Polyhedral approximation of ellipsoidal uncertainty sets via extended formulations: a computational case study

Bärmann, Andreas; Heidt, Andreas; Martín, Alexander; Pokutta, Sebastian; Thurner, Christoph

doi:10.1007/s10287-015-0243-0

Cited by 10 publications

(9 citation statements)

References 13 publications

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“…In [4] and [5] the authors adopt ellipsoidal uncertainty sets to solve robust network design problems. Compared to stochastic optimization, it has better computational tractability.…”

Section: Uncertainty Setmentioning

confidence: 99%

Solving the bifurcated and nonbifurcated robust network loading problem with k‐adaptive routing

2018

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We experiment an alternative routing scheme for the Robust Network Loading problem with demand uncertainty. Named k-adaptive, it is based on the fact that the decision-maker chooses k second-stage solutions and then commits to one of them only after realization of the uncertainty. This routing scheme, with its corresponding k-partition of the uncertainty set, is dynamically defined under an iterative method to sequentially improve the solution. The method has an inherent characteristic of multiplying the number of variables and constraints after each iteration, so that additional measures are introduced in the solution strategy in order to control time performance. We compare our k-adaptive results with the ones obtained through other routing schemes and also verify the effectiveness of the methods utilized using several realistic instances from SNDlib.

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“…In [4] and [5] the authors adopt ellipsoidal uncertainty sets to solve robust network design problems. Compared to stochastic optimization, it has better computational tractability.…”

Section: Uncertainty Setmentioning

confidence: 99%

Solving the bifurcated and nonbifurcated robust network loading problem with k‐adaptive routing

2018

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“…In addition, note that more involved uncertainty descriptions (e.g., ellipsoidal sets stemming from normal distributions) can also be handled via efficient polyhedral approximation methods. 65 We stress that our proposed ARO framework can handle uncertainty in all model parameters, including left-hand-side, right-hand-side and objective function coefficients. The only exception lies with parameters that directly multiply in the deterministic model those continuous variables upon which we have decided to adjust (the possible implications of this exception are minor, but will be addressed later).…”

Section: Accepted Articlementioning

confidence: 99%

Multi‐stage adjustable robust optimization for process scheduling under uncertainty

2016

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Variations in parameters such as processing times, yields, and availability of materials and utilities can have a detrimental effect in the optimality and/or feasibility of an otherwise "optimal" production schedule. In this paper, we propose a multi-stage adjustable robust optimization approach to alleviate the risk from such operational uncertainties during scheduling decisions. We derive a novel robust counterpart of a deterministic scheduling model, and we show how to obey the observability and non-anticipativity restrictions that are necessary for the resulting solution policy to be implementable in practice. We also develop decision-dependent uncertainty sets in order to model the endogenous uncertainty that is inherently present in process scheduling applications. A computational study reveals that, given a chosen level of robustness, adjusting decisions to past parameter realizations leads to significant improvements, both in terms of worst-case objective as well as objective in expectation, compared to the traditional robust scheduling approaches.

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“…Work in the second group include Gouveia et al (2013), Ballerstein and Michaels (2014), Bärmann et al (2014), Buchanan and Butenko (2014), Godinho et al (2014), Lancia and Serafini (2014) and Leggieri et al (2014). Examples of work in the third group include Kaibel (2011), Fiorini et al (2011, 2012a, 2012b), Faenza et al (2012, Gillis and Glineur (2012) and Kaibel and Walter (2014).…”

Section: Introductionmentioning

confidence: 99%

Limits to the scope of applicability of extended formulations theory for LP models of combinatorial optimisation problems

Diaby

Karwan

2017

IJMOR

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Abstract:The purpose of this paper is to bring to attention and to make a contribution to the issue of defining/clarifying the scope of applicability of extended formulations (EFs) theory. Specifically, we show that EFs theory is not valid for relating the sizes of descriptions of polytopes when the sets of the descriptive variables for those polytopes are disjoint, and that new definitions of the notion of 'projection' upon which some of the recent extended formulations works [such as Kaibel (2011), Fiorini et al. (2011, 2012a, 2012b, Faenza et al. (2012), Gillis and Glineur (2012) and Kaibel and Walter (2014), for example] have been based can cause those works to over-reach in their conclusions.Keywords: extended formulations; combinatorial optimisation; computational complexity; linear programming.Reference to this paper should be made as follows: Diaby, M. and Karwan, M.H. (2017) 'Limits to the scope of applicability of extended formulations theory for LP models of combinatorial optimisation problems', Int.

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Polyhedral approximation of ellipsoidal uncertainty sets via extended formulations: a computational case study

Cited by 10 publications

References 13 publications

Solving the bifurcated and nonbifurcated robust network loading problem with k‐adaptive routing

Solving the bifurcated and nonbifurcated robust network loading problem with k‐adaptive routing

Multi‐stage adjustable robust optimization for process scheduling under uncertainty

Limits to the scope of applicability of extended formulations theory for LP models of combinatorial optimisation problems

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