Mixed uncertainty sets for robust combinatorial optimization

Dokka, Trivikram; Goerigk, Marc; Roy, Rahul

doi:10.1007/s11590-019-01456-3

Cited by 9 publications

(6 citation statements)

References 19 publications

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“…Different uncertainty sets and their geometric relationship are studied in [LDF11]. Recently mixed uncertainty sets, combining most of the popular uncertainty classes into one set, were studied in [DGR20]. Next to the classical robust optimization approach, several less conservative approaches have been introduced.…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Robust Optimization using Unsupervised Deep Learning

Goerigk¹,

Kurtz²

2020

Preprint

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Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called the uncertainty set, containing all scenarios against which we wish to protect. An ongoing challenge in the recent literature is to derive uncertainty sets from given historical data.In this paper we use an unsupervised deep learning method to construct non-convex uncertainty sets from data, which have a more complex structure than the typically considered sets. We show that the trained neural networks can be integrated into a robust optimization model by formulating the adversarial problem as a convex quadratic mixed-integer program. This allows us to derive robust solutions through an iterative scenario generation process. In extensive computational experiments, we compare this approach to a current state-ofthe-art approach, which derives uncertainty sets by kernel-based support vector clustering. We find that uncertainty sets derived by the unsupervised deep learning method can give a better description of data, leading to robust solutions that considerably outperform the comparison method both with respect to objective value and feasibility.

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Section: Introductionmentioning

confidence: 99%

Data-Driven Robust Optimization using Unsupervised Deep Learning

Goerigk¹,

Kurtz²

2020

Preprint

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“…where F ∈F min k∈F f (x x x,c c c k ) F ∈F max k∈F f (x x x,c c c k ) ∈ [0, 1]. Observe that ( 13) is a special case of the mixed-uncertainty robust optimization problem discussed in [9], where uncertainty sets are given and we would like to solve min…”

Section: Approximation Algorithms For the Robf Problemmentioning

confidence: 99%

“…In [9] it has been shown that solving the nominal problem min x x x∈X f (x x x, ĉ c c) with the cost verctor ĉ c c = F ∈F m(F ) 1…”

Section: Approximation Algorithms For the Robf Problemmentioning

confidence: 99%

Robust optimization with belief functions

Goerigk¹,

Kasperski²,

Zieliński³

2023

Preprint

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In this paper, an optimization problem with uncertain objective function coefficients is considered. The uncertainty is specified by providing a discrete scenario set, containing possible realizations of the objective function coefficients. The concept of belief function in the traditional and possibilistic setting is applied to define a set of admissible probability distributions over the scenario set. The generalized Hurwicz criterion is then used to compute a solution. In this paper, the complexity of the resulting problem is explored. Some exact and approximation methods of solving it are proposed.

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“…In the following, we may also write c i = c i + d i to denote the upper bound on the costs of item i in interval or budgeted uncertainty sets. Many more uncertainty sets have been considered, including ellipsoidal uncertainty sets [BTN98,CG17], data-driven polyhedral sets based on statistical testing [BGK18] or machine learning [SHY17], or even combinations of multiple sets simultaneously [BSS19,DGR20].…”

Section: Problem Definitionsmentioning

confidence: 99%

Benchmarking Problems for Robust Discrete Optimization

Goerigk¹,

Khosravi²

2022

Preprint

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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. Usually, a robust problem becomes harder to solve than its nominal counterpart, even if it remains in the same complexity class. For this reason, specialized solution algorithms have been developed. To further drive the development of stronger solution algorithms and to facilitate the comparison between methods, a set of benchmark instances is necessary but so far missing. In this paper we propose a further step towards this goal by proposing several instance generation procedures for combinations of minmax, min-max regret, two-stage and recoverable robustness with interval, discrete or budgeted uncertainty sets. Besides sampling methods that go beyond the simple uniform sampling method that is the de-facto standard to produce instances, also optimization models to construct hard instances are considered. Using a selection problem for the nominal ground problem, we are able to generate instances that are several orders of magnitudes harder to solve than uniformly sampled instances when solving them with a general mixed-integer programming solver. All instances and generator codes are made available online.

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Mixed uncertainty sets for robust combinatorial optimization

Cited by 9 publications

References 19 publications

Data-Driven Robust Optimization using Unsupervised Deep Learning

Data-Driven Robust Optimization using Unsupervised Deep Learning

Robust optimization with belief functions

Benchmarking Problems for Robust Discrete Optimization

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