A decomposition approach for multidimensional knapsacks with family?split penalties

The optimization of Multidimensional Knapsacks with Family-Split Penalties has been introduced in the literature as a variant more classical Knapsack and Multi-Knapsack problems. This problem deals set items partitioned families, when single item is picked to maximize utility, then all its family must be picked. Items from same can assigned different knapsacks, this situation split penalties are paid. arises real applications various fields. paper proposes new exact fast algorithm based on specific Combinatorial Benders Cuts scheme. An extensive experimental campaign computationally shows validity proposed method superior performance compared both commercial solvers state-of-the-art approaches. also addresses algorithmic flexibility scalability issues, investigates challenging cases, analyzes impact parameters behavior. Moreover, it applicability approach wider class realistic problems, including fixed costs related each knapsack utilization. Finally, further possible research directions considered.