An effective dynamic programming algorithm for the minimum-cost maximal knapsack packing problem

作者：Furini Fabio; Ljubic Ivana^*; Sinnl Markus

来源：European Journal of Operational Research, 2017, 262(2): 438-448.

DOI：10.1016/j.ejor.2017.03.061

• Combinatorial optimization
• Maximal knapsack packing
• Minimal knapsack cover
• Dynamic programming
• Integer programming

Given a set of items with profits and weights and a knapsack capacity, we study the problem of finding a maximal knapsack packing that minimizes the profit of the selected items. We propose an effective dynamic programming (DP) algorithm which has a pseudo-polynomial time complexity. We demonstrate the equivalence between this problem and the problem of finding a minimal knapsack cover that maximizes the profit of the selected items. In an extensive computational study on a large and diverse set of benchmark instances, we demonstrate that the new DP algorithm outperforms a state-of-the-art commercial mixed-integer programming (MIP) solver applied to the two best performing MIP models from the literature.

• 出版日期2017-10-16