A Generic Branch-and-Cut Algorithm for Multiobjective Optimization Problems: Application to the Multilabel Traveling Salesman Problem

Authors:
Nicolas Jozefowiez;Gilbert Laporte;Fré/dé/ric Semet
Affiliations:
CNRS, LAAS, F-31077 Toulouse, France/ and Université/ de Toulouse, UPS, INSA, INP, ISAE, LAAS, F-31077 Toulouse, France;CIRRELT, HEC Montré/al, Montré/al, Qué/bec H3T 2A7, Canada;Laboratoire d'Automatique, Gé/nie Informatique et Signal, É/cole Centrale de Lille, Cité/ Scientifique, 59651 Villeneuve d'Ascq Cedex, France
Venue:
INFORMS Journal on Computing
Year:
2012

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Abstract

This paper describes a generic branch-and-cut algorithm applicable to the solution of multiobjective optimization problems for which a lower bound can be defined as a polynomially solvable multiobjective problem. The algorithm closely follows standard branch and cut except for the definition of the lower and upper bounds and some optional speed-up mechanisms. It is applied to a routing problem called the multilabel traveling salesman problem, a variant of the traveling salesman problem in which labels are attributed to the edges. The goal is to find a Hamiltonian cycle that minimizes the tour length and the number of labels in the tour. Implementations of the generic multiobjective branch-and-cut algorithm and speed-up mechanisms are described. Computational experiments are conducted, and the method is compared to the classical ε-constraint method.