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Knapsack problems with dependencies through non-additive measures and Choquet integral

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  • Beliakov, Gleb

Abstract

In portfolio selection problems the items often depend on each other, and their synergies and redundancies need to be taken into account. We consider the knapsack problem in which the objective is modelled as the Choquet integral with respect to a supermodular capacity which quantifies possible synergies. We provide various formulations which lead to the standard linear mixed integer programs, applicable to small and large portfolios. We also study scalability of the solution methods and compare large problems defined with respect to 2-additive capacities which model pairwise interactions, and linear knapsack with respect to the Shapley values of these capacities.

Suggested Citation

  • Beliakov, Gleb, 2022. "Knapsack problems with dependencies through non-additive measures and Choquet integral," European Journal of Operational Research, Elsevier, vol. 301(1), pages 277-286.
    • Handle: RePEc:eee:ejores:v:301:y:2022:i:1:p:277-286
    DOI: 10.1016/j.ejor.2021.11.004
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    1. Mayag, Brice & Bouyssou, Denis, 2020. "Necessary and possible interaction between criteria in a 2-additive Choquet integral model," European Journal of Operational Research, Elsevier, vol. 283(1), pages 308-320.
    2. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2009. "A characterization of the 2-additive Choquet integral through cardinal information," Post-Print halshs-00445132, HAL.
    3. Corrente, Salvatore & Greco, Salvatore & Ishizaka, Alessio, 2016. "Combining analytical hierarchy process and Choquet integral within non-additive robust ordinal regression," Omega, Elsevier, vol. 61(C), pages 2-18.
    4. Fujimoto, Katsushige & Kojadinovic, Ivan & Marichal, Jean-Luc, 2006. "Axiomatic characterizations of probabilistic and cardinal-probabilistic interaction indices," Games and Economic Behavior, Elsevier, vol. 55(1), pages 72-99, April.
    5. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011. "A representation of preferences by the Choquet integral with respect to a 2-additive capacity," Theory and Decision, Springer, vol. 71(3), pages 297-324, September.
    6. Greco, Salvatore & Mousseau, Vincent & Słowiński, Roman, 2014. "Robust ordinal regression for value functions handling interacting criteria," European Journal of Operational Research, Elsevier, vol. 239(3), pages 711-730.
    7. Grabisch, Michel & Kojadinovic, Ivan & Meyer, Patrick, 2008. "A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package," European Journal of Operational Research, Elsevier, vol. 186(2), pages 766-785, April.
    8. Marichal, Jean-Luc & Mathonet, Pierre, 2011. "Weighted Banzhaf power and interaction indexes through weighted approximations of games," European Journal of Operational Research, Elsevier, vol. 211(2), pages 352-358, June.
    9. Michel Grabisch & Christophe Labreuche, 2010. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," Annals of Operations Research, Springer, vol. 175(1), pages 247-286, March.
    10. Michel Grabisch & Guilherme Dean Pelegrina & Leonardo Tomazeli Duarte & Joao Marcos T. Romano, 2020. "An unsupervised capacity identification approach based on Sobol’ indices," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03220895, HAL.
    11. Galli, Laura & Martello, Silvano & Rey, Carlos & Toth, Paolo, 2021. "Polynomial-size formulations and relaxations for the quadratic multiple knapsack problem," European Journal of Operational Research, Elsevier, vol. 291(3), pages 871-882.
    12. Alberto Caprara & David Pisinger & Paolo Toth, 1999. "Exact Solution of the Quadratic Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 125-137, May.
    13. Chateauneuf, Alain & Jaffray, Jean-Yves, 1989. "Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 263-283, June.
    14. Pelegrina, Guilherme Dean & Duarte, Leonardo Tomazeli & Grabisch, Michel & Romano, João Marcos Travassos, 2020. "The multilinear model in multicriteria decision making: The case of 2-additive capacities and contributions to parameter identification," European Journal of Operational Research, Elsevier, vol. 282(3), pages 945-956.
    15. Mikhail Timonin, 2012. "Maximization of the Choquet integral over a convex set and its application to resource allocation problems," Annals of Operations Research, Springer, vol. 196(1), pages 543-579, July.
    16. Arcidiacono, Sally Giuseppe & Corrente, Salvatore & Greco, Salvatore, 2021. "Robust stochastic sorting with interacting criteria hierarchically structured," European Journal of Operational Research, Elsevier, vol. 292(2), pages 735-754.
    17. Lucie Galand & Patrice Perny & Olivier Spanjaard, 2010. "A Branch and Bound Algorithm for Choquet Optimization in Multicriteria Problems," Lecture Notes in Economics and Mathematical Systems, in: Matthias Ehrgott & Boris Naujoks & Theodor J. Stewart & Jyrki Wallenius (ed.), Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems, pages 355-365, Springer.
    18. Schäfer, Luca E. & Dietz, Tobias & Barbati, Maria & Figueira, José Rui & Greco, Salvatore & Ruzika, Stefan, 2021. "The binary knapsack problem with qualitative levels," European Journal of Operational Research, Elsevier, vol. 289(2), pages 508-514.
    19. Michel Grabisch & Agnieszka Rusinowska, 2020. "k -additive upper approximation of TU-games," Post-Print halshs-02860802, HAL.
    20. Bottero, M. & Ferretti, V. & Figueira, J.R. & Greco, S. & Roy, B., 2018. "On the Choquet multiple criteria preference aggregation model: Theoretical and practical insights from a real-world application," European Journal of Operational Research, Elsevier, vol. 271(1), pages 120-140.
    21. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    22. Galand, Lucie & Perny, Patrice & Spanjaard, Olivier, 2010. "Choquet-based optimisation in multiobjective shortest path and spanning tree problems," European Journal of Operational Research, Elsevier, vol. 204(2), pages 303-315, July.
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    2. Torra, Vicenç, 2023. "The transport problem for non-additive measures," European Journal of Operational Research, Elsevier, vol. 311(2), pages 679-689.
    3. Brunelli, Matteo & Corrente, Salvatore, 2024. "Modeling criteria and project interactions in portfolio decision analysis with the Choquet integral," Omega, Elsevier, vol. 126(C).
    4. Zhang, Xinwei & Yan, Yong & Wang, Lilin & Wang, Yang, 2024. "A ranking approach for robust portfolio decision analysis based on multilinear portfolio utility functions and incomplete preference information," Omega, Elsevier, vol. 122(C).

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