A hybrid evolutionary approach to the quadratic knapsack problem

Abstract

The quadratic knapsack problem is an extension of the well known 0-1 knapsack problem. In the quadratic knapsack problem profit values are associated not only with individual objects as in the 0-1 knapsack problem, but also with pairs of objects. The profit value associated with a pair of objects is added to the overall profit if both objects of the pair belong to the knapsack. Being an extension of the 0-1 knapsack problem, this problem is also NP-Hard. In this paper we have proposed a hybrid evolutionary approach to the problem, combining a steady-state genetic algorithm with a greedy heuristic. We have compared our approach with two previously proposed generational genetic algorithms. On the problem instances considered, our hybrid approach obtained better quality solutions in shorter time. Copyright © 2007 IICAI.