2004 | OriginalPaper | Buchkapitel
Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem
verfasst von : Ricardo Fukasawa, Jens Lysgaard, Marcus Poggi de Aragão, Marcelo Reis, Eduardo Uchoa, Renato F. Werneck
Erschienen in: Integer Programming and Combinatorial Optimization
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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The best exact algorithms for the Capacitated Vehicle Routing Problem (CVRP) have been based on either branch-and-cut or Lagrangean relaxation/column generation. This paper presents an algorithm that combines both approaches: it works over the intersection of two polytopes, one associated with a traditional Lagrangean relaxation over q-routes, the other defined by bound, degree and capacity constraints. This is equivalent to a linear program with exponentially many variables and constraints that can lead to lower bounds that are superior to those given by previous methods. The resulting branch-and-cut-and-price algorithm can solve to optimality all instances from the literature with up to 135 vertices. This doubles the size of the instances that can be consistently solved.