Computing upper bounds for a LBPP with and without probabilistic constraints

  • Authors:

  • Hugo Rodríguez;Pablo Adasme;Abdel Lisser;Ismael Soto

  • Affiliations:

  • Departamento de Ingenieria Eléctrica, Universidad de Santiago de Chile, Santiago, Chile;Departamento de Ingenieria Eléctrica, Universidad de Santiago de Chile, Santiago, Chile and Laboratoire de Recherche en Informatique, Université Paris Sud, Orsay Cedex, France;Laboratoire de Recherche en Informatique, Université Paris Sud, Orsay Cedex, France;Departamento de Ingenieria Eléctrica, Universidad de Santiago de Chile, Santiago, Chile

  • Venue:
  • INOC'11 Proceedings of the 5th international conference on Network optimization
  • Year:
  • 2011

Quantified Score

Hi-index 0.00

Visualization

Abstract

In this paper, we compute upper bounds for a generic linear bilevel programming problem (LBPP) using the iterative min-max (IMM) algorithm proposed in [4,5]. Neither in [4] nor in [5] the authors give optimal solutions for this problem or gaps to measure IMM efficiency. To this purpose, we implement the construction method proposed by Jacobsen [3] to generate valid test instances with their respective optimal solutions. Afterward, we add to these valid test instances knapsack probabilistic constraints in the upper-level sub-problem as in [4,5]. The latter allows us to compute upper bounds for stochastic bilevel instances as well. Our numerical results show average relative gaps of 43.97% for the valid test instances and 28.93% while adding probabilistic constraints.