on Computing
Probabilistic analysis of a heuristics for the dual bin packing problem
Information Processing Letters
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Probabilistic analysis of algorithms for dual bin packing problems
Journal of Algorithms
BISON: a fast hybrid procedure for exactly solving the one-dimensional bin packing problem
Computers and Operations Research
A PTAS for the Multiple Subset Sum Problem with different knapsack capacities
Information Processing Letters
Better approximation algorithms for bin covering
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Artificial Intelligence - special issue on computational tradeoffs under bounded resources
The Multiple Subset Sum Problem
SIAM Journal on Optimization
Electronic Commerce Research
A 3/4-Approximation Algorithm for Multiple Subset Sum
Journal of Heuristics
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Global Cut Framework for Removing Symmetries
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
A new algorithm for optimal bin packing
Eighteenth national conference on Artificial intelligence
An improved algorithm for optimal bin packing
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
An exact algorithm for the dual bin packing problem
Operations Research Letters
Combining multiple representations in a genetic algorithm for the multiple Knapsack problem
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
Integrating symmetry, dominance, and bound-and-bound in a multiple knapsack solver
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
A memetic immunological algorithm for resource allocation problem
ICARIS'11 Proceedings of the 10th international conference on Artificial immune systems
Automatically exploiting subproblem equivalence in constraint programming
CPAIOR'10 Proceedings of the 7th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Algorithms for scheduling of chemotherapy plans
Computers in Biology and Medicine
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Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in multi-agent systems and distributed systms, and can also be found as subproblems of scheduling problems. We propose bin completion, a branch-and-bound strategy for one-dimensional, multicontainer packing problems. Bin completion combines a bin-oriented search space with a powerful dominance criterion that enables us to prune much of the space. The performance of the basic bin completion framework can be enhanced by using a number of extensions, including nogood-based pruning techniques that allow further exploitation of the dominance criterion. Bin completion is applied to four problems: multiple knapsack, bin covering, min-cost covering, and bin packing. We show that our bin completion algorithms yield new, state-of-the-art results for the multiple knapsack, bin covering, and min-cost covering problems, outperforming previous algorithms by several orders of magnitude with respect to runtime on some classes of hard, random problem instances. For the bin packing problem, we demonstrate significant improvements compared to most previous results, but show that bin completion is not competitive with current state-of-the-art cutting-stock based approaches.