An Artificial Bee Colony Algorithm for the Quadratic Knapsack Problem

Abstract

In this paper we have proposed a new hybrid approach combining artificial bee colony algorithm with a greedy heuristic and a local search for the quadratic knapsack problem. Quadratic knapsack problem belongs to traditional knapsack problem family and it is an extension of the well-known 0/1 knapsack problem. In this problem profits are also associated with pairs of objects along with individual objects. As this problem is an extension of the 0/1 knapsack problem, it is also $\mathcal{NP}$-Hard. Artificial bee colony algorithm is a new swarm intelligence technique inspired by foraging behavior of natural honey bee swarms. Performance of our algorithm on standard quadratic knapsack problem instances is compared with the other best heuristic techniques. Results obtained on these instances show that our hybrid artificial bee colony algorithm is superior to these techniques in many aspects.