RAIRO - Operations Research

Table of Contents - April 2009 - Volume 43, Issue 02  

Research Article

Tractable algorithms for chance-constrained combinatorial problems

Olivier Klopfenstein

France Télécom R&D, 38-40 rue du gl Leclerc, 92130 Issy-les-Moulineaux, France; olivier.klopfenstein@orange-ftgroup.com

Université de Technologie de Compiègne, Laboratoire Heudiasyc UMR CNRS 6599, 60205 Compiègne Cedex, France

Abstract

This paper aims at proposing tractable algorithms to find effectively good solutions to large size chance-constrained combinatorial problems. A new robust model is introduced to deal with uncertainty in mixed-integer linear problems. It is shown to be strongly related to chance-constrained programming when considering pure 0–1 problems. Furthermore, its tractability is highlighted. Then, an optimization algorithm is designed to provide possibly good solutions to chance-constrained combinatorial problems. This approach is numerically tested on knapsack and multi-dimensional knapsack problems. The results obtained outperform many methods based on earlier literature.

(Received April 17 2007)

(Accepted July 15 2008)

(Online publication April 28 2009)

Key Words:

  • Integer linear programming;
  • chance constraints;
  • robust optimization;
  • heuristic.

Mathematics Subject Classification:

  • 90C10;
  • 90C15