Robust Approach to Restricted Items Selection Problem

We consider the robust version of items selection problem, in which the goal is to choose representatives from a family of sets, preserving constraints on the allowed items' combinations. We prove NP-hardness of the deterministic version, and establish polynomially solvable special cases. Next,...

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Published inarXiv.org
Main Author Drwal, Maciej
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 22.07.2019
Subjects
Algorithms
Parameter uncertainty
Polynomials
Robustness (mathematics)
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Abstract We consider the robust version of items selection problem, in which the goal is to choose representatives from a family of sets, preserving constraints on the allowed items' combinations. We prove NP-hardness of the deterministic version, and establish polynomially solvable special cases. Next, we consider the robust version in which we aim at minimizing the maximum regret of the solution under interval parameter uncertainty. We show that this problem is hard for the second level of polynomial-time hierarchy. We develop an exact solution algorithm for the robust problem, based on cut generation, and present the results of computational experiments.
AbstractList We consider the robust version of items selection problem, in which the goal is to choose representatives from a family of sets, preserving constraints on the allowed items' combinations. We prove NP-hardness of the deterministic version, and establish polynomially solvable special cases. Next, we consider the robust version in which we aim at minimizing the maximum regret of the solution under interval parameter uncertainty. We show that this problem is hard for the second level of polynomial-time hierarchy. We develop an exact solution algorithm for the robust problem, based on cut generation, and present the results of computational experiments.
Author Drwal, Maciej
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SubjectTerms Algorithms
Parameter uncertainty
Polynomials
Robustness (mathematics)
Title Robust Approach to Restricted Items Selection Problem
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