Approximating Multiobjective Knapsack Problems

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.

• 저널Management Science · 48(12) · 1603–1612
• 토픽Advanced Multi-Objective Optimization Algorithms · Computational Theory and Mathematics
• DOI10.1287/mnsc.48.12.1603.445
• 저자Thomas Erlebach, Hans Kellerer, Ulrich Pferschy