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

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 syne...

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Bibliographic Details
Published in:European journal of operational research Vol. 301; no. 1; pp. 277 - 286
Main Author: Beliakov, Gleb
Format: Journal Article
Language:English
Published: Elsevier B.V 16.08.2022
Subjects:
Capacities
Choquet integral
Fuzzy measures
Fuzzy sets
Integer programming
Optimisation
Shapley value
Integer programming
Fuzzy sets
Fuzzy measures
Shapley value
Choquet integral
Optimisation
Capacities
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary: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.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2021.11.004