Malaguti, EnricoParonuzzi, PaoloSantini, Alberto2025-10-242025-10-242025Malaguti 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-y1862-4472http://hdl.handle.net/10230/71657Data de publicació electrònica: 10-09-2025This 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.application/pdfengThis 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/.info:eu-repo/semantics/article2025-10-24https://dx.doi.org/10.1007/s11590-025-02252-yPackingKnapsack problemsFairnessInteger linear programmingDynamic programminginfo:eu-repo/semantics/openAccess