A branch-and-bound algorithm for the two-dimensional vector packing problem
Computers and Operations Research
There is no asymptotic PTAS for two-dimensional vector packing
Information Processing Letters
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Discrete Applied Mathematics
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Computers and Intractability: A Guide to the Theory of NP-Completeness
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PPSN V Proceedings of the 5th International Conference on Parallel Problem Solving from Nature
A two-dimensional vector packing model for the efficient use of coil cassettes
Computers and Operations Research
EMO '09 Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization
PISA: a platform and programming language independent interface for search algorithms
EMO'03 Proceedings of the 2nd international conference on Evolutionary multi-criterion optimization
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EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
The min-conflict packing problem
Computers and Operations Research
Journal of Discrete Algorithms
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IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
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IEEE Transactions on Evolutionary Computation
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
Performance assessment of multiobjective optimizers: an analysis and review
IEEE Transactions on Evolutionary Computation
Operations Research Letters
Iterative approaches for solving a multi-objective 2-dimensional vector packing problem
Computers and Industrial Engineering
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In this paper, a multi-objective 2-dimensional vector packing problem is presented. It consists in packing a set of items, each having two sizes in two independent dimensions, say, a weight and a length into a finite number of bins, while concurrently optimizing three cost functions. The first objective is the minimization of the number of used bins. The second one is the minimization of the maximum length of a bin. The third objective consists in balancing the load overall the bins by minimizing the difference between the maximum length and the minimum length of a bin. Two population-based metaheuristics are performed to tackle this problem. These metaheuristics use different indirect encoding approaches in order to find good permutations of items which are then packed by a separate decoder routine whose parameters are embedded in the solution encoding. It leads to a self-adaptive metaheuristic where the parameters are adjusted during the search process. The performance of these strategies is assessed and compared against benchmarks inspired from the literature.