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Recoverable Robust Combinatorial Optimization Problems [chapter]

Adam Kasperski, Adam Kurpisz, Paweł Zieliński
2013 Operations Research Proceedings  
This paper deals with two Recoverable Robust (RR) models for combinatorial optimization problems with uncertain costs.  ...  In this paper, we generalize the RR models to a class of combinatorial optimization problems with uncertain costs and provide new positive and negative complexity results in this area.  ...  [9] ): ROB P : OPT Rob = min X∈Φ C Rob (X) = min X∈Φ max S∈S C S (X). (2) In this paper, we investigate two Recoverable Robust (RR) models for combinatorial optimization problems with uncertain element  ... 
doi:10.1007/978-3-319-00795-3_22 dblp:conf/or/KasperskiKZ12 fatcat:hhvoqlinezeydlpyl2hsm5ziw4

Recoverable robust spanning tree problem under interval uncertainty representations

Mikita Hradovich, Adam Kasperski, Paweł Zieliński
2016 Journal of combinatorial optimization  
A strongly polynomial time, combinatorial algorithm for the recoverable spanning tree problem is first constructed.  ...  This paper deals with the recoverable robust spanning tree problem under interval uncertainty representations.  ...  Indeed, the recoverable spanning tree problem can be generalized by considering its robust version.  ... 
doi:10.1007/s10878-016-0089-6 fatcat:lre4j4jss5go5ocumnjst527h4

On the Recoverable Traveling Salesman Problem [article]

Marc Goerigk and Stefan Lendl and Lasse Wulf
2021 arXiv   pre-print
We discuss consequences for approximability results in the more general area of recoverable robust optimization.  ...  In this paper we consider the Recoverable Traveling Salesman Problem (TSP).  ...  U Γ 1 = {c ∈ R E : c e = Conclusions Recoverable combinatorial optimization problems are a natural generalization of classic problems that arise in the area of robust optimization.  ... 
arXiv:2111.09691v1 fatcat:nlhs4ec22ngmhp2ubclv5mleuu

Benchmarking Problems for Robust Discrete Optimization [article]

Marc Goerigk, Mohammad Khosravi
2022 arXiv   pre-print
Robust discrete optimization is a highly active field of research where a plenitude of combinations between decision criteria, uncertainty sets and underlying nominal problems are considered.  ...  In this paper we propose a further step towards this goal by proposing several instance generation procedures for combinations of min-max, min-max regret, two-stage and recoverable robustness with interval  ...  On scenario aggregation to approximate robust combinatorial optimization problems.  ... 
arXiv:2201.04985v1 fatcat:yb46i4nnlvef3pt7bcuvdupplu

Robust combinatorial optimization under convex and discrete cost uncertainty

Christoph Buchheim, Jannis Kurtz
2018 EURO Journal on Computational Optimization  
In this survey, we discuss the state-of-the-art of robust combinatorial optimization under uncertain cost functions.  ...  While mostly concentrating on the classical concept of strict robustness, we also cover more recent two-stage optimization paradigms.  ...  Recoverable Robustness Recoverable robust optimization problems have been introduced in [86] .  ... 
doi:10.1007/s13675-018-0103-0 fatcat:klr5pmyca5a5hbh2kev4ubb3dq

The Recoverable Robust Two-Level Network Design Problem

Eduardo Álvarez-Miranda, Ivana Ljubić, S. Raghavan, Paolo Toth
2015 INFORMS journal on computing  
This balance between robustness and recoverability is what defines a recoverable robust optimization problem.  ...  Recoverable Robustness is a new modeling approach (see Liebchen et al. (2007 Liebchen et al. ( , 2009 ) that combines the advantages of two stage optimization under uncertainty and robust optimization.  ...  The Recoverable Robust TLND (RRTLND) Problem In this section we provide references to the recent applications of the recoverable robust optimization, define the RRTLND problem and study the properties  ... 
doi:10.1287/ijoc.2014.0606 fatcat:u2gt33zw3jdxxglbfroxlzntre

An s–t connection problem with adaptability

David Adjiashvili, Rico Zenklusen
2011 Discrete Applied Mathematics  
A characterization of the feasible set is provided for f = 1 and several links are established between ARCP and other combinatorial optimization problems, including a new combinatorial optimization problem  ...  We study a new two-stage version of an s-t path problem, which we call adaptable robust connection path (ARCP).  ...  This work proposed a general recipe for designing two-stage robust problems from any combinatorial optimization problem.  ... 
doi:10.1016/j.dam.2010.12.018 fatcat:tzut6phbgva75jqpvwszd67vla

Recoverable Robustness by Column Generation [chapter]

P. C. Bouman, J. M. van den Akker, J. A. Hoogeveen
2011 Lecture Notes in Computer Science  
Recently, a new approach has been developed that combines the best of these two: recoverable robustness.  ...  Well-known approaches to create plans that take possible, common disturbances into account are robust optimization and stochastic programming.  ...  In this paper we present a new approach for solving recoverable robust optimization problems. We use column generation for recoverable robust optimization.  ... 
doi:10.1007/978-3-642-23719-5_19 fatcat:xelcwsylu5foheyeclldfew32q

Robustness Concepts for Knapsack and Network Design Problems Under Data Uncertainty [chapter]

Manuel Kutschka
2016 Operations Research Proceedings  
The robust optimization problem asks to find an optimal solution that is feasible for any possible data realization in this uncertainty set.  ...  In particular, robust linear optimization offers several advantages over other  ...  In Chapter 7, we consider the recoverable robust knapsack problem which is an integrated two-stage problem.  ... 
doi:10.1007/978-3-319-28697-6_48 dblp:conf/or/Kutschka14 fatcat:v2cycpxhxzfybfl72w7rk6p6iy

Recoverable robust spanning tree problem under interval uncertainty representations [article]

Mikita Hradovich, Adam Kasperski, Pawel Zielinski
2016 arXiv   pre-print
A polynomial time, combinatorial algorithm for the recoverable spanning tree problem is first constructed.  ...  This paper deals with the recoverable robust spanning tree problem under interval uncertainty representations.  ...  Indeed, the recoverable spanning tree problem can be generalized by considering its robust version.  ... 
arXiv:1606.01342v2 fatcat:fjpgpxjww5fmtbudeiken5mcmm

An Investigation of the Recoverable Robust Assignment Problem [article]

Dennis Fischer and Tim A. Hartmann and Stefan Lendl and Gerhard J. Woeginger
2020 arXiv   pre-print
We investigate the so-called recoverable robust assignment problem on balanced bipartite graphs with 2n vertices, a mainstream problem in robust optimization: For two given linear cost functions c_1 and  ...  Finally, we study the variant where matching M_1 is frozen, and where the optimization goal is to compute the best corresponding matching M_2, the second stage recoverable assignment problem.  ...  optimization problem is called the recoverable selection problem.  ... 
arXiv:2010.11456v1 fatcat:rywqge2xrrghfbdabwjwtdbv5q

Decomposition approaches for recoverable robust optimization problems

J.M. van den Akker, P.C. Bouman, J.A. Hoogeveen, D.D. Tönissen
2016 European Journal of Operational Research  
In this paper, we solve recoverable robust optimization problems by the technique of column generation. We consider two types of decomposition approaches: separate recovery and combined recovery.  ...  More recently, another approach has been developed that combines the best of these two: recoverable robustness.  ...  [10] , [11] ) In this paper we present a new approach for solving recoverable robust optimization problems. We use column generation for recoverable robust optimization.  ... 
doi:10.1016/j.ejor.2015.12.008 fatcat:aowo7w5z2nc4dhoedoq4qw5biu

Recoverable robust knapsacks: the discrete scenario case

Christina Büsing, Arie M. C. A. Koster, Manuel Kutschka
2011 Optimization Letters  
Applying this approaches to the call admission problem on a single link of a telecommunication network leads to a recoverable robust version of the knapsack problem.  ...  In this paper, we show that for a fixed number of discrete scenarios this recoverable robust knapsack problem is weakly NP-complete and any such instance can be solved in pseudo-polynomial time by a dynamic  ...  Related Results The knapsack problem is one of the basic problems in combinatorial optimization.  ... 
doi:10.1007/s11590-011-0307-1 fatcat:z23en4eppzf3jkm3sfzhinb4ga

Optimal matroid bases with intersection constraints: Valuated matroids, M-convex functions, and their applications [article]

Yuni Iwamasa, Kenjiro Takazawa
2020 arXiv   pre-print
Finally, we present applications of our generalized problems in the recoverable robust matroid basis problem, combinatorial optimization problems with interaction costs, and matroid congestion games.  ...  We also show the NP-hardness of some variants of these problems, which clarifies the coverage of discrete convex analysis for those problems.  ...  In Section 7, we present applications of our generalized problems in recoverable robust matroid basis problems, combinatorial optimization problems with interaction costs, and matroid congestion games.  ... 
arXiv:2003.02424v2 fatcat:dmgyphtl4rcodk5g76n7tnavqi

Recoverable Robust Representatives Selection Problems with Discrete Budgeted Uncertainty [article]

Marc Goerigk, Stefan Lendl, Lasse Wulf
2021 arXiv   pre-print
Recoverable robust optimization is a multi-stage approach, where it is possible to adjust a first-stage solution after the uncertain cost scenario is revealed.  ...  We analyze this approach for a class of selection problems.  ...  Furthermore, the setting of recoverable robustness has been applied to other combinatorial problems as well, including knapsack [BKK11] , shortest path [Büs12] and spanning tree [HKZ17] problems.  ... 
arXiv:2008.12727v2 fatcat:mwdl26jklzed7mps56mul5opvu
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