| 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. |
