An Efficient Algorithm for the Knapsack Sharing Problem

The Knapsack Sharing Problem (KSP) is an NP-Hard combinatorial optimization problem, admitted in numerous real world applications. In the KSP, we have a knapsack of capacity c and a set of n objects, namely N , where each object j, j = 1, . . . , n, is associated with a profit p j and a weight w j . The set of objects N is composed of m different classes of objects Ji , i = 1, . . . , m, and N = ⋃m i=1 Ji . The aim is to determine a subset of objects to be included in the knapsack that realizes a max-min value over all classes. In this article, we solve the KSP using an approximate solution method based upon tabu search. First, we describe a simple local search in which a depth parameter and a tabu list are used. Next, we enhance the algorithm by introducing some intensifying and diversifying strategies. The two versions of the algorithm yield satisfactory results within reasonable computational time. Extensive computational testing on problem instances taken from the literature shows the effectiveness of the proposed approach.