This webpage contains information on the instances used for the experiments in the following paper:

Talla Nobibon, F. and Leus, R. (2014).  Complexity results and exact algorithms for robust knapsack problems.  Journal of Optimization Theory and Applications, 161(2), 533-552.  (pdf) (DOI) ((more elaborate) working paper)

The instances are save as .txt files. Each instance is identified by:

• its number of items, ranging from 1000 to 10000.

• an index number, between 1 and 27.

Therefore, an instance may be named as follows: Input_1000_2, where 1000 indicates the number of items.

In each file, the first line contains four numbers. The first one is the number of items (n) and the second one is the number of scenarios (|S|).   The third (respectively the fourth) number is the value of the parameter that determines the variability level of the profits (respectively the weights) in the different scenarios.

There are subsequently two times |S| lines corresponding with the |S| scenarios. Each line 2l–1 contains n columns, with column i containing the profit of item i for scenario l.  Similarly, each line 2l contains n columns, with column i containing the weight of item i for scenario l.  In the last line of the input file, there is a single number representing the budget.  For our experiments, this value is multiplied by 0.4 (respectively 0.8) to obtain a tight (respectively loose) budget.

The instances are grouped into three files, one file corresponding with each value of n:

• n = 1000

• n = 5000  [ file is too large to be put on-line; please contact us by e-mail if you wish to obtain these instances ]

• n = 10000  [ file is too large to be put on-line; please contact us by e-mail if you wish to obtain these instances ]