• Corpus ID: 245906373

Benchmarking Problems for Robust Discrete Optimization

  title={Benchmarking Problems for Robust Discrete Optimization},
  author={Marc Goerigk and Mohammad Khosravi},
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… 



Mixed uncertainty sets for robust combinatorial optimization

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

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.

Robust discrete optimization and network flows

This work proposes a robust integer programming problem of moderately larger size that allows controlling the degree of conservatism of the solution in terms of probabilistic bounds on constraint violation, and proposes an algorithm for robust network flows that solves the robust counterpart by solving a polynomial number of nominal minimum cost flow problems in a modified network.

Recoverable robust knapsacks: the discrete scenario case

This work considers the complexity status of this recoverable robust knapsack problem, extends the classical concept of cover inequalities to obtain stronger polyhedral descriptions and presents two extensive computational studies to investigate the influence of parameters k and ℓ to the objective and evaluate the effectiveness of the new class of valid inequalities.

On scenario aggregation to approximate robust combinatorial optimization problems

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

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.

Exploiting the Structure of Two-Stage Robust Optimization Models with Exponential Scenarios

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.