J Optim Theory Appl manuscript No. (will be inserted by the editor) Complexity Results and Exact Algorithms for Robust Knapsack Problems

Abstract This paper studies the robust knapsack problem, for which solutions are, up to a certain point, immune from data uncertainty. We complement the works found in the litera-ture, where uncertainty affects only the profits or only the weights of the items, by studying the complexity and approximation of the general setting with uncertainty regarding both the profits and the weights, for three different objective functions. Furthermore, we develop a scenario-relaxation algorithm for solving the general problem and present computational results. Keywords knapsack problem · robustness · scenario-relaxation algorithm · NP-hardness · approximatio