| Abstract: |
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 singleobjective 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. |
