A variant of the classical knapsack problem is considered in which each item associated with an integer weight and a qualitative level. We define dominance relation over feasible subsets given set show that this defines preorder. propose dynamic programming algorithm to compute entire non-dominated rank cardinality vectors we state two greedy algorithms, efficiently single efficient solution.

Suppose we are planning a hiking trip; and we are, therefore, interested in filling a knapsack with items that are considered necessary for the trip. There are N different item types that are deemed desirable; these could include bottle of water, apple, orange, sandwich, and so forth. Each item type has a given set of two attributes, namely a weight (or volume) and a value that quantifies the l...