Accelerating Benders Decomposition by Local Branching

Authors:
Walter Rei;Jean-François Cordeau;Michel Gendreau;Patrick Soriano
Affiliations:
Département de management et de technologie, ESG, UQÀM, Montréal, Québec H3C 3P8, Canada, and CIRRELT, Montréal, Québec H3C 3J7, Canada;Service de l'enseignement de la gestion des opérations et de la logistique, HEC Montréal, Montréal, Québec H3T 2A7, Canada, and CIRRELT, Montréal, Québec H3C 3J7, Can ...;Département d'informatique et de recherche opérationnelle, Université de Montréal, Montréal, Québec H3C 3J7, Canada, and CIRRELT, Montréal, Québec H3C 3J7, ...;Service de l'enseignement des méthodes quantitatives de gestion, HEC Montréal, Montréal, Québec H3T 2A7, Canada, and CIRRELT, Montréal, Québec H3C 3J7, Canada
Venue:
INFORMS Journal on Computing
Year:
2009

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Abstract

This paper shows how local branching can be used to accelerate the classical Benders decomposition algorithm. By applying local branching throughout the solution process, one can simultaneously improve both the lower and upper bounds. We also show how Benders feasibility cuts can be strengthened or replaced with local branching constraints. To assess the performance of the different algorithmic ideas presented in this hybrid solution approach, extensive computational experiments were performed on two families of network design problems. Numerical results clearly illustrate their benefits.