A hybrid metaheuristic for the Knapsack Problem with Forfeits

In this paper, we present a novel hybrid metaheuristic for the Knapsack Problem with Forfeits (KPF). KPF is a recently introduced generalization of the Knapsack Problem. In this variant, a penalty cost incurs whenever both items composing a so-called forfeit pair belong to the solution. Our proposed algorithm, called GA–CG Forfeits, combines the strengths of the Genetic and Carousel Greedy paradigms. In this work, we define the algorithm and compare it with two previously proposed heuristics on a set of benchmark instances. In these tests, GA–CG Forfeits provided significantly better solutions than the other two algorithms on all instances.