Algorithms and complexity results for the 0-1 knapsack problem with group fairness

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• dc.contributor.author Malaguti, Enrico
• dc.contributor.author Paronuzzi, Paolo
• dc.contributor.author Santini, Alberto
• dc.date.accessioned 2025-10-24T16:54:29Z
• dc.date.available 2025-10-24T16:54:29Z
• dc.date.issued 2025
• dc.date.updated 2025-10-24T16:54:29Z
• dc.description Data de publicació electrònica: 10-09-2025
• dc.description.abstract This paper presents an exact algorithm for a generalisation of the classical 0-1 Knapsack Problem, called the Knapsack Problem with Group Fairness. In this problem, items are partitioned into classes, and fairness constraints affect the number of items that can or must be chosen from each class. The problem was introduced by Patel et al. (in: Dignum (eds) Proceedings of the 20th International Conference on Autonomous Agents and MultiAgent Systems. International Foundation for Autonomous Agents and Multiagent Systems, 2021), where approximation algorithms are discussed. This paper describes the first exact solution approaches for the Knapsack Problem with Group Fairness, based on integer linear programming formulations and a dynamic programming algorithm. The latter allows us to establish the complexity of the problem. Finally, a set of computational experiments on benchmark instances derived from the knapsack literature compare the effectiveness of the alternative solution approaches.
• dc.description.sponsorship Alberto Santini was funded by the Spanish Ministry of Science, Innovation and Universities and by the European Social Fund Plus (ESF+) through grant RYC2022-035269-I via MCIN/AEI/10.13039/501100011033 of the "Ramón y Cajal" programme and through grant PID2024-161521OA-I00 of the programme "Proyectos de Generación de Conocimiento 2024" of the Spanish Ministry of Science, Innovation and Universities. Enrico Malaguti and Paolo Paronuzzi were funded by the Air Force Office of Scientific Research under award number FA8655-25-1-7013.
• dc.format.mimetype application/pdf
• dc.identifier.citation Malaguti E, Paronuzzi P, Santini A. Algorithms and complexity results for the 0-1 knapsack problem with group fairness. Optim Lett. 2025 Oct 6. DOI: 10.1007/s11590-025-02252-y
• dc.identifier.doi https://dx.doi.org/10.1007/s11590-025-02252-y
• dc.identifier.issn 1862-4472
• dc.identifier.uri http://hdl.handle.net/10230/71657
• dc.language.iso eng
• dc.publisher Springer
• dc.relation.ispartof Optimization Letters. 2025 Oct 6
• dc.relation.projectID info:eu-repo/grantAgreement/ES/4PE/PID2024-161521OA-I00
• dc.rights This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by/4.0/
• dc.subject.keyword Packing
• dc.subject.keyword Knapsack problems
• dc.subject.keyword Fairness
• dc.subject.keyword Integer linear programming
• dc.subject.keyword Dynamic programming
• dc.title Algorithms and complexity results for the 0-1 knapsack problem with group fairness
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion