The inverse k-max combinatorial optimization problem

Classical combinatorial optimization concerns finding a feasible subset of a ground set in order to optimize an objective function. We address in this article the inverse optimization problem with the k-max function. In other words, we attempt to perturb the weights of elements in the ground set at...

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Bibliographic Details
Published in:Yugoslav Journal of Operations Research Vol. 33; no. 2; pp. 309 - 322
Main Authors: Nhan, Tran, Nguyen, Kien, Hung, Nguyen, Toan, Nguyen
Format: Journal Article
Language:English
Published: University of Belgrade 2023
Subjects:
bottleneck
combinatorial algorithms
convex
inverse optimization
k-max
ISSN:0354-0243, 1820-743X
Online Access:Get full text
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Summary:Classical combinatorial optimization concerns finding a feasible subset of a ground set in order to optimize an objective function. We address in this article the inverse optimization problem with the k-max function. In other words, we attempt to perturb the weights of elements in the ground set at minimum total cost to make a predetermined subset optimal in the fashion of the k-max objective with respect to the perturbed weights. We first show that the problem is in general NP-hard. Regarding the case of independent feasible subsets, a combinatorial O(n2 log n) time algorithm is developed, where n is the number of elements in E. Special cases with improved complexity are also discussed.
ISSN:0354-0243
1820-743X
DOI:10.2298/YJOR220516037N