## Description

On this page, instances for the the Two-Stage selection problem under continuous budgeted uncertainty set could be found. In addition, information with regard to the size of instances provided as well as an overall description of the considered method of instance generation is available. For more general purposes, the instance generator software is also accessible through a link to our github repository. Finally, if more detail about theory or application of this method is desired, the main publication introducing this method could also be reached.

It must be noticed that in order to refer to the parameters of the robust selection problem, we use n for the number of items, p for the number of items we need to choose. Moreover, we use Ci as the first-stage cost of item i, ci as the second-stage nominal value of item i [n] and di for the second-stage  deviation of item i. Also we refer to the parameter controlling how many items might deviate to its upper bound in the second-stage as Г.

Method Description:

For all i [n], we choose Ci , ci , di iid uniformly from {1, . . . , 100}.

## Instance Format

Here the instance set consists of three different folders with different problem size. There are problems with n=100, p=25 in the first folder, problems with n=100, p=50 in the second one and problems with n=100, p=75 in the third one. Furthermore, in all three folders we fix Γ ∈ {400, 800, 1000, 1200}. For each problem size, we generate 50 instances, thus each folder has 200 instances. The instance files are named as “instancenpΓ-0-x”, where x represents the number of instance (1 x 50). In addition, each instance file contains four lines. The first line represents n, p and Γ the second line forms Ci for i ∈ [n] and the third and fourth lines show ci and di for i ∈ [n], respectively.

## Generator Software

Although it is a good idea to have a library of instances for the robust optimization problems, it is not possible to upload all possible combination of problem parameters on a website. Alternatively, the generator software could be accessed so that any instance size could be generated. Therefore, it is possible to access a C++11 code which is used as the generator software.

## Reference

This page has been created based on the information provided in the following paper:

• Goerigk, M., & Khosravi, M. (2022). Benchmarking Problems for Robust Discrete Optimization. arXiv preprint arXiv:2201.04985.