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Approximating Multiobjective Knapsack Problems
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DOI：10.1287/mnsc.48.12.1603.445.png)
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Abstract
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For multiobjective optimization problems, it is meaningful to compute a set of solutions covering all possible trade-offs between the different objectives. The multiobjective 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 nondominated feasible solutions, the Pareto frontier, are studied. For the multiobjective one-dimensional knapsack problem, a practical fully polynomial-time approximation scheme (FPTAS) 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 multiobjective m-dimensional knapsack problem, the first known polynomial-time approximation scheme (PTAS), based on linear programming, is presented.
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