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

Mancini, S., Meloni, C., Ciavotta, M. (2022). A decomposition approach for multidimensional knapsacks with family-split penalties. INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH [10.1111/itor.13207].

A decomposition approach for multidimensional knapsacks with family-split penalties

Ciavotta M.
2022

Abstract

The optimization of Multidimensional Knapsacks with Family-Split Penalties has been introduced in the literature as a variant of the more classical Multidimensional Knapsack and Multi-Knapsack problems. This problem deals with a set of items partitioned in families, and when a single item is picked to maximize the utility, then all items in its family must be picked. Items from the same family can be assigned to different knapsacks, and in this situation split penalties are paid. This problem arises in real applications in various fields. This paper proposes a new exact and fast algorithm based on a specific Combinatorial Benders Cuts scheme. An extensive experimental campaign computationally shows the validity of the proposed method and its superior performance compared to both commercial solvers and state-of-the-art approaches. The paper also addresses algorithmic flexibility and scalability issues, investigates challenging cases, and analyzes the impact of problem parameters on the algorithm behavior. Moreover, it shows the applicability of the proposed approach to a wider class of realistic problems, including fixed costs related to each knapsack utilization. Finally, further possible research directions are considered.
Articolo in rivista - Articolo scientifico
benders cuts; decomposition methods; discrete optimization; integer programming; knapsack problems;
English
8-set-2022
2022
none
Mancini, S., Meloni, C., Ciavotta, M. (2022). A decomposition approach for multidimensional knapsacks with family-split penalties. INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH [10.1111/itor.13207].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/395682
Citazioni
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
Social impact