Approximating Multiobjective Knapsack Problems
研究多目标背包问题，提出一种实用的完全多项式时间近似方案（FPTAS）用于一维情形，以及首个基于线性规划的多项式时间近似方案（PTAS）用于多维情形，帮助计算帕累托前沿的近似解集。
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.