Formulations and algorithms for the recoverable Γ-robust knapsack problem

One of the most frequently occurring substructures in integer linear programs (ILPs) is the knapsack constraint. In this paper, we study ways to deal with uncertainty in the coefficients of such constraints. We combine the budget uncertainty set of Bertsimas and Sim (Math Program Ser B 98:49–71, 200...

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Autores principales:	Christina Büsing, Sebastian Goderbauer, ArieM.C.A. Koster, Manuel Kutschka
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2019
Materias:	90C10 90C57 90C47 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/4668faafaa9740f19abf0c4b62d8a7d6
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spelling	oai:doaj.org-article:4668faafaa9740f19abf0c4b62d8a7d62021-12-02T05:01:10ZFormulations and algorithms for the recoverable Γ-robust knapsack problem2192-440610.1007/s13675-018-0107-9https://doaj.org/article/4668faafaa9740f19abf0c4b62d8a7d62019-03-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2192440621001106https://doaj.org/toc/2192-4406One of the most frequently occurring substructures in integer linear programs (ILPs) is the knapsack constraint. In this paper, we study ways to deal with uncertainty in the coefficients of such constraints. We combine the budget uncertainty set of Bertsimas and Sim (Math Program Ser B 98:49–71, 2003; Oper Res 52(1):35–53, 2004) with a recovery action, i.e., in order to restore feasibility up to k items may be removed when the actual coefficients are known. We present three different approaches to formulate this recoverable robust knapsack (rrKP) as ILP, including a novel compact reformulation of quadratic size. The other two formulations have exponentially many variables and/or constraints. To keep the ILPs small in practice, we develop separation algorithms, not only for the exponential formulations, but also for the compact reformulation. An experimental comparison of six different approaches to solve the rrKP on a carefully designed set of benchmark instances reveals that a lazy constraint-and-variables approach for the compact reformulation outperforms other alternatives.Christina BüsingSebastian GoderbauerArieM.C.A. KosterManuel KutschkaElsevierarticle90C1090C5790C47Applied mathematics. Quantitative methodsT57-57.97Electronic computers. Computer scienceQA75.5-76.95ENEURO Journal on Computational Optimization, Vol 7, Iss 1, Pp 15-45 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	90C10 90C57 90C47 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
spellingShingle	90C10 90C57 90C47 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95 Christina Büsing Sebastian Goderbauer ArieM.C.A. Koster Manuel Kutschka Formulations and algorithms for the recoverable Γ-robust knapsack problem
description	One of the most frequently occurring substructures in integer linear programs (ILPs) is the knapsack constraint. In this paper, we study ways to deal with uncertainty in the coefficients of such constraints. We combine the budget uncertainty set of Bertsimas and Sim (Math Program Ser B 98:49–71, 2003; Oper Res 52(1):35–53, 2004) with a recovery action, i.e., in order to restore feasibility up to k items may be removed when the actual coefficients are known. We present three different approaches to formulate this recoverable robust knapsack (rrKP) as ILP, including a novel compact reformulation of quadratic size. The other two formulations have exponentially many variables and/or constraints. To keep the ILPs small in practice, we develop separation algorithms, not only for the exponential formulations, but also for the compact reformulation. An experimental comparison of six different approaches to solve the rrKP on a carefully designed set of benchmark instances reveals that a lazy constraint-and-variables approach for the compact reformulation outperforms other alternatives.
format	article
author	Christina Büsing Sebastian Goderbauer ArieM.C.A. Koster Manuel Kutschka
author_facet	Christina Büsing Sebastian Goderbauer ArieM.C.A. Koster Manuel Kutschka
author_sort	Christina Büsing
title	Formulations and algorithms for the recoverable Γ-robust knapsack problem
title_short	Formulations and algorithms for the recoverable Γ-robust knapsack problem
title_full	Formulations and algorithms for the recoverable Γ-robust knapsack problem
title_fullStr	Formulations and algorithms for the recoverable Γ-robust knapsack problem
title_full_unstemmed	Formulations and algorithms for the recoverable Γ-robust knapsack problem
title_sort	formulations and algorithms for the recoverable γ-robust knapsack problem
publisher	Elsevier
publishDate	2019
url	https://doaj.org/article/4668faafaa9740f19abf0c4b62d8a7d6
work_keys_str_mv	AT christinabusing formulationsandalgorithmsfortherecoverablegrobustknapsackproblem AT sebastiangoderbauer formulationsandalgorithmsfortherecoverablegrobustknapsackproblem AT ariemcakoster formulationsandalgorithmsfortherecoverablegrobustknapsackproblem AT manuelkutschka formulationsandalgorithmsfortherecoverablegrobustknapsackproblem
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Formulations and algorithms for the recoverable Γ-robust knapsack problem

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