Abstract
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.
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Erlebach, T., Kellerer, H., Pferschy, U. (2001). Approximating Multi-objective Knapsack Problems. In: Dehne, F., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 2001. Lecture Notes in Computer Science, vol 2125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44634-6_20
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DOI: https://doi.org/10.1007/3-540-44634-6_20
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