Instances for the Linear Bilevel Problem

This repository contains a collection of instance files used in the computational experiments reported in: Calvete, H. I., Galé, C., Iranzo, J. A., & Laguna, M. (2025). Scatter search with path relinking for linear bilevel problems. European Journal of Operational Research, 326(3), 439-450. Calvete, H. I., Gale, C., & Mateo, P. M. (2008). A new approach for solving linear bilevel problems using genetic algorithms. European Journal of Operational Research, 188(1), 14-28. The instances correspond to the Linear Bilevel Problem (LBP), a special case of Bilevel Problems where both the objective functions and the constraints are linear and the variables are continuous. The instances are provided as plain text files. File name convention Each .txt file name follows the format p$n$_$P2$_$Pm$_$ID$.txt, where: $n$: total number of variables. $P2$: percentage of variables controlled by the lower-level decision-maker relative to the total number of variables $n$. $Pm$: percentage of constraints relative to the total number of variables $n$. $ID$: sequential identifier for instances with identical dimensions. Example: the file p40_30_80_27.txt corresponds to an instance with 40 total variables. Of these, 12 variables (30% of 40) are controlled by the lower-level decision-maker, and there are 32 constraints (80% of 40). Since multiple instances share these characteristics, this file represents the 27th instance in its category. File structure Each .txt file contains the numerical data required to define the LBP instance, organized as follows: $m$: number of constraints. $n$: total number of variables. $n_1$: number of upper-level variables. $n_2$: number of lower-level variables. $c_1$: vector of length $n_1$ representing the coefficients of the upper-level variables in the upper-level objective function. $c_2$: vector of length $n_2$ representing the coefficients of the lower-level variables in the upper-level objective function. $d_2$: vector of length $n_2$ representing the coefficients of the lower-level variables in the lower-level objective function. $A_1$: $m \times n_1$ matrix corresponding to the coefficients of the upper-level variables in the constraints. $A_2$: $m \times n_2$ matrix corresponding to the coefficients of the lower-level variables in the constraints. $b$: vector of length m representing the right-hand side of the constraints. Contact For any questions or further information regarding these instances, please contact José A. Iranzo at [e-mail].