The {0,1}-knapsack problem with qualitative levels
This work addresses a theoretical optimization problem, likely incremental as it builds on the classical knapsack problem with new qualitative constraints.
The paper tackles a variant of the knapsack problem with qualitative levels by defining a dominance relation and proposing algorithms, including dynamic programming to compute non-dominated rank cardinality vectors and greedy methods for efficient solutions.
A variant of the classical knapsack problem is considered in which each item is associated with an integer weight and a qualitative level. We define a dominance relation over the feasible subsets of the given item set and show that this relation defines a preorder. We propose a dynamic programming algorithm to compute the entire set of non-dominated rank cardinality vectors and we state two greedy algorithms, which efficiently compute a single efficient solution.