The polynomial robust knapsack problem

This paper introduces a new optimization problem, namely the Polynomial Robust Knapsack Problem. It generalises the Robust Knapsack formulation to encompass possible relations between subsets of items having every possible cardinality. This allows to better describe the utility function for the decision maker, at the price of increasing the complexity of the problem. Thus, in order to solve realistic instances in a reasonable amount of time, two heuristics are proposed. The first one applies machine learning techniques in order to quickly select the majority of the items, while the second makes use of genetic algorithms to solve the problem. A set of simulation examples is finally presented to show the effectiveness of the proposed approaches.