## Description

Instances for the Recoverable selection problem under discrete budgeted uncertainty set could be found on this page. Here, we use n, p, Г and k when referring to the number of items, number of items one wants to choose, budget to control the amount of uncertainty and recovery parameter, respectively. Furthermore, cost of each item must be chosen from a given interval; thus, we use the n-vectors c and d to show the lower bound and the deviation of the correspondence interval.

This page will be updated regularly

## Instance Format

The first four numbers used to label each instance file represent n, p, Г and k in the exact same order. In addition, the last number shows the instance number with the given size. For each considered size 50 instances are generated. The instance files contain four lines. The first line demonstrates n, p, Г and k. The second line depicts the first stage cost of items. The third and fourth lines illustrate the n-vectors c and d, respectively.

## Output

## Software Tool

On the following link, the generator codes for the given set of instances can be found. The correspondence folder contains three files named “main, selection and sel”. The main-file introduces the input parameters. The selection-file consists of all the function we used and the sel-file has all the classes and their parameters which are defined. The input parameters, which should be given through the command line (if using ubuntu) are different for each problem.

In this setting the parameters must be given the the exact following order for the selection problem:

**n**: number of items

**p**: number of items to be selected

**gamma**: number of items that can exceed their nominal value

**param**: method of instance generation (param=1 for RR-DB-1)

**random seed**: this allows the user to generate different instances when all other parameters are the same

## Reference

The information on this page has been created based on the paper “**Benchmarking Problems for Robust Discrete Optimization**” by Dr. Marc Goerigk (Network and Data Science Management, University of Siegen, Germany) and Mohammad Khosravi (Network and Data Science Management, University of Siegen, Germany).