A reduction dynamic programming algorithm for the bi-objective integer knapsack problem

作者：Rong Aiying^*; Figueira Jose Rui

来源：European Journal of Operational Research, 2013, 231(2): 299-313.

DOI：10.1016/j.ejor.2013.05.045

• Multi-objective programming
• Integer knapsack problem
• Dynamic programming
• Dominance relation
• Core concept
• State reduction

This paper presents a backward state reduction dynamic programming algorithm for generating the exact Pareto frontier for the hi-objective integer knapsack problem. The algorithm is developed addressing a reduced problem built after applying variable fixing techniques based on the core concept. First, an approximate core is obtained by eliminating dominated items. Second, the items included in the approximate core are subject to the reduction of the upper bounds by applying a set of weighted-sum functions associated with the efficient extreme solutions of the linear relaxation of the multi-objective integer knapsack problem. Third, the items are classified according to the values of their upper bounds; items with zero upper bounds can be eliminated. Finally, the remaining items are used to form a mixed network with different upper bounds. The numerical results obtained from different types of bi-objective instances show the effectiveness of the mixed network and associated dynamic programming algorithm.

• 出版日期2013-12-1