Fast approximation schemes for multi-criteria combinatorial optimization
Fast approximation schemes for multi-criteria combinatorial optimization
Dynamic programming revisited: improving knapsack algorithms
Computing - Special issue on combinatorial optimization
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Multicriteria Optimization
Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach
IEEE Transactions on Evolutionary Computation
Committee selection with a weight constraint based on a pairwise dominance relation
ADT'11 Proceedings of the Second international conference on Algorithmic decision theory
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For multi-objective optimization problems, it is meaningful to compute a set of solutions covering all possible trade-offs between the different objectives. The multi-objective knapsack problem is a generalization of the classical knapsack problem in which each item has several profit values. For this problem, efficient algorithms for computing a provably good approximation to the set of all non-dominated feasible solutions, the Pareto frontier, are studied. For the multi-objective 1-dimensional knapsack problem, a fast fully polynomial-time approximation scheme is derived. It is based on a new approach to the single-objective knapsack problem using a partition of the profit space into intervals of exponentially increasing length. For the multi-objective m-dimensional knapsack problem, the first known polynomial-time approximation scheme, based on linear programming, is presented.