## Description

Instances for the recoverable selection problem under discrete uncertainty set could be found on this page. Here, we use n, p, N and k when referring to the number of items, number of items one wants to choose, number of scenarios and recovery parameter, respectively.

This page will be updated regularly

## Instance Format

The first four numbers used to label each instance file represent n, p, N 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 N+2 lines. The first line demonstrates n, p, N, k. The second line is a n-vector representing cost of each item in the first stage and the remaining lines illustrate N different scenarios including n item costs in the second stage.

## 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

**N**: number of scenarios

**delta**: the maximum number of items which can be changed in the second stage

**param**: method of instance generation (param=0 for sampling RR-D-1)

**R**: methods of sampling or starting the HIRO (R=1 for RR-D-1)

**timelimit**: the time limit for finishing the process, in particular for the HIRO

**budget**: maximum permitted adjustment for each member of a scenario

**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).