The quadratic knapsack problem

The quadratic knapsack problem is a relevant N P -hard combinatorial optimization problem, inspired, since the Seventies, by a number of real-world applications. After its formal definition in 1980, it was subject to intensive research, especially in the last two decades. No recent review on this problem appeared in the literature after a well-known survey, published in 2007 but updated to 2003. The purpose of this work is to provide a thorough overview of classical and recent results on the quadratic knapsack problem. We examine mathematical models, linearizations and reformulations. We review upper bounds, exact algorithms, heuristic and metaheuristic approaches, and provide a comparison of their computational performance. • Linearizations. • Upper bounds. • Exact algorithms. • Approximation algorithms and Heuristics. • Computational results.