Benders, metric and cutset inequalities for multicommodity capacitated network design

Authors:
Alysson M. Costa;Jean-François Cordeau;Bernard Gendron
Affiliations:
Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, Brazil 13560-970;Chaire de recherche du Canada en distributique and Centre de recherche sur les transports, HEC Montréal, Montréal, Canada H3T 2A7;Département d'informatique et de recherche opérationnelle, and Centre de recherche sur les transports, Université de Montréal, Montréal, Canada H3C 3J7
Venue:
Computational Optimization and Applications
Year:
2009

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Abstract

Solving multicommodity capacitated network design problems is a hard task that requires the use of several strategies like relaxing some constraints and strengthening the model with valid inequalities. In this paper, we compare three sets of inequalities that have been widely used in this context: Benders, metric and cutset inequalities. We show that Benders inequalities associated to extreme rays are metric inequalities. We also show how to strengthen Benders inequalities associated to non-extreme rays to obtain metric inequalities. We show that cutset inequalities are Benders inequalities, but not necessarily metric inequalities. We give a necessary and sufficient condition for a cutset inequality to be a metric inequality. Computational experiments show the effectiveness of strengthening Benders and cutset inequalities to obtain metric inequalities.