Benchmarking Problems for Robust Discrete Optimization
@article{Goerigk2022BenchmarkingPF,
title={Benchmarking Problems for Robust Discrete Optimization},
author={Marc Goerigk and Mohammad Khosravi},
journal={ArXiv},
year={2022},
volume={abs/2201.04985}
}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…
Figures and Tables from this paper
table 1 
figure 1 
figure 10 
table 10 
figure 11 
table 11 
figure 12 
table 12 
figure 13 
table 13 
figure 14 
table 14 
figure 15 
table 15 
figure 16 
figure 17 
figure 18 
figure 19 
figure 1–4 
figure 2 
table 2 
figure 20 
figure 21 
figure 22 
figure 22 
figure 23 
figure 24 
figure 25 
figure 26 
figure 27 
figure 28 
figure 29 
figure 3 
table 3 
figure 30 
figure 4 
table 4 
figure 5 
table 5 
figure 6 
table 6 
figure 7 
table 7 
figure 8 
table 8 
figure 9 
figure 9 
table 9
References
SHOWING 1-10 OF 51 REFERENCES
Generating Hard Instances for Robust Combinatorial Optimization
- Computer ScienceEur. J. Oper. Res.
- 2020
Mixed uncertainty sets for robust combinatorial optimization
- Computer ScienceOptimization Letters
- 2019
This paper proposes an approach to go beyond the classic setting, by assuming multiple uncertainty sets to be prepared, each with a weight showing the degree of belief that the set is a “true” model of uncertainty, and shows that it is as easy to model as theclassic setting.
A Lagrangian dual method for two-stage robust optimization with binary uncertainties
- Computer ScienceOptimization and Engineering
- 2022
This paper presents a new exact method to calculate worst-case parameter realizations in two-stage robust optimization problems with categorical or binary-valued uncertain data and proposes an alternative Lagrangian dual method that circumvents these difficulties and is readily integrated in either algorithm.
On scenario aggregation to approximate robust combinatorial optimization problems
- Computer ScienceOptim. Lett.
- 2018
This paper presents a simple extension of the midpoint method based on scenario aggregation, which improves the current best K-approximation result to an $$(\varepsilon K)$$(εK)-approximating for any desired $$\varpsilon > 0$$ε>0.
Representative scenario construction and preprocessing for robust combinatorial optimization problems
- Computer Science, MathematicsOptim. Lett.
- 2019
This paper presents a linear program to construct a representative scenario for the uncertainty set, which gives an approximation guarantee that is at least as good as for previous methods.
Heuristic and exact algorithms for the max-min optimization of the multi-scenario knapsack problem
- Computer ScienceComput. Oper. Res.
- 2008
Exploiting the Structure of Two-Stage Robust Optimization Models with Exponential Scenarios
- Mathematics, Computer ScienceINFORMS J. Comput.
- 2021
A heuristic algorithm is developed that dualizes the linear programming relaxation of the inner maximization problem in the reformulated model and iteratively generates cuts to shape the convex hull of the uncertainty set to create a more effective hybrid Benders algorithm.
Approximating combinatorial optimization problems with the ordered weighted averaging criterion
- Computer ScienceEur. J. Oper. Res.
- 2020
On the complexity of a class of combinatorial optimization problems with uncertainty
- Computer Science, MathematicsMath. Program.
- 2001
This is the first known example of a robust combinatorial optimization problem that is NP-hard in the case of scenario-represented uncertainty but is polynomially solvable in the CASE where uncertainty is represented by means of interval estimates for the weights.
Data-driven robust optimization
- Computer ScienceMath. Program.
- 2018
This work proposes a novel schema for utilizing data to design uncertainty sets for robust optimization using statistical hypothesis tests, and shows that data-driven sets significantly outperform traditional robust optimization techniques whenever data is available.