Using Bound Sets in Multiobjective Optimization: Application to the Biobjective Binary Knapsack Problem

This paper is devoted to a study of the impact of using bound sets in biobjective optimization. This notion, introduced by Villareal and Karwan [19], has been independently revisited by Ehrgott and Gandibleux [9], as well as by Sourd and Spanjaard [17]. The idea behind it is very general, and can therefore be adapted to a wide range of biobjective combinatorial problem. We focus here on the biobjective binary knapsack problem. We show that using bound sets in a two-phases approach [18] based on biobjective dynamic programming yields numerical results that outperform previous ones, both in execution times and memory requirements.